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At last, the lightnings faded. Pekka slumped, and held herself up by hanging on to the table in front of which she stood. “Well, we got through another one,” she said in a gravelly voice. Through dazzled eyes, Fernao saw the sweat on her forehead, saw the skin stretched tight on her high cheekbones. Casting that spell looked to have aged her five years, maybe ten.

Fernao started to say something, but drew in a breath and coughed. The breath was ripe-rank-with the odor of corruption. Ilmarinen coughed, too, coughed and said, “We ought to do more work with the windows open.”

“Or else work with a convergent series,” Siuntio put in.

“These are the older animals?” Fernao asked.

“A lot older now,” Ilmarinen said. “Actually, you’re smelling the way they were a while ago, so to speak. They don’t stink at all now; they’re long past that.”

“I… see,” Fernao said slowly. “This is what the mathematics said you would be doing, but seeing the mathematics is not the same as seeing the thing itself.”

“It should be.” Siuntio’s voice held a touch of disapproval.

He was a master mage indeed, a master at a level to which Fernao could only aspire. If he truly did see the mathematics and the reality as one and the same-and Fernao was willing to believe he did-his powers of visualization were also well beyond those of the Lagoan mage. Somewhat cowed, Fernao said, “And what of the younger rats?”

Siuntio clucked again. He said, “You know what the mathematics say. If you must have the confirmation, examine their enclosures.”

“Aye, Master,” Fernao said with a sigh. He knew what he would find when he walked over to that row of cages, and find it he did: they were empty. There was no sign that rats had ever lived in them. He whistled, one soft, low note. “ Were they ever really there? Where did they go?”

“They’re gone now, by the powers above-that’s where the energy discharge came from,” Ilmarinen said. “And suppose you define real for me, when you’ve got a year you’re not doing anything else with.” No, he had no trouble being colloquially rude in classical Kaunian.

“In any case, where-or when-they may have gone is mathematically undefined, and so must be meaningless,” Siuntio said.

Femao made a discontented noise, down deep in his throat. “I have not been through the calculations as thoroughly as you have, of course, but this solution does not strike me as if it ought to be undefined.”

Pekka stirred. She didn’t seem quite so ravaged as she had just after she finished the spell. “I agree,” she said. “I believe there is a determinate solution to the question. If we can find it, I believe it will be important.”

“I’ve looked. I haven’t found one,” Ilmarinen said. He didn’t say, If I can’t find one, it isn‘t there, but that was what he meant.

“It may be just as well if we don’t look too hard,” Siuntio said. “The implications of the convergent series are alarming enough-how long before mages start robbing the young of time to give to the old and rich and vicious? But if you youngsters are right, the possibilities from the divergent series are even worse.”

“More paradoxical, certainly,” Pekka said. Fernao thought about the young rats. He nodded. The Kuusaman mage had found the right word.

“Sorcery abhors paradox.” Siuntio’s voice was prim.

“Most of the sorcerers here at the university abhor us,” Ilmarinen said. “We scare them to death, too: almost literally, after a couple of our experiments. This one didn’t even break any windows; we’re getting better control. Shall we go celebrate living through another one with some food and some spirits?”

“Aye!” Pekka said, as if he’d thrown her a cork float while she was drowning. Siuntio nodded. So did Fernao. But he ate and drank absently, for the distinction between the real world and the world of calculation blurred in his mind. By Pekka’s abstracted expression, he thought her mind was going down the same ley line as his. He wondered if it led anywhere.

Trasone stood on the northern bank of the Wolter and looked across the river toward the Mamming Hills beyond. He couldn’t see much of the hills; snow flurries cut his vision short. Chunks of drift ice floated down the Wolter toward the Narrow Sea.

Here in Sulingen, the snow that stuck on the ground was gray, ranging toward black. So much of the city had burned as the Algarvians battled block by block to seize it from King Swemmel’s men. Trasone turned to Sergeant Panfilo, who stood a few feet away. He waved a magnificent, all-encompassing Algarvian wave. “It’s ours at last!” he shouted. “Isn’t that bloody fornicating wonderful?”

“Oh, aye, it’s terrific, all right.” Panfilo pointed east. “We still haven’t got quite all of it.” Fresh smoke rose from the pockets where Unkerlanter soldiers still stubbornly hung on. The sergeant turned away from them, back toward the parts of Sulingen the Algarvians had won. Fresh smoke rose from them, too, here and there-Unkerlanter dragons and egg-tossers kept reminding the Algarvians the war went on. Panfilo gestured in disgust. “It wasn’t supposed to be a fight about Sulingen. We were supposed to take this place and then go on to the cursed hills and the cinnabar in them.”

Trasone spat. “You know that. I know that. Nobody bothered to tell the stinking Unkerlanters.”

“Now, boys!” That was Major Spinello’s cheery voice. Trasone didn’t know how the battalion commander did it. Had he not known better, he would have suspected Spinello of keeping his spirits up with nostrums and potions. But even food had a hard time coming into Sulingen, let alone drugs. Spinello went on, “Aren’t you proud of our magnificent victory?”

“One more victory like this and we won’t have any soldiers left at all,” Trasone answered. Spinello didn’t mind if his soldiers spoke their minds. He always spoke his.

Panfilo said, “Even if we do finally clean out the Unkerlanters, we won’t be able to cross the Wolter and get into the Mamming Hills till spring. That’s not how it was supposed to work.”

“How many things do work out just the way you want them to?” Spinello asked. “I can only think of-” He stopped, a surprised look on his face. In normal, conversational tones, he said, “I’ve been blazed.” He crumpled to the snow- and soot-streaked ground.

“Sniper!” Trasone screamed as he threw himself flat. Panfilo also lay on the ground; he was shouting the same thing. Trasone crawled over to Major Spinello and started to drag him off toward some rubble nearby. Panfilo helped. “How bad is it, sir?” Trasone asked.

“Hurts,” Spinello answered. When the two soldiers dragged him over a broken brick, he began to shriek.

Once they got him behind the wreckage-so the Unkerlanter sniper, wherever he was, would have a harder time getting a good blaze at any of them-Trasone and Panfilo examined the wound. It went through the right side of Spinello’s chest and back. The major kept on shrieking and writhing while they looked him over. Trasone took that in stride. He’d helped too many wounded men to do anything else.

“Through the lung,” Panfilo said. “That’s not good.”

“No,” Trasone said. “But he’s not bleeding too much, the way they do sometimes. If we can get him out of here and the healers can slow him down and work on him, he’s got a chance. He’s an officer, and he’s a noble-if we can haul him out of here, they’ll sure as blazes sling him under a dragon and fly him off.”

“All right, let’s try it,” Sergeant Panfilo said. “He’s not a bad fellow.”

“Pretty fair officer,” Trasone agreed as each of them draped one of Spinello’s arms over his shoulder. “Of course, if it was you or me, we’d take our chances right here in Sulingen.” Panfilo nodded. They both scrambled to their feet and hauled Spinello off toward the closest dragon farm, a few hundred yards from the Wolter. Perhaps mercifully, the wounded major passed out before they got there.