Cornelia Parker at Whitworth Art Gallery, Manchester

Cornelia Parker has thought long and hard about what it means to be an artist in the 21st century. She knows that our world is in acute physical peril. She also knows that, for millions, global warming is the least of their worries. She has interviewed Noam Chomsky about environmental catastrophe but she has also listened to Palestinian Muslims talking about what it means to have the ground stolen from beneath their feet.

Crucially, Parker understands that she is an artist, not a documentary-maker or an anthropologist. Context, scale, material, rhythm and a touch of mystery are essential if her expressions of horror, laced with a base note of hope, are to reach us with their poetic raison d’être intact. Her gift for excavating art out of civilisation’s most damaged faultlines made her an inspired choice to open the Whitworth in Manchester after its £15m renovation.

With free entry and a collection of over 55,000 works ranging from textiles to contemporary art, the Whitworth — part of Manchester university — is a vital pillar of municipal life but also just one artery of a body made up of many other disciplines. Thanks to her 360-degree radar, the first question Parker put to Whitworth director Maria Balshaw on being invited to exhibit was: “Who can you introduce me to?”

Top of her list were Kostya Novoselov and Andre Geim, the university’s Nobel Prize-winning physicists. Other collaborators include novelist Colm Tóibín, who was Manchester’s professor of creative writing from 2011-12, the engineering professor Stuart Lyon, and the Greater Manchester police force.

Such alpha expertise gives Parker’s show a resonance that outstrips that of any she has done before. Tóibín has written a short story for the catalogue which illuminates Parker’s practice through his sumptuous knowledge of modern poets such as Eliot, Lowell and Derek Mahon. Professor Lyon took apart a gun for her. The police donated a couple more.

Theoretically, the coup de grâce is her collaboration with Novoselov. Together with Geim, he is responsible for groundbreaking research on graphene, “a wonder material” extracted from graphite that could revolutionise our power sources. Working with Parker, Novoselov succeeded in cooking up a nano-sized fragment from a pencil drawing by William Blake. On the opening night, a breath from the scientist on that speck was responsible for igniting the firework display — billed as a “meteorite shower” — which crowned the evening. As sparklers go, these were stellar, even if for most people it was impossible to perceive any difference between their spirit-lifting bling and those bought in your local shop.

Nevertheless, such exchanges between science and art (which were responsible for the glory of the Renaissance) are praiseworthy. And William Blake also provided Parker with her most fruitful encounter. Watercolours by the 18th-century visionary — part of a bequest made by John Edward Taylor, the owner of the Manchester Guardian in Victorian times — hang in the gallery that opens Parker’s show.

Like Parker, Blake’s imagination was kindled by his fury at injustice. His radical politics — anti-Church, anti-state, anti-Newton — went hand in hand with an inner spiritual fire out of which he fashioned elaborate mythologies. Here is his famous image, “The Ancient of Days”, which shows the prophet Urizen crouched at the edge of a sulphuric void; responsible, to Blake’s mind, for the “dark, satanic mills” of the industrial revolution. Why, raged Blake, did this “rich and fruitful land” — which had Manchester at its hub — result in “babes reduced to misery”?

Blake thought big yet believed the world could be seen in a grain of sand. Parker also perceives universal truths in tiny particulars: this show contains work made from punctured balloons, silver scraped from photochemicals, cracks in the pavement and the contents of her garden shed. She has mixed snake venom with ink as the basis for veined, intricate symmetries; she has scorched paper with red-hot pokers to create surfaces that resemble singed, cross-stitched embroideries; she has sewn wire made from bullets through paper to make patterns that look like delicate, frothy sprays or wobbly, tensile cages.

Over the years Parker has occasionally wavered from her formal rigour, notably when she shut Tilda Swinton in a glass box, unaware that such paparazzi-pleasing performances would dismay those who loved her work for its shy, meditative interiority.

Happily, Whitworth curator Mary Griffiths has allowed that inward, abstract voice to sing. The most boisterous piece in the main gallery, which now gazes through a glass wall on to the park beyond, is Rodin’s “The Kiss”, on loan from the Tate, which Parker has wrapped in a ball of string. Yet even that understated piece of mischief, picked up by photographs of statues in the City of London which Parker has draped in nets, subtly feeds into her aesthetic linchpin: the grid.

That vocabulary roots her in a modernist lineage that stretches back via the shimmering lines of Agnes Martin, through Mondrian and back to neo-Platonic forms. Here, its most spectacular incarnation is “War Room”. After die-cutting double sheets of the paper used for making remembrance poppies into rows of empty florals, she has pinned it over walls and ceiling to create a sanguineous temple whose shattered curtains oscillate as the papers minimally shift. In the centre, four unforgiving naked lightbulbs — cousins of the sinister lamp in Picasso’s “Guernica” — taint her chapel with the mood of a torture chamber.

Parker understands that she is an artist, not a documentary-maker or an anthropologist

“War Room”’s pristine, blood-red lines inevitably recall the tragic geometries of European war cemeteries. In the twin gallery on the other side of the main hall, the immaculate yet elemental disorder of “Cold Dark Matter” denies simple metaphors. Made in 1991, it was born when she invited the British army to explode her garden shed, then suspended its charred, tattered contents — a hot-water bottle, a flipper, a metal bucket — from the ceiling in a perfect square of destruction.

In an interview in the fine catalogue, Parker recalls that its construction was motivated by her anger at Hollywood’s “fetishisation” of the explosion. Twenty-five years on, too many non-fictional bombs have given the work a darker, more enduring resonance. Both visually and emotionally, it chimes with Parker’s more recent and arguably finest series which, like the best poems of Blake, is inspired by Jerusalem.

After several visits to that blessed, beleaguered city, Parker is clearly filled with outrage. Yet it is her capacity to channel that anger into silent, linear scores of suffering that makes her one of the few British contemporary artists to rival the sophisticated political poetry of artists such as Walid Raad from Lebanon and Rashid Rana from Pakistan.

Drawing on childhood memories of games — hopscotch, don’t step on the cracks — which she subsequently played with her own daughter, Parker started her Jerusalem cycle in London when she poured liquid rubber into cracks in the pavements of Bunhill Fields, where Blake is buried, and cast the resulting grid in bronze. Then in East Jerusalem, the city’s most troubled heartland, she secretly performed the same operation with latex and smuggled the result home in her suitcase.

Now the two sculptures crouch together in the central hall. Balanced on thorn-sharp pins, their black, ragged lines exuding the covert menace of their histories, they are a truly contemporary response to the 18th-century poet’s dream that Christ’s feet trod British earth in ancient time. If Parker makes serious work about the Middle East it is because she knows that what happens there is urgent for us here. Briefly, then, the occupied territory is made occupier. Well done to the Whitworth for inviting Parker on to their ground.

Until May 31, manchester.ac.uk/whitworth

Slideshow photographs: David Levene