Gilhaelith was slipping ever deeper into the bottomless pit of tar and there was nothing he could do about it. He'd tried everything, but his geomancy was useless without some kind of a crystal to serve as a focus, and he had none. He'd even attempted to use one of his ever-troubling gallstones, but under the strain it had burst into jagged fragments that were causing him agony. Before they passed, should he live that long, he'd be wishing he were dead.

His only other resort had been mathemancy, that strange branch of the Secret Art Gilhaelith had developed long ago. It proved singularly useless. Mathemancy was a philosopher's Art, ill-suited to any kind of direct action, much less such immediate peril.

Gyrull, Matriarch of Snizort, had abducted him to scry out the remnants of a village lost in the Great Seep seven thousand years ago. Afterwards, she'd kept Gilhaelith beside her, refusing him the use of his globe and the other geomantic instruments he'd brought with him as his means of escape. But the tunnel into the Great Seep had failed, its shell of frozen tar had cracked and hot tar had been forced in. The lyrinx had fled with their relics, just in time. Gilhaelith had tried to follow but he'd not been quick enough.

He took the numbers again, raising a series of random integers to their fourth powers to see what pattern they offered. It was awesomely bad. He tried again, with an even worse result.

The tar now reached to his hips, its suction far too great for him to pull himself out. Ribbons of liquid tar, from a breach in the roof, began to fold onto his head and shoulders, its bituminous reek burning his nose, throat and lungs.

And it was hot. Not burning hot, not enough to blister, but uncomfortable and getting worse. Eventually, if he survived long enough, he would simmer like a crab in a pot. Fortunately, he wouldn't survive. In a few minutes, when that great oozing clot came down on his head, he would suffocate.

A possibility slid into Gilhaelith's mind as if it had been whispered in his ear — to couple his two very different Arts. Geomancy was hopeless because he lacked a crystal to draw power and focus it. Mathemancy was not a tool for directing power at all. But what if…?

If he could create a phantom mathemantical crystal, and use it to draw power and focus it, might that be the solution? It was a last resort — such a crystal must pull power directly into his head. A little too much would cook him from the inside, a gruesome, slow death. A lot too much and he would suffer the agonising fate of anthracism, human internal combustion, though that would not take long to kill him.

The very idea of such a crystal felt alien, and it reminded him of those links the amplimet had drawn throughout Snizort, including one to him. Could it be directing him for some purpose of its own? Too bad — without a crystal he was going to die.

He slipped further into the tar, which was now creeping up his groin. It felt hotter than before. Fortunately he'd worked out the mathemancy of crystals long ago, though to create one with numbers, purely in his mind, was another thing entirely. Still, he had always relished challenges.

Gilhaelith began to construct a crystal in layers, beginning at its base and building towards the apex. It was painfully slow — literally painful, he thought wryly. By the time tar had risen to his waist, the phantom crystal was only half done. His shoulders were covered with ribbony black epaulettes; it was dripping down his forehead, clotting over his eyes, and rubbing just smeared it everywhere.

As Gilhaelith built another layer, the tar seemed to dissolve beneath his feet and he slid down to his chest. A bucket-sized clot landed on his head, pushing him face-first into liquid tar, which was forced up his nostrils. Though he clawed it away, he could not clear his nose enough to breathe.

Turning his head sideways, he managed to get a breath through his mouth. Hum'! The layers went more quickly as he approached the tapering apex of the crystal. Only one layer to go. As he sucked another breath, the rest of the clot fell, burying him completely. And it was so hot. His feet were cooking.

But the crystal was done. Gilhaelith looked for power but found none — the field, which had been waxing and waning for days, was dying. The tunnel had failed because the phy-nadrs had not been able to maintain sufficient power to keep it frozen.

Yet for what he planned, only a little power was required. Gilhaelith sought in another direction and discovered a drifting loop of field, cut off from the rest. He drew power into the phantom crystal but there was not enough to energise it.

He had barely enough breath to try again. He found another loop, this one strong as the field waxed dangerously. The node was desperately overloaded and something had to give. But if it just lasted another minute …

His lungs were shuddering for air; fire burned behind his temple as the crystal powered up at last. Gilhaelith used a geo-mantic spell to drive heat from the tar surrounding him, into the seep itself.

He kept at it until the heat licked from his skull to his stomach, the first sign of anthracism. He had to let go. Would it be enough? As the spell faded, a most bitter cold enveloped him, as though he'd been frozen into a block of ice. Then, as the heat of the seep attacked that rigid, frigid shell of tar, it shattered into a thousand pieces.

The shards broke away from his body, leaving him in a cavity lined with fractured tar. The suction was gone; it was solid underfoot. The mosaic fell from his eyes and he could see. Gilhaelith took hold of the still-hard shell of the tunnel and, with a wriggle and a shake, pulled himself onto the floor.

He hurt all over and, behind his eyes, needles pushed relentlessly into the bone. He'd tried too hard and damaged something. He began to crawl blindly down the tunnel. That was where Matriarch Gyrull, who had come pounding back for him, found Gilhaelith. Tossing him over her shoulder, she clawed the last chilly remnants of tar from his nostrils and raced off.

The next few hours were a blur of belching fumes, pounding feet and panicky lyrinx. Gilhaelith saw nothing, for the pain was so all-enveloping he could not open his eyelids. And he was so cold — he could feel the shape of his stomach in ice.

He was carried through a myriad of tunnels, with Gyrull cursing and turning this way and that, and her growing escort hard put to restrain their terror. There was fire underground and they couldn't find a way out, though that wasn't their greatest fear. Gilhaelith had learned enough of their language to deduce that many of the escapeways had been cut off and they expected the unstable node to explode at any time.

They reached the base of a pit with steep sides. The lyrinx made a living tower which Gyrull climbed to get out, a box of relics strapped to her chest, and Gilhaelith, folded over in an elongated travesty of the foetal position, tucked under one arm. The gamy odour of her sweat was intense.

Before she reached the top, the phantom crystal picked up wild fluctuations from the field that seared his forebrain. Gyrull muttered something.

'What?' he croaked, but she did not answer. He could just see out of the crack of one eye. It was dark and he felt so very cold. Beyond the walls, the battle still raged — the groans of the maimed, the clash of weapons against armour, the thudding of catapult balls into walls, ground and tar seeps. Fire flickered in half a hundred places.

She climbed over the rim of the pit and set off without looking back to see if her fellows were following. Gilhaelith supposed they had sacrificed themselves to give their matriarch a chance, or to get the treasure away.