The idea of explaining artists' works in terms of problems and solutions is ... not so common in film studies. It can be fruitful to consider that sometimes filmmakers face common problems and that they compete to solve them, or to find different problems they can solve. —David Bordwell, from Web site commentary on Ratatouille 

One of the reasons I'm so stuck on Theo Angelopoulos's The Travelling Players (1975)—number one on my all-time best list, if you must know—involves this very notion of problem-solving. Because, at least in my opinion, based on the film's internal clues, Angelopoulos was facing a big one here—something that even halfway through the filming he hadn't come to grips with, perhaps because he wasn't quite sure what it was. But what seems certain is this: that more than his usual perfectionist striving was needed to bring this meticulously crafted epic to life. 

Which in the film's second half he serendipitously discovers—of course serendipitously, since that's what's been missing all along. Chance, randomness, indeterminacy--like punctuated equilibrium in evolutionary theory, where a sudden break in "natural" continuity ushers in waves of new life forms. No more the "absolute" master, like an obsessed totalitarian deity—it's almost as if he's decided to throw the film away. So the tablecloth comes off, at the wedding banquet on the beach, and suddenly we're in medias res, in a new, unpredictable space. "Let's try it and see what happens"—a discovery infinitely repeatable, if only in strategically measured bursts. As Angelopoulos has been systematically "rediscovering" ever since, about three or four times per film ...

So too P.T. Anderson in his semisurreal Adam Sandler vehicle Punch-Drunk Love (2002), which actually serves up a double dose of random—first the anomalous bouncing pianola, then the car crash with no other purpose than to turn the film inside-out: wherever we were before this happened, we're definitely not there now. But of course there's more, and Anderson keeps upping the ante. Like the scene of Sandler talking on the phone, back to the camera so we have an optimal view of his neck, in a room so devoid of sensory stimulation he might as well be peddling widgets at Guantanamo. It's minimalism upon minimalism, and the implied bet here is that Anderson can keep us interested—or maybe even fascinated, in a perverse, movie-movie kind of way. (It's a bet he almost loses, by the way, though against these odds "almost" seems equivalent to winning the lottery.) Or another logistic gambit: the "relationship"—such as it is—between Sandler's incredible shrinking schmo and poor Emily Watson, who's obviously befuddled by it all. A lot of critics frowned on this amorous coupling--as in "Why would an intelligent woman like that ever ...?" etc—but here's what I think went down: "OK Adam, your job is to be as unavailable as possible ... and yours, dear Emily, is to 'love' this inaccessible dolt in spite of everything he does." Which of course is a recipe for failure, and what's a capable actress to do? So when Watson ultimately falls back on, well ... mothering the damn infant, it's like throwing in the towel—yo, Billy Madison wins again! Though if ever she'd actually cracked the mysteries of Sandler, all we'd have to show for it is another conventional romance. Instead of the indeterminate, risk-taking masterpiece we ultimately do get. Winning for losing's the name of this gambler's game. Not what you'd expect from Hollywood ...