Making links: The Russian Linesman

A show curated by artist of the moment Mark Wallinger connects seemingly unrelated works. It's both pleasing and puzzling, finds Tom Lubbock

Go in and you find yourself in the most boring sort of corridor: off-white walls, strip lighting on the ceiling, grey office carpet on the floor. Go a few yards along, and it turns a right angle to the right, and goes on the same. But go a few yards more and it turns another right angle – straight up. The carpeted floor rises directly in front of you, meets you like a wall. The whole corridor goes up with it, a shaft opening above your head. You look up into it. After a few yards, the corridor turns again, to the left, and out of view.

It's a beautiful illusion of deorientation. The impossible path invites, and you can believe briefly in your weightlessness, in your power to step out upwards on to the unused dimension, like a space-man or superhero. Monika Sosnowska's Corridor is a simple bit of carpentry that spins our spatial bearings on their axis.

But coming back out of Corridor, you may notice, framed by its entrance, on the other side of the gallery, a monitor showing a video by Bruce Nauman. He's standing on one foot. His torso is bent forward, his other leg is raised behind him, he makes a kind of corkscrew form, and with a joggling, hopping movement, he's gradually rotating himself on the spot. But the film has been inverted, the floor is above him, and he seems to be turning round on the ceiling. Only connect?

These are two pieces from the middle of Mark Wallinger Curates: the Russian Linesman. It's a show at the Hayward Gallery put together by the artist, opening tomorrow, and its timing is chancily perfect. Last week, Wallinger's colossal statue of a stallion won the Ebbsfleet Landmark commission, and for the moment he's British artist of the hour. His exhibition may surprise some of his new fans and critics. It has got works, art and not art, going back from now to ancient Rome (though no horses that I noticed). Making links between them is the puzzle and pleasure of this rich, original and fascinating anthology.

Frontiers, Borders and Thresholds is Wallinger's subtitle. (But no starting gates either.) His most basic theme is lines: lines literal and metaphorical, outlines, pathways, dividing lines, territorial boundaries, the lines between reality and illusion, belief and unbelief. His main title refers to the 1966 World Cup Final, and a literal line marked on the grass, and the uncertain path of a ball, and a still-disputed call, and the difference between England's victory or not.

Like any anthology, it stands both on the quality of its individual contents and on the quality of the links among them. Let me give you some more. Here's an Italian sculpture from the 1930s, Renato Giuseppe Bertelli's Continuous Profile (Head of Mussolini). It takes the outline of Mussolini's profile, and makes it its edge all the way round. It's like a fat chessman. It's like a head spinning on a potter's wheel. It's like a solid thing with a built-in blur. (The pity is, it's Mussolini.) And near it, an old Roman head with double faces back to back. Connect?

Or here are three great oblong sheets of glass up against the wall. But no, they're not. They're areas of empty air, outlined by lengths of black yarn stretched taut, pieces by the minimalist sculptor Fred Sandback. And on the opposite wall there's a Dürer print. It illustrates how to do perspective drawing by stretching a string from an object to the eye passing through the picture's surface, a string that represents the I-beam. And nearby there's a film of Philippe Petit doing his 1974 tightrope between the Twin Towers. Connect?

Yes, lines, outlines, taut lines, illusions, doubles. There are plenty of illusions and doubles, replications and ambiguities. There's a piece by Vija Celmins with a lump of rock and beside it a perfect copy of this lump of rock – a doubling with a replica. There's a copy of a feature that Marcel Duchamp had in his New York flat, a single door that is hinged between two doorways, so it could only close one at a time – a replication of a doubling! (And a threshold, too.)

Snap. These are finely chosen things, and they fit their themes remarkably well – a little too well, too neatly, and the curating becomes static, not dynamic. There are professional curators, whose job is to devise themes and assemble shows that prove them. Excellent exhibitions they may arrange, but they follow single-issue agendas, and their exhibits are examples. Artist-curators can show another approach. They put together exhibits in a way that's more like how art itself is put together.

That's mostly how it goes in The Russian Linesman. The case isn't so clear or so tight. The juxtapositions are tenuous and tangential and a little mysterious. Why is a gigantically enlarged image of a flea from Robert Hooke's Micrographia (1665) just along the wall from a series of Eadweard Muybridge's photographic split-second breakdown studies of humans and animals in motion (1887)?

There seems to be something relating them, something on the edge of vision, something I can't quite put my finger on – is it just the idea of living creatures being subjected to a scientific transformation? But no, move along the same wall, and there it is. We're back with Bruce Nauman's Revolving Upside Down, another study of human motion, and a man acting like a performing flea! And then across to Corridor...

That's how things should go, with a subplot rather than a plot. It should progress through degrees of separation, and distant family resemblances, in a network of touch points, and then suddenly there's a convergence where all kinds of overlaps and echoes strike.

As the show goes to its end, and the emphasis moves to war and death, the links become increasingly elusive, and I wasn't sure if it had lost its ways or I had, and either way that was OK. There's that painting from the National Gallery, A Dead Soldier, formerly thought by Velazquez, now Anon, but still with the distinction of having inspired Manet – is he like that borderline figure, The Unknown Warrior, both famous and anonymous, and is that why he's here?

And how about Raw Footage, a sequence of found films collected by the Dutch artist Aernout Mik, from things shot by news agencies during the Yugoslav wars but never screened. You can see why not. They show the complete intersection between casual everyday life and warfare, with men eating and joking and hanging out in a wood and firing mortars at an unseen enemy. Normality and terror – another borderline experience?

But then backtrack around the corner to where we started, in Corridor with its happy illusions. What connection can you string from here to there? Another case of not believing your eyes?

The Russian Linesman stretches its points. It deals in both the smallest differences and the biggest differences, the most delightful illusions and the most driven beliefs, and suggests that there's only a narrow step between them. (See World Cup Finals. See civil wars.)

This is how Mark Wallinger's art performs, too. The show is curating-as-manifesto. In his work, seeing and believing are always in question. It links up the optical, the political, the metaphysical. It does it with the most minimal transformations and illusions. It does it with dramatic spectacle, like Jesus arriving on the fourth plinth in Trafalgar Square, like a replica of Brian Haw's Parliament Square protest encampment arriving in Tate Britain, or by sheer scale. And what else will that incredibly enormous white national emblem be doing, but forcing us to believe, and not to believe, our own eyes?

Mark Wallinger Curates: the Russian Linesman, Hayward Gallery, London SE1 (0871 663 2500), runs to 4 May; then touring to Leeds Art Gallery (0113-247 8248), 16 May to 28 June, and Glynn Vivian Art Gallery, Swansea (01792 516 900), 18 July to 20 September

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