The virtual art gallery comes of age: The National Gallery does it with computers, the Tate does it with real paintings. Andrew Graham-Dixon reports on how museums are beginning to undermine their own traditional hierarchies

'I NEVER go to museums. I avoid their odour, their monotony and severity,' wrote the Fauve painter Maurice Vlaminck at the start of this century. The Fauves wanted to burn museums down, the Futurists to blow them up. The visible permanence that they gave to old hierarchies of value seemed not only dishonest; it ran counter to the spirit of modernity itself, the spirit of speed, change and vital instability. Seen as attics or mausoleums, places where art was sent to gather dust, museums came to stand for dead history and for the petrification of thought. 'Museums,' said Picasso, 'are just a lot of lies.'

Museums have never been just about art. They are the places that reveal, more directly than anywhere else, the ways in which a culture chooses to make sense of the past. And they have changed. The new museum is a place that constantly challenges its own preconceptions through rehangs and reorderings of its collections; a place that attempts to see every side of every argument (aesthetic, sociological, political, philosophical) that might be advanced about the objects in its care; a place dedicated to uncertainty.

The most experimental version of the new museum in this country, and perhaps the closest thing yet to the museum of the future, is on the first floor of the Sainsbury Wing of the National Gallery. It is called the Micro Gallery, and the most revolutionary thing about it is that it contains no pictures at all. Instead, it contains a row of touch-sensitive computer screens which visitors can use to call up television images of all the paintings in the National Gallery.

The Micro Gallery contains the possibility of the home museum, where the whole history of art has been shrunk to the dimensions of the microchip: an art museum without art, in which pictures have been made obsolete by their reproductions. The drawback is that the Micro Gallery is, on its own, a deeply unsatisfying way of experiencing paintings. It homogenises them, abolishes their crucial singularities of scale and texture and colour and turns them into pixellated ghosts of their true selves. The most interesting thing about it is its subversive relationship to the rest of the museum.

The Micro Gallery enables people to construct customised routes through the National Gallery. If you want to see every painting of the Nativity in the collection, the computer system will print out a floor plan of the galleries showing the location of each picture. It enables the visitor to step across the boundaries of national school and chronology according to which the collection is arranged; and it encourages a planned defiance of the museum's own principles of organisation.

But the Micro Gallery also suggests the subtle links between a culture's habits of thought and its technology. The technology of the computer and of the word processor has made it easier than ever before to rearrange text, image and almost any form of any information. When you know that whatever you have written or thought can be reordered at the touch of a button, it becomes increasingly difficult to sustain the belief that there is just one correct way to structure anything.

In the Micro Gallery, pictures have become units of visual information, free-floating in the electrical ether of a machine's circuits. But there is a real version too. There is a museum that has taken the principles of information technology, the principles of constant change and reordering, to heart - it has applied them to real pictures hung on real walls. It is called the Tate Gallery.

'New Displays 1993' opened last week at the Tate. For the third year running (the policy will continue indefinitely) the museum has entirely rehung its collections. The reason given in the pamphlet accompanying the latest rehang is simple: 'The Tate has not nearly enough room to show all its treasures at once'. Nicholas Serota, the museum's director, would like British historic and modern art to remain in the building on Millbank, and wants to see a new Tate building constructed to house international modern. So it could be argued that his rotational system of display, under which many of the Tate's most famous pictures disappear periodically from view, is really a strategy devised to call attention to the museum's lack of space.

But the character of this new hang, which is bold and weird in equal measure, rules that out. Too much pleasure has been taken for it to seem like a mere tactic. It is the reordering itself, the constant changes made to the historical argument that any one hang represents, which now seems the entire point of Tate policy. Once a year, Serota pushes DELETE, COPY, MOVE. The new museum is not a graveyard of objects. It is a database.

The latest hang of the Tate opens with a display that makes this blatantly apparent. Walking along the spine of the building, through the Duveen Galleries, you encounter first Rodin (several sculptures have been loaned by the V&A), then four Matisse reliefs and Jacob Epstein's would-be primitivist Jacob and the Angel, then a group of predominantly Minimalist sculptures including Carl Andre's Equivalent Eight, alias The Bricks. Three competing versions of radicalism.

But this tells such a madly abbreviated story of 20th-century sculpture that it comes across as a parody of a conventional museum display: it retells the evolutionary myth of radical modernism so cursorily that you have to disbelieve it. The Tate flaunts the fact that it does not (cannot) tell The Whole Truth. The new hang is full of willed incoherence. It has often been said that the Tate is too many museums in one, but under Serota it makes a peculiar virtue of that. The displays are at their oddest and most challenging when they exploit the schizophrenic nature of the Tate as a museum of the 20th century, designed to represent local and international developments side by side. The current Tate hang often seems to be making a joke of the differences. On the one hand, in the display given over to Cubism, you see Picasso and Braque pushing back the frontiers of human perception; nearby, there is a display given over to the New English Art Club, whose members (with the exception of Sickert) misunderstood or ignored the implications of modern art. Mark Rothko introduces a new register of tragic feeling into western art in his Seagram Foundation murals; the adjoining gallery reveals Adrian Stokes painting dull little still lives by the hundred, Britain's sub- Morandi.

But it can be argued that the texture of art, in this or any other century, is much more closely mirrored by the Tate than it is, say, by MOMA in New York, with its exclusive focus on masterpieces. The Tate's unevenness is a form of honesty: its blend of the local and the international, the idiosyncratic and the universally acclaimed, the second-rate and the masterly, is vigorously true to reality. Its messiness is authentic.

If the old museum was the place to see how culture makes sense of history, the new museum reveals something altogether different. It suggests that history cannot be made sense of, or rather that it can be made sense of in so many ways, and according to so many competing theories, that no one organisation of a museum's necessarily partial contents can aspire to correctness. It demonstrates the extent to which old radical strategies, the desire to destabilise received ideas and values, have become intellectual conventions. The Tate is not ahead of its time in this, it is of its time. The Fauves wanted to burn the museums down, but if they were alive now they would probably not bother with the Tate. It burns itself down once a year anyway.