Visual Arts TILDA SWINTON Serpentine Gallery, London

"Please come and go quietly," reads the sign on the wall of the Serpentine Gallery and, for once, visitors seem to be taking notice. Their light tread, though, is not in deference to authority, but out of respect for the person whose slight form exerts such an extraordinary power over this room and forms the centrepiece of "The Maybe", one of this year's most inspired shows.

In an apparently sealed glass cabinet, four feet above the floor, wearing a blue shirt and navy trousers, lies Matilda Swinton (1960- ), the strangest work of art this side of Disneyland. Tilda (as she likes to be known) is asleep, her red hair splayed across a pure-white pillow. Beside her are placed her spectacles and a jug of water. You may recognise Tilda from the films of Derek Jarman; she is a talented actress with a passionate performing style, but it is here in the gallery that Tilda is giving the greatest performance of her life.

"The Maybe" is the creation of Tilda and the artist Cornelia Parker. More a lying-in- state than a "performance piece", it represents the latest and most extreme in a series of exhibitions (Damien Hirst's sheep, Hans Ulrich Obrist's second-hand clothes show) at a gallery increasingly renowned for its headline-grabbing shock value.

As an experience it is, at first, not dissimilar to visiting Lenin's tomb. The difference, of course, is that the viewers have come more out of curiosity than reverence, and the object is not dead, only sleeping. Moving up to the glass, seeing the gentle rise and fall of her body, we feel a sense of having being conned into voyeurism. Rather than becoming Snow White or Sleeping Beauty, Tilda is transformed into a museum exhibit, a specimen, and she's not alone. Her new context is confirmed by the contents of the glass cabinets that fill the gallery's three other rooms. Carefully directed through the exhibition, by the time you reach Tilda's dormant form you are accustomed to scrutinising this strange and eclectic collection of rare artefacts.

Here is Napoleon's rosary, Turner's watercolour box, Charles Dickens's last pen, Robert Maxwell's shoe lasts, one of Churchill's half-smoked cigars, the manuscript of Wilfred Owen's Strange Meeting. Looking at these objects we instinctively "fill in the gaps", visualising Napoleon's pudgy fingers numbering the beads, Captain Scott's dying hands clawing at the drawstring of his last bag of provisions. Livingstone's hat and Stanley's pith helmet, placed at arm's length, grow ghostly bodies as we attempt to imagine the two men shaking hands. The theme of meeting, with man and with death, is one common thread through an exhibition that operates on several levels, not least that of wit.

The final exhibit in particular is a Frankensteinian joke that juxtaposes the preserved brain of the 18th-century computer whiz-kid Charles Babbage with Faraday's Magneto Spark apparatus. More profoundly, there is the visual wit by which Tilda's prone form is reflected by both Arthur Askey's suit and the rug and cushions from Sigmund Freud's analyst's couch.

Such potential levity aside, though, the central question posed by Parker is why we should need to exhibit such objects. The simplest answer is for their value as historical documents. We might marvel at the size of Robert Maxwell's feet and Churchill's cigars, but all these exhibits are much more than this. All that remains of their erstwhile owners, they feed our suspicions that something of a person's essence can be communicated through the material possessions with which they were once so familiar. They are traces of memory.

With Matilda Swinton (1960-), however, we have the opposite. While the material of her being is apparently tangible, she is less "with us" than the owners of the objects that surround her. Tilda is merely a body. Her spirit temporarily departed, she enacts a little death that mocks our attempts to extract meaning from inanimate objects and offers a sobering intimation of mortality.

n Until 10 Sept (0171-928 6363)