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Right off the bat, Peter Greenaway wants to make clear that he’s never really taken himself seriously as a filmmaker — although like so many of the paradoxes that comprise Greenaway’s identity, it’s not wise to take such a claim too seriously.

“This is a terrible confession to speak to you,” he says via Skype from a tiny house on the Atlantic coast where he goes on weekends (the rest of his time he spends in Amsterdam, mostly). “There’s always that sense of being removed from the activity, of taking a step back and trying to look at it with not a sarcastic or derivative attitude, but certainly a considerable irony.”

Such cheekiness is plenty apparent in Greenaway’s filmography, which spans 16 features, ranging from the Terry Gilliam-esque irreverence of “The Falls” (1980), a three-hour catalog of eccentric survivors of an imaginary cataclysm, to the obsessive brain-dump that is “The Tulse Luper Suitcases” (2003-04), a tricksy trio of features centered on his cinematic alter ego, the elusive Tulse Luper.

Greenaway boasts what is arguably the most playful c.v. of any major living director, overflowing with visual puns, mathematical puzzles and imaginary languages. He’s obsessed with lists, maps and all manner of taxonomic tools that humans have designed to make sense of a chaotic world (that’s his structuralist impulse in action), even as he so clearly takes pleasure in subverting those very same systems (for which he’s been labeled a “poststructuralist” by those who share his affinity for classification).

Now 80, the director of such arthouse shockers as 1989 cannibalism satire “The Cook, the Thief, His Wife & Her Lover” and 1996’s NC-17-rated “The Pillow Book” hasn’t mellowed one bit. He’s still working — Greenaway is wrapping “Walking to Paris,” a years-in-the-making portrait of Romanian sculptor Constantin Brâncuși’s trip to the European art capital — and still battling in his own defiant way against the idea that cinema is a medium for telling stories; he’s convinced it’s capable of so much more.

“We created our cinema on the notion of illustrated text, but I always objected to it. Every time I started writing a script, I thought, ‘What am I doing here? I want to make moving pictures!’” Greenaway says.

“I never planned to be a film director,” he explains. “I wanted to be a painter from a very young age. There’s nothing in my family to suggest a support system of any sort, and yet, through a series of happy accidents, I ended up at art school in the very early ’60s. At the time, all art schools had film clubs, the Nouvelle Vague was in full swing and it was an exciting period for Italian cinema, so those were my references.”

“Breathless” by Jean-Luc Godard electrified him. Alain Resnais’ “Last Year at Marienbad” blew his mind, and quickly became his favorite film.

“It has crazy ideas where the people don’t have names, and it’s all about memory, which is remarkably unreliable,” he says. “I’m not a tremendous devotee of abstract art. I still believe in notions of forms and figuration, but it was the film that traveled closest to the wind, to the idea of being an abstract film. It stripped away anecdotal information and replaced it by other sorts of anecdotal information.” Upon seeing it, Greenaway realized, “I wanted to make the abstract art of cinema in a sense.”

After being rejected by the Royal College of Art’s film program, Greenaway found work with the Central Office of Information, or COI, Britain’s post-war “marketing and publicity” (i.e. propaganda) department, as a film editor. “I was constantly making films about Concorde and about hovercraft and all those things for which the British patted themselves on the back, but all the time, I was deeply distressed and amused by this use of propaganda,” Greenaway says. “And it’s still going on, isn’t it? We’re now in this era of extraordinary false news.”

A decade and a half spent assembling such material gave Greenaway an incredibly sophisticated sense of how to put images together, which he applied to a series of experimental short films, a handful of which had attracted critical acclaim.

“I’d made quite a lot of films, which were related to all kinds of fashions in filmmaking. I was fascinated by land art, planting ball bearings as if they were seeds. I wanted to use the language of cinema to discuss that,” he says, “but I want the largest possible audience. Along came this extraordinary phenomenon called Channel Four, who suddenly decided because it was run by academics and university people that we needed something a little more intelligent, a little more provocative.”

Thus, Greenaway found fresh support for such follies as he’d been making for years. If “The Falls” could be seen as the absurdist culmination of the short-form work he’d done before, 1982’s “The Draughtsman’s Contract” was a critical and popular breakthrough. Like “Last Year at Marienbad,” the film is a brain-teaser of sorts, though Greenaway insists the mystery is not so complicated as it seems. (Indeed, he explains it all quite well in the director’s commentary, for any looking for insights.)

“I was always very conscious that we had a very literary cinema. I mean, cinema is meant to be about pictures, but you can’t go to a producer with 17 prints and schemes about serial painting and convince them. Traditionally, what a producer needs is a script, and a script is a text, and text is literature,” Greenaway explains.

And so Greenaway pushed back, testing the boundaries of the medium, delivering just enough plot to keep audiences interested, while bending the forms as much as he could possibly get away with.

“I had another sort of serious problem: If I wasn’t very interested in narrative, how the hell was I going to hang everything together? All of us use narrative. Events happen during the day, and we tell our wives, our dogs, our doctors, our dentists about what happened to us. But narration is extremely ephemeral and anecdotal,” he says.

Therefore, Greenaway looked to other systems by which to structure his films. “‘The Cook, the Thief, His Wife & Her Lover’ is an illustrated menu. A menu consists of hors d’oeuvres all the way to the coffee, so I used that as a structure,” he explains. “In ‘Drowning by Numbers,’ the title tells you everything: It’s a film simply about numbers. It’s all a very self-conscious way of saying, ‘This isn’t reality, it’s a film.’ A film is a construct. Let’s play with the artificiality.”

There it is again: the notion of play, so central to Greenaway’s aesthetic. To say that he isn’t serious about his art would be absurd, and yet the best way to appreciate his work is to relax and embrace the spirit of renegade experimentation. Look how he uses color in “The Cook…,” luxuriate in the choreography and compositions of “Prospero’s Books,” laugh at the bawdy excess of “Eisenstein in Guanajuato” (an outing-cum-homage to the Russian silent master).

“The really exciting days of cinema were probably the last 10 years of silent cinema, when they demanded that the pictures told the story,” Greenaway says. Since the introduction of sound, cinema has been shackled to literature, he says. Movies are obsessed with realism — as painting once was, until the invention of the camera liberated art. “Photography created the greatest century of painting we’ve ever known,” he says.

But the movies are stuck, he believes. “Cinema hasn’t even reached its Cubist period yet,” Greenaway once told an interviewer.

He’s done his part to shock, only to be shocked in return by the institutional embrace.

“I think it was David Hockney who said, ‘If you reach 80 in England and you can still boil an egg, watch out, they’ll pin a medal on you,’” he laughs, repeating a joke made nearly a decade earlier, upon receiving BAFTA’s career achievement award. “So I thought, ‘Fuck it. I’m going to really make films I really want to.’”

Getting older hasn’t tamed him one bit. “The death date for most white males in Europe is 81 and a half, so I have one and a half years left,” he says. “Let’s hope I can stretch that out a bit. I have loads and loads of movie scripts all ready to go.” Like “Joseph,” a scandalously sacrilegious inquiry into Jesus’ paternity which Greenaway describes as a “cataclysmic collapse of Christianity in one go.”

Or “a dialogue between Stalin and Dracula,” who reveals his secret to the Russian leader. “As a vampire, he doesn’t suck blood. He does something much more powerful. He feeds off of human semen from source. So there’s another sensational movie I want to make,” Greenaway pitches, well aware that one will never see the light of day.

“At the end of this summer, I’m supposed to make a film with Morgan Freeman about death, that tries to find a reasonable notion for suicide. I believe death is unnecessary.”