Duchamp first gained notoriety when he mocked aesthetic tradition by painting a moustache on the Mona Lisa. He also gave a salacious nickname to Leonardo's sybil: he added a caption which claimed she had a hot arse. His "readymades" - a snow shovel, a bicycle wheel, a gleaming urinal - questioned the arcane status of art works. In 1923 he abandoned his masterpiece, the so-called "Large Glass", in which an elusive bride teases and exhausts a gaggle of automated bachelors. When its glass panels grew a thick skin of dust in his studio, he admired the lunar alienation of its new surface. It was dropped in transit, and splintered from side to side; Duchamp claimed that the damage improved it.
Moving to New York in the 1920s, he announced that he had given up painting. His avocation now was chess, or simply breathing. He emerged briefly from retirement to make an appearance as an interior decorator: he painted the elevator in a friend's house to match her floral wallpaper. Yet for all his beatified indifference, Duchamp (as Calvin Tomkins argues in his excellent biography) has had more of an influence on art in this century than the idiosyncratic, inimitable Picasso.
With his contempt for the manufacture of "retinal" illusions, he became the ironically permissive patron of artists for whom art is whatever they say it is - a pile of bricks, a pickled sheep, their own bottled bodily fluids. He turned the artist into a performer (even if the performance, as when Warhol filmed Duchamp doing nothing for 20 minutes, is non-existent). During the 1950s, a right-wing senator, perhaps confusing Cubists with Cubans, denounced him for subverting the American way of life, and a critic committed to the existential melodrama of Abstract Expressionism called him "a corrupter of youth". Duchamp laughed silently at the fuss, and said that he was aspiring to a state of ideal inertia, or waiting to die. When he managed the latter feat in 1968, his widow noted that he looked "pleased". Le Figaro accorded him an obituary footnote in its chess column, which might also have pleased him.
Duchamp's nonchalance emerges, in Tomkins's account, as the key to his enigmatic, recessive character. His behaviour had a psychopathic chilliness (just as Picasso, mimicking the deity, identified creativity with murder: he once commented, as he wrestled wet clay into the shape of a dove, that to make a bird he first had to wring its neck). As Tomkins points out, his artistic resignation was complemented by a series of emotional refusals, cruel denials of intimacy. In photographs, his thin, pursed lips anaesthetise or mortify his face. He married his first wife, a tubby heiress, as a joke - although, as Andre Breton said of Duchamp's puns, the "mathematical rigour" of the jest expelled anything so lowly and forgivably human as comedy. When his father-in-law denied Duchamp's bride a dowry, he blandly informed her that he was a penniless gold-digger. She felt, she said, "annihilated". After annihilation, he prescribed depilation: sex could only be contemplated if she got rid of her pubic hair. Even though she obeyed, they were divorced six months later.
Inevitably, Duchamp's distaste for creativity - his own most of all - entailed disgust at the notion of creation itself. Art reproduces the world; it is an idea made flesh. Duchamp could not forgive the act of incarnation, which is why he redefined art as a cerebral exercise, best left unrealised. But mental power resembled erotic control, as one of his more candid metaphors disclosed. He wanted, he said, "to grasp things with the mind the way the penis is grasped by the vagina". A thought could work like the muscular rictus which seasoned sailors used to call "the Singapore grip".
Duchamp devised an apparatus to embody this castration complex: a masturbation machine, with a contractile vagina of "meshed springs and ball bearings", self-lubricated and activated - without risk to the male's tender member - by remote control. The bride in the "Large Glass" is just such a voracious mantis, whose bachelors (modelled on chocolate grinders) onanistically exert themselves in the lower panel of the construction. Rather than creatively igniting life, Duchamp treated the making of art as an expenditure of seed. He gave a kinky keepsake to one of his mistresses: a design of biomorphic blobs preserved between celluloid and black satin. Instead of pigment he used his own squirted semen.
His last, secret work - which you have to peep at, squinting through apertures in a rusticated door at the Philadelphia Museum of Art - was another transfixed and terrified study of the forbidden creative source: a flagrant nude, with spread legs and a shaved, gaping vagina. Tomkins, who has investigated this orifice, reports that "it has no inner labia, and ... looks disturbingly like a vertical, speaking mouth". What it's saying, however, remains inaudible. Or perhaps it is the spectator's job to put words into that muted, needy cavity.
Breton acclaimed Duchamp for erecting a treacherous light-house, kept "luminously erect, to guide future ships in a civilisation which is ending". Tomkins knew Duchamp during his last decade in New York, and the artist he celebrates is an amiable American populist, not the nihilistic prophet of the European avant-garde. Duchamp's conceptual whimsies fell in, Tomkins thinks, with the American fondness for practical jokes and wisecracks. He also industrialised the creative process, like Warhol who called his studio The Factory: in America, Duchamp proclaimed, the only legitimate works of art were the products of engineering - skyscrapers, suspension bridges, or plumbing fixtures like the pissoir which he exhibited in 1917 and entitled "Fountain". Though he officially disdained art, he took advantage of its commercialisation in New York and earned his living "mainly by buying and selling the works of other artists".
Calvin Tomkins's study makes for a valiantly cheery account of Duchamp, challenging what Francis Picabia's wife called his "pitiless pessimism". Still, I'm not sure I am convinced. The last time I plugged my eye to the Philadelphia peep hole, and peered through the screen of mouldered brick to the blearily sunny landscape where the headless nude reposes, that lipless, loquacious fons et origo looked to me - I must confess - like a dead end.