Matthew Barney: The bizarre genius of Björk's boyfriend

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This year, two high-profile London exhibitions, the V&A's Surreal Things and Dali & Film at Tate Modern, have shown that classic Surrealism is still big at the box office – but also that the old, strange juxtapositions no longer seem so uncanny. In art, our sense of the inexplicable, constantly needs to be refreshed: that's why a major draw this autumn will be Matthew Barney's show at the Serpentine Gallery, London.

Not that the work of the protean 40-year-old American – sculptor, conceptualist, performance artist, film-maker, fabulist – is inexplicable per se. Barney has always explained his creations in some detail, but invariably in ways that make little sense outside his own hermetic terms of reference. Muscular hypertrophy, Japanese whaling practices, Manx legend, masonic lore, theories of sexual indifferentiation: all have a place in his mythology, but the viewer isn't necessarily required to piece together the whole conceptual jigsaw. Any one of Barney's abstrusely exotic images can serve as an entry point into his world, whether it's a blood-spattered bagpiper in a pink busby, satyrs tussling in the back of a neon-lit limo, or gym equipment made of Teflon.

An art-world star since making a splash in New York in the early 1990s, Barney has not only won critical acclaim – The New York Times called him "the most important American artist of his generation" – but has also gradually attained something like household-name status. That's largely a result of his Cremaster cycle (1995-2002), a quintet of delirious, quasi-narrative films with lavish production values; screened in cinemas, they achieved cult crossover success with the constituency that reveres David Lynch and David Cronenberg. Barney is now widely considered a film-maker, but the forthcoming exhibition at the Serpentine, his first major British show, should serve as a reminder of his true scope.

Taking in sculpture, installation, performance, drawings and film, the show centres on Drawing Restraint, a multimedia series that Barney began in 1987. In particular, the show relates to Barney's film Drawing Restraint 9, which he made two years ago with his partner, and equal in imaginative idiosyncrasy, Icelandic avant-pop queen Björk. The couple play visitors on a Japanese whaling ship, the Nisshin Maru, who end up ritually carving each other's bodies into chunks of blubber. Marine matter finds its way into the related sculptures too, barely describable hybrid objects that brazenly confound the traditional canon of workable materials. Holographic Entry Point (2005), for example, consists of "self-lubricating plastic, polycaprolactone thermoplastic, shrimp shells, sea shells, cement, wood, steel...", and that's just the start of the menu.

Any initial description of Barney's work risks looking like a hoax, spoofing the perceived excesses of the blockbuster avant-garde. That's why his creations have to be seen to be believed: their unorthodox visual and tactile impact speaks for itself. It's true that Barney's output, tempered with grotesque humour, could be regarded as partly a joke in the Dada tradition: the matter-of-factness with which he expounds his quasi-scientific systems certainly suggests a sly parody of theoretical discourse in art. When I interviewed Barney in the late 1990s, this soft-spoken man described what he called the "metabolism" of one of his pieces: "It starts in glucose as a state of potential, moves to a glucose-sucrose blend of candy, on to sucrose, passes through petroleum jelly, then goes on to the starches, to tapioca, meringue and pound cake – but adding eggs at the end to the complex carbohydrates."

Nearly all Barney's commentaries are in this oracular mode, yet their earnestly systematic nature suggests that he's serious about them, and inviting us to take them seriously too. Many rise to the challenge: over a decade, Barneyology has effectively become a specialist field of modern art theory. Most critics, however, are happy to throw in the towel and exhort viewers simply to revel in the work's multi-layered exuberance.

In all his irreducible oddity, Barney appears to have sprung fully formed from his own brow; in fact, his mother was an abstract painter. He was born in San Francisco and raised in Idaho; his high-school prowess as a football quarterback led to recruitment by Yale, where he enrolled in pre-medical studies and sculpted. He left his studies after sidetracking into a career as a model, an occupation that informed some of his ideas about performance: it taught him, he said, "how the subject must have the ability to evacuate his or her body for the transformation to take place". Barney has certainly specialised in evacuating all signs of a real self from his body. In his films, special-effects prosthetics make him the Lon Chaney of conceptual art, his guises including a dandyish tap-dancing man-goat and the executed American murderer Gary Gilmore.

Physicality is central to Barney's work, which involves considerable feats of athletic daring: Cremaster 3, for example, is structured around his twin ascents of a lift shaft in the Chrysler Building and of the Guggenheim Museum in New York. The Drawing Restraint series began as a set of performances in which Barney encumbered himself with weights, harnesses and elastic to make the act of drawing physically difficult.

The wildly disparate elements in Barney's universe combine to make a vast but inscrutable mythology that can really only be

decoded imaginatively from within, once you immerse yourself in its mad resonances. Its parameters take in high culture and pop (pastiche grand opera at one end, speed metal and country at the other), a murky brew of belief systems (Celtic creation myths, freemasonry, Mormon, Brazilian candomblé), a fascination with androgyny, asexual reproduction, metamorphosis, drag (transsexual but also trans-species). Barney uses places and people too as material, as "found objects": buildings such as the Guggenheim or Budapest's Opera House; locations including the Isle of Man and the Utah salt flats; names such as Ursula Andress, Norman Mailer, sculptor Richard Serra, all guest stars in the Cremaster cycle. Barney's pseudo-narratives thrive on arbitrary geographical, historical and thematic connections, which generate visual and conceptual "rhymes". For example, Gary Gilmore's grandmother allegedly had an affair with Barney's childhood hero Harry Houdini, while bees are a key item of Mormon symbolism: hence in Cremaster 2, strands of images associating death, escapology and beehives in Utah.

It's hard to trace obvious sources for Barney's imagination, although he has cited Joseph Beuys and Bruce Nauman as influences. While he is often compared to Jeff Koons and Damien Hirst, the closest affinity among contemporaries – in terms of elaborating quasi-scientific thought systems – is Britain's self-deprecatingly boffinish Keith Tyson.

Previously married to a forensic psychology graduate named Mary Farley, Barney now lives with Björk, with whom he has a four-year-old daughter, Isadora. It's one of the few celebrity households where you'd really want to be a fly on the wall. Drawing Restraint 9 presents itself rather like the couple's lyrical, orgiastic love ritual: if Cremaster has been called Barney's Ring cycle, then the new film is his Tristan and Isolde. The pair rarely comment on their relationship, but Björk has volunteered that working from Barney's laconic directions was "like solving a murder mystery". She has also commented, in typically Björkian style, "He's a bit of a submarine."

Since Cremaster, Barney's megastar status has led some critics to decry bombast, while it's undeniable that his shock value has been slightly dampened by familiarity. At the recent Manchester International Festival, there was a decidedly mixed press response to Barney's segment of the performance "variety" show Il Tempo del Postino. Featuring cars, a bull, a female contortionist and Barney wearing a live dog on his head, it caused many UK critics to sniff, although an enthusiastic Richard Dorment in the Daily Telegraph saw the piece as "about nothing less than the psycho-sexual origins of Islamic fundamentalism". As for Barney's film-making, it must be said that Drawing Restraint 9 has a tone of laborious solemnity that is considerably less alluring than Cremaster's delirious efflorescence.

Even so, the prospect of a new full-scale exhibition, of seeing Barney's objects first hand in all their monumental opacity, is hugely exciting. Whether or not you're familiar with Barney's work, chances are that you'll still come away with a sense of mystery left decisively intact. That's as it should be. As the elusive artist has put it, "I try to protect myself and my work. I want there to be a fraction of my work that even I don't understand."

Matthew Barney: Serpentine Gallery W2 (020 7298 1515, www.serpentinegallery.org), 20 September to 11 November. 'Drawing Restraint 9' opens on 28 September. The documentary 'Matthew Barney: No Restraint' is released on DVD on 24 September