Joan Smith: Why Lady Gaga belongs in a museum

Did she looked a bit chilly? Stepping off a plane in Toronto on Friday, Lady Gaga wore sheer purple gloves, matching tights over black knickers and a leather top with open sides.

But she had to live up to the startling outfit she wore to Maxim's restaurant in Paris the night before, when she appeared in a transparent leopard-print body stocking and heel-less platform boots.

Being Lady Gaga is hard work. She never appears out of character: each public appearance is carefully calibrated. In an age of extremes, she and her team have to go that much further, appropriating and subverting fashion. Those boots, which she was still wearing on arrival in Toronto, are a brilliant example of Gaga's wit: when millions of women are tottering around in painfully high stilettos, what does she do but make heels vanish altogether?

Lady Gaga has an intuitive grasp of how to flourish on her own terms in celebrity culture. Last week's punishing schedule – flying to Paris after a concert in Michigan, making her catwalk debut for Thierry Mugler and then heading back to Toronto for another performance – produced an unbroken stream of images to coincide with her new single. But it would be wrong to write her off as the über-celebrity of a shallow age.

In a charmless article last year, the cultural commentator Camille Paglia heaped praise on Madonna but chided Gaga for her sexually explicit displays, claiming that the singer "obsessively traffics in twisted sexual scenarios and solipsistic psychodramas". She complained about Gaga's lack of expression when performing, failing to recognise that the singer deliberately refuses to expose herself emotionally; the clue is in the title of Gaga's song "Poker Face".

Lady Gaga isn't Cheryl Cole, revealing her feelings in interviews; she's a superb performance artist invented by a former New York art student called Stefani Germanotta. Her adopted persona allows her to write songs and act out fantasies that draw on art, pop, sci-fi movies and images of women in pornography.

Madonna is an obvious influence, although Lady Gaga has a better voice. So is Andy Warhol, while her thesis at the Tisch School of Arts was on Spencer Tunick and Damien Hirst.

I'm not a fan of Hirst, but it's impossible to understand Lady Gaga outside an artistic tradition that experiments with sensationalism and the body's susceptibility to objectification. Her videos have an unearthly beauty reminiscent of Fritz Lang's Metropolis, but there's also something disturbing about the way she incorporates images from slasher movies in her performances.

Gaga rarely explains, leaving it to the audience to decide what it all means, although she did say this about the meat dress she wore at the MTV video music awards: "If we don't stand up for our rights soon, we're going to have as much rights as the meat on our bones. And I am not a piece of meat." This was interpreted as a feminist statement, a meditation on ageing, and an attack on our attitudes to meat, while enraging animal rights' organisations.

The consternation created by her costumes and performances is surely the whole point of Lady Gaga. Give that woman the Turner prize.

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