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Curatorial coup: Nairy Baghramian and Phyllida Barlow share a show at the Serpentine

It's a good idea, from time to time, to forget what art is. We vaguely know what it's meant to be. But imagine you didn't know, and then you came across it, and tried to work out from scratch what role it might have in our lives. There's something that lies on the floor by the entrance. It's a small object. It has the form of a plastic inflatable, with ridged seams, roughly the shape of a biscuit tin, or a small cushion, but not firmly inflated, so that its form is rather squashy. But clearly it isn't literally squashy. It is black, and polished, and solid. It must have been cast in some hard medium – hard rubber, in fact. Doorstopper is its name. Nairy Baghramian made it.

And in an adjoining room there's a pair of chaotic blobs that block your path, as high as a man. Each one is like a huge snowball of rubbish, as if it had rolled along, accumulating plaster, fabric, sacking, bits of polystyrene, and getting caught up and impaled on a ring of plywood. These blobs have nothing hidden about their materials or making. They are messily stuck together. They're called Untitled: Double Act, and made by Phyllida Barlow. What could these things be doing in our lives? And what are they doing in their own company?

These two art-works, these two artists – of course that's what they are – now appear in the same exhibition at the Serpentine Gallery, and unexpectedly. In advance, even if you knew these two sculptors separately, you'd hardly think to find them sharing a show, just the pair of them. Nairy Baghramian was born in Iran in 1971, and works in Berlin. Her sculptural language evokes ironically a world of minimal design. Phyllida Barlow is an English artist, born in 1944, and has been a long-term and influential teacher at the Slade. Her sculptural language looks like it grew up on a farm. Bringing them together is a very remote and unobvious idea. But when you see it done – the enormous differences between them, the surprising and tangential connections – it's an inspiration, a vivid double-act, a real stroke of curating.

Take an immediate tour of the Serpentine's spaces. The works aren't actually allowed to mingle or occupy the same room. It would be more than confrontation. Their physical natures are so alien, their presences would simply jam. But clearly we're being pushed a dramatic meeting. And as you move between them, you feel their differences at every level. What a roster of contrasts. Fat, spare. Rough, smooth. Dirty, clean. Sticky, polished. Chaotic, precise. Colourful, monochrome. Raw, processed. Messy, pure. Mixed-up, streamlined. Hand-made, tooled. Heavy, light. Massive, precarious. Sluggish, clipped. You could line up these various opposites, and produce two character types, say, or two very basic principles. Sancho Panzo and Don Quixote? Matter and spirit?

Baghramian's pieces can be so fine as to be almost not there. There's one called Invigilator, for example, and it's a spindle-thin framework, like an upright, slightly wonky goal, just touching against a wall. It's a strict sensation. You feel its thinness between finger and thumb. You feel its dark wiry lines shrinking towards nothing. It's tuned towards weightlessness, dematerialisation. All around, arcing edges and curving sheets cut through the air.

In the next room you find Baghramian's main piece: Class Reunion. It's a group of 18 elements, all uprights (except for one that has fallen to the floor). The title, the gathering, the standing-up - all suggest personages. And each one is basically a stand, a single pole or several legs, with a kind of head-form at the top. At least, that's how you see it collectively. Individually, these "heads" might be more reminiscent of coat-hooks, chair-arms, handles, crutches, gear-sticks, truncheons. Nothing is specifically identifiable. They're carefully made to be on the edge of recognition.

Baghramian is operating between the body and design. Her forms are not exactly regular. Their tooling is very smooth and probably machine-made, but their contours are slightly organic, twisting, undulating. They echo something we're already familiar with in our world, things that are deliberately manufactured to fit our bodies, such as furniture and medical equipment. These objects have an abstract curvaceousness, a generalised body-form to them. Baghramian sculptures play a variation on these man-made limbs.

Quasi-prosthetic bodies, then. At the same time, her work has a surface to it that is mysterious and inhuman in its perfection. The captions will tell you that the material is either polished aluminium or cast rubber, though sometimes I'm not sure which. Whichever, your hand is both tempted and doesn't dare. The fear of finger marks keeps you back. Noli me tangere. And more than that, it's as if this object and its realisation has an unknown and unearthly nature, that mustn't be violated.

At this point, any comparison with Barlow's works appears a bit mad. Turn to a piece like Untitled: Hive. It's a cake made out of a skip. It is piled up from sheets of miscellaneous stuff – layers on layers of corrugated cardboard, polystyrene, plywood, underlay. And from this, an approximate house-like form is cut out with a handsaw, I suppose, or possibly a chainsaw. Everything is rough and raw and exposed. You know what it's made of, and how it was made. You could rough it up yourself and it wouldn't really matter. Its force is in its plain making, the tight pressing down of layers and their violent cutting through.

Barlow can go excessively big. In the central gallery there are two huge long grey, roughcast wedges, mouse-cheeses – Untitled: Columns – one lying flat out, one on end and scraping the high ceiling. But horizontal or vertical, there's a power of inertia. Even the pointing-upward one is saved from any chance of aspiration. From its very tip trails down an anticlimax – a weak strip of multi-coloured plastic tape, which then pools on the floor in a dense tangle of spaghetti. Not a cascade, a flop. (Incidentally, you can see some more Barlow wedges, by themselves, at Voltaire Studio gallery in south London.)

What might be a signature is Untitled: Wall Blob, something palm-doodled by a giant, idly balled together from cement, plaster, polystyrene, burlap, with a bit of added paint. But everything looks like it has been done very fast and half-unconscious, as if on principle. Is improvisation essential to its energy? Is imperfection necessary to its human touch? No, its crucial effect is something else, something almost sub-human. Barlow's sculpture manages to be a kind of vegetable creation, mossy, overgrown, entangled, matter out of our grasp.

This makes it a radical antithesis to Baghramian's sculpture, whose fashioning is almost superhuman in its aura of perfection. In fact, both have retreated from hand-making, in very opposite directions. Still, we can recognise them both as something creaturely too, in their gestures and their feelings. And they perform for us, in two different comic modes, one low and one high. The Barlow creature is a thick and heavy catastrophe. The Baghramian creature has an untouchable, impossible finesse. They make up two casts of characters – cartoon characters, really.

And while they are artworks, in the sense that they are a show, a spectacle, an entertainment, and obviously presented in an art gallery, they also exist like company, co-habitants, world-sharers, entities that we can relate to directly. They belong to two very different species, and we ourselves to a third, somewhere in between.

Nairy Baghramian and Phyllida Barlow, Serpentine Gallery, London W2 (020 7402 6075; Serpentinegallery.org) to 13 June, free; Phyllida Barlow, Bluff, Studio Voltaire, London SW4 (020 7622 1294; Studiovoltaire.org) to 29 May, free