As a prelude to the New York Film Festival, the Film Society Of Lincoln Center, the fest’s parent organization, hosted a series called Opening Acts, in which it was possible to see previous works by NYFF directors on the big screen. Last week, I rewatched Zodiac—my favorite film of the ’00s and one that, even after untold viewings, still tantalizes with its mysteries and open ends. The film is structured almost as a calculus problem: The closer the clues bring us to the killer’s identity, the more the narrative seems to approach an asymptote.

To varying degrees, David Fincher’s greatest films—Zodiac, Seven, and, with its competing depositions, The Social Network—are procedurals about the acquisition of knowledge. Their plots are obsessively concerned with what we know, what we can prove, whose perspective we’re seeing, and how we can learn more. Go to the library. Look at the files. The Internet is written in ink.

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While it doesn’t rise to Zodiac levels of brilliance, Fincher’s Gone Girl (Grade: A), which opened the festival last night, turns that subject inward. On the surface, it’s a potboiler about a journalist, Nick (Ben Affleck), whose writer wife, Amy (Rosamund Pike, in a long-overdue star-making turn), goes missing; all the clues point to him. But the deeper mystery of the film is the puzzle of their marriage: who they were when they met, what guises they put on as they got to know each other, and who they turned out to be when a move to Missouri and a recession strained their partnership.

To avoid spoiling any twists, I didn’t read Gillian Flynn’s novel, which she adapted for the screen herself in a superbly layered script. A flip-through of the book suggests that the film remains largely faithful to the source but has been distilled and rearranged in a few significant ways. The knotted, chronologically loose narrative isn’t quite as programmatic in its he-said-she-said structure, though as in the novel (and Zodiac), there’s the habit of beginning scenes with dates, in title cards that count the days since Amy’s disappearance.

In the attention-grabbing prologue, Nick is shown petting his wife’s head. In voice-over, he imagines cracking it open in order to understand the thoughts and feelings inside. From the soap-commercial serenity of the lighting to the lack of eye contact between the leads to the use of sound (with the violence in Affleck’s voiceover offset by Trent Reznor and Atticus Ross’ chime-like compositions), the opening shot embodies all of the movie’s contradictions. What do we know about this couple, really? What can we, as outsiders, ever know? Are we witnessing domestic terror or domestic bliss? Given that Fincher’s previous whodunits dealt with serial killers, the darkest implication of Gone Girl is that a husband and wife’s attempts to understand each other could be every bit as enigmatic.

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With an unflagging pace, Fincher makes this material elegant through his peerless mise en scène. There’s a breathtaking cut from an engagement kiss to Nick getting his tongue swabbed by the police. The varied visual styles contrast the seediness and desperation of small-town Missouri with the posh elegance to which Amy has grown accustomed.

Even the tone can’t be trusted; although the films’ narrative shapes are quite different, Fincher, at a press conference following the screening, acknowledged the importance of Psycho as an influence. Gone Girl begins as a surprisingly generic investigation thriller in the Presumed Innocent mode before gradually rising to Paul Verhoeven levels of exaggerated, comic trashiness. (There are some horrifyingly funny scenes involving Neil Patrick Harris as a creep with a designer pad.) But the focus is fundamentally on two people trying to navigate each other’s secrets and headspaces, in ways that they, let alone the viewer, could hardly hope to understand.

There are clues that may not be clues. Perceptions of Amy and Nick are mitigated through diary entries and the media. Photographs conceal as much as they reveal. The Leftovers’ Carrie Coon, terrific as Nick’s twin sister, and a quite-good Tyler Perry, playing a celebrity attorney, are pretty much the only figures on-screen who can be taken at face value.

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As with almost all of Fincher’s movies, Gone Girl has too much going on in it to absorb in one viewing, and I’d like to see it again before indulging in further hyperbole. (At least one plot element, apparently already controversial from the novel, sticks in my craw; the movie’s take on various forms of assault doesn’t exactly qualify as enlightened.) But this is a far richer film than Fincher’s The Girl With The Dragon Tattoo—and one that, I suspect, will be remembered with his best.

Gone Girl is hardly the festival’s most cutting film about the recession; indeed, the plight of the dispossessed seems to be a recurring theme. I may just not have been in the mood for Horse Money, Pedro Costa’s latest portrait of the residents of Lisbon’s former Fontainhas neighborhood. The film continues the docu-poetic style of his excellent Colossal Youth (2006), following further developments in the life of Ventura. An even greater challenge, Horse Money may set my new personal benchmark for “too cryptic” and “too austere.”

I will echo the ongoing praise for the Dardennes’ masterful Two Days, One Night (Grade: A-), which casts Marion Cotillard as Sandra, a woman fighting to keep her job after returning from medical leave. During that time her employer—a solar energy company that ostensibly represents the modern, clean Europe but adheres to the same bottom-line logic as any other company—has discovered its workload can be handled with 16 instead of 17. Rather than take responsibility for the layoff, the bosses put it to a vote, giving the employees the choice of taking Sandra back or accepting a 1,000-euro bonus.

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While it would be reductive to call the film a simple allegory, Two Days, One Night bluntly comments on the state of European Union. Sandra is recovering from clinical (as opposed to economic) depression. As she goes door to door trying to convince her colleagues to vote for her—the title refers to the amount of time she spends canvassing—the film conveys in miniature the difficulties of persuading countries with varied needs to support each other.

Finally, Heaven Knows What (Grade: A-), starring newcomer Arielle Holmes as a version of herself, is a breakthrough for the Safdie brothers, a vivid procedural about the desperation and isolation of life as a homeless junkie in New York. Even more grippingly than Oren Moverman’s Time Out Of Mind, also showing in the fest, the movie conveys the day-to-day struggles of life on the skids. (The opening-credits single take in the hospital is a stunner.) Shot with long lenses that essentially telescoped the actors from across the street, the movie visualizes the Upper West Side so claustrophobically that the events barely seem to occur on the same planet as the gentrified city usually depicted on screen. The alien-landscape effect is aided by a relentless, mood-setting electronica score. You would never guess that much of the film is set just blocks from where the festival unspools.