Marvels challenge our normal perception

Anish Kapoor's new show is a wonder - exactly as intended. Banality is the last thing you would expect from this sculptor. From the moment you walk into the forecourt of the Royal Academy in London, where a column of vast steel spheres bubbles up towards the rival sun, its globe reflected to infinity, you are in a land of marvels.

Inside, a golden expanse radiates through the galleries like a sun-filled sky. Go closer and the glow turns out to be nothing but a huge yellow wall. Closer still and the wall becomes literally nothing: a hollow, a colossal dimple in which your eyes drown in the search for some definitive form. From visual richness to nil visibility, the transition is as smooth as the colour.

In another gallery, a great rusting hull rises to the cupola above, before descending in graceful sweeps like billowing sails. Somehow, it resolves into a mouth, or a tunnel, or at least an opening into darkness: another seductive hollow that draws you into its void.

So far, so typical. Anyone who saw the magnificent Marsyas stretching all the way through the Turbine Hall at London's Tate Modern gallery in 2002 will have some sense of the potential excitement of this ship in a bottle with its soaring, dipping, polymorphous form. But I notice its title is Hive. And the mind is sparked to imagine the flight of the bee through some crevice into the obliterating darkness of that immense vessel, the hive: origin of both maker and honey.

By now, anyone visiting this show will have heard the gun going off at 20-minute intervals. This cannon, primed by a black-clad firing squad, shoots blood-red wax at 80km/h. The explosion is breathtaking, the room is thrashed and splattered, its floor a Jackson Pollock aftermath. The ejaculate drips and solidifies. It's a painting in progress. It's a sculpture. It's a performance and a period piece, too, invoking the history of art.

It is also, in no particular order, ear-splitting, thrilling, disgusting, cathartic and blatantly melodramatic. There is no reason why the viewer shouldn't feel as excited by the action - high-speed release of visceral colour - as struck by the art analogies, or shocked by the gory residue.

And this is a departure for Kapoor, as it seems to me. In most of his crimson works, the colour has been gorgeously symbolic. No thoughts of blood on the hands, or anywhere else. Cervix, breast and womb: all lyrically evoked as undulating forms in perfect powder-puff pigment. There are several early works here for comparison.

But with Shooting Into the Corner, bloodshed is irresistibly called to mind. Scarlet war paint, you might call it, were it not that the waxiness of the substance returns you to those bees. Something molten, something extruded: an act of creation as well as decimation. What Kapoor has made here is a honeycomb of connecting ideas.

The most momentous work is probably Svayambh (Sanskrit for self-generated), enacted right through the five main galleries. A red train, a ship, a loaf the size of a lorry but shaped exactly like the archway between each room, glides with imperceptible slowness along deadly blood-red rails, smearing the Royal Academy with more of this war paint as it passes.

Perhaps the building deforms the block; perhaps the block defiles the building. Paintings long gone, people transported to their deaths, sealed chambers, ships in the night: a vast range of associations fills the mind even as the body recoils. It is exactly what one hopes for from Kapoor: a strong physical sensation as well as the active revelation of one's own cognitive phenomena.

But awesome as it is, I confess to having felt more spellbound before one of his polished steel mirrors - a rectangle as big as a cinema screen, into which the world seemed to crowd and then vanish in an instant. Stand before it and yet you are not there, walk away and your departure makes an appearance. Scenes arrive inexplicably from nowhere.

The optical effects could be efficiently explained, beyond doubt, but not the perceptual experiences of a world inverted, miniaturised, speeded and slowed, of the sheer animation flashing across this immobile surface. The room swoons, the walls arch, far-off figures circle like apparitions in a crystal ball.

When Kapoor uses gold instead of silver, the scene is translated into the past: people turn hazy, spotlights glow like candles. A change of shape produces new speeds and configurations. That these almost invisible surfaces - non-objects - should have such different characters is a testimony to Kapoor's gifts as a sculptor. Everything here is achieved, after all, by manipulating substance, form and colour.

Static, kinetic, weightless, solid, empty, replete, visible, invisible: everything Kapoor makes seems to encompass its opposite too, to be effectively a double object. And while detractors used to complain that his work was quasi-spiritual populism, it seems clear from this show, that it accepts as many interpretations as there are viewers.

Sexual, psychological, religious, physical, aesthetic: each response is as legitimate as the next, right down to honest admiration for Kapoor's superb engineering. This openness to all is an exceptional achievement. And what is different - richer - about this exhibition is that the work no longer depends so much on brilliantly calculated illusions to stimulate the mind and eye.

Anish Kapoor at the Royal Academy, London, to December 11

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