The Thinking Woman's Guide to Real Magic

the room. She had seen Aruendiel use similar barriers in spell-making, although she had never seen him use more than one circle at a time.

“All right, I see what’s holding you,” Nora said aloud. “Now, how do I get through it?”

She tried spells for knocking down walls, for breaking pottery, for opening locked doors, for snapping your opponent’s spear like a toothpick, for splitting an object into two smaller, equal-sized versions of itself—any spell that seemed remotely relevant, and some that weren’t. Her rainmaking tic was back. Snow filled the air and then covered the floor with a dusting of white.

Yet after she finished every spell Aruendiel was still locked away like a mummy in a museum case.

Was he still breathing? She kept stopping to check. Sometimes it was hard to tell. She was watching him, hardly breathing herself, when she heard footsteps. The white figure of the ice demon, somewhat grimier than before, emerged from the darkness.

“Oh, it’s you,” Nora said tiredly. The demon had thrown off her spell, and no doubt it had come to eat her now. The prospect did not seem as terrible as it once had.

The ice demon clumped toward her, then stopped a few feet away. Aruendiel’s still form had caught its attention. “That’s no good,” the demon said. “I can’t eat that one. I can’t get to him.”

“I know,” Nora said.

The demon’s round mouth curled in frustration. “He’s dying. Soon he will be no good to anyone.”

“I know.” Nora clenched her teeth. She added, a little nastily: “But you’re a demon. You can’t get through a little magical barrier like that?”

“He’s locked up the same way I was in the glass bottles,” the demon said. “That is terrible, terrible magic.

“And it wasn’t fair, what you did,” it added sulkily. “You made me fall, and I couldn’t get up. And the weather is growing dangerously hot. I could have melted.”

“Wait.” Nora looked up, her eyes sharp with dawning comprehension. “You mean this spell here—the one that’s keeping him trapped—is the same spell Dorneng used to put you in those bottles?” She remembered how Dorneng had slipped that gelatinous insect-creature into a similar bottle, back in Semr. It must be some kind of impermeability spell that he’d used to store magical specimens, she thought—something that blocks all magic.

“It’s terrible to use magic that way. It’s a good thing I ate that magician.”

“Well, except that, now that he’s dead, he can’t undo this spell.” Nora glanced hopelessly at Aruendiel, and then looked away, frowning. “Dorneng didn’t need to put an aging spell on Aruendiel,” she said suddenly. “Dorneng just had to somehow catch him in this impermeability spell, and then he was cut off from any source of magic— fire, wood, water, whatever.” Trapped, Aruendiel was helpless, and then he began to grow old. Or, rather, without magic, his true age consumed him.

Another piece clicked into place: “That’s why Hirizjahkinis didn’t know Aruendiel was here! She couldn’t sense his magic.”

“If you could undo that bad magic and let him out, I could eat him,” the ice demon pointed out.

“If I could undo the bad magic, you certainly could not eat him,” Nora retorted. If she could undo the magic. Her elation at figuring out Dorneng’s stratagem faded. She knew nothing about impermeability spells; she was no closer to freeing Aruendiel.

“I’m hungry,” the demon said.

“Oh,” she said, finally realizing what the demon was getting at. “You want more poetry.”

There was not much left on memory’s shelves to feed the demon. The only verses that came floating out of the darkness were the lines that some kid in her section always insisted were not a real poem, they weren’t about anything.

“‘So much depends’—” she began.

When she finished, the ice demon had not moved. Nora watched it with some apprehension, waiting for it to demand more. But the demon sat down heavily, leaning against the wall with the calm deliberation of someone who is occupied entirely with internal matters of digestion and happy to have it that way. “Oh,” it said, and for the first time Nora thought she could hear something like contentment in its voice.

So it took William Carlos Williams to satiate an ice demon’s ravenous appetite for human feeling. That fact would be an interesting addition to a classroom discussion—but looking back at Aruendiel, Nora felt black and empty, almost as though her soul had indeed been consumed. The thing that everyone remembered about that poem was that Williams had written it while watching at the bedside of a sick child. What Nora could not recall now—if she had ever known—was whether the patient had ever recovered.

Aruendiel’s bony hand twitched spasmodically. A sign of returning vitality? She watched closely for a time, she called his name, but the hand did not move again.

“I’m sorry, Aruendiel,” Nora said helplessly. “I just don’t know what to do.” She worked another few spells at random, trying anything. Nothing changed. Aruendiel’s lank, white-haired body still hung motionless in its invisible prison. The curved lines that bound him still marked the floor and walls, roughly outlined in black charcoal.

Those circles. She had not really considered them before. The burned stick that Dorneng must have used to draw them still lay on the floor.

Maybe the answer was very simple. “What happens if I just erase the circles?” Nora asked aloud, her hand already reaching toward the circle on the floor. But she pulled back, warned by a fiery prickling in her fingertips. If she wasn’t careful, she’d be blasted across the room again.

Perhaps the circle could be magically persuaded to erase itself. She tried a spell to command the streak of charcoal on the floor, and found the material impervious to her suggestion. She stared at the three circles, unwilling to admit defeat. They reminded her of something. For some reason, she was thinking of her parents’ driveway in New Jersey. The smooth, gray cement right in front of the garage.

If you could make the circles invisible—no, that wouldn’t work.

Now it came to her why she was thinking of her parents’ driveway. EJ drawing a circle in yellow chalk on the cement, tracing the bottom of a garbage can.

What on earth had he been doing? He wanted her to calculate pi, that was it. He was supposed to be helping her with a couple of geometry problems, and instead he made her calculate pi from scratch. Typical. It didn’t help her grade. That was just a week before he died.

Nora forced her thoughts back to the situation at hand. What about just blasting the floor into bits? Again, a solution beyond her powers. She glanced up to make sure that Aruendiel was breathing.

In her mind’s eye, EJ was still bending over, chalk in hand, to write on the driveway. He was writing formulas, including some that she hadn’t had yet in school. He liked to do that sort of thing. He was showing off, but he also thought she’d get something out of the advanced stuff.

“This is what you need to know about circles and spheres, Nora,” he’d said.

What I need to know. She sat very still, as though by listening hard she could remember what he had said next.

x² + y² + z² = r²

The alien symbols swam lazily out of the depths. Dimly she recognized them: It was the Cartesian formula for a sphere. You plug in the coordinates from the x-axis, the y-axis, and the z-axis. Add up the squares, and the number on the other side of the equals sign, the r², is the square of the sphere’s radius.

What if, instead of trying to break into Aruendiel’s cage, you just made it much, much bigger?

The charred stick was already in her hand, the same stick that had drawn the circles. She rolled it back and forth between her palms, then rubbed a space on the stone floor clean. She wrote EJ’s formula down slowly, making each letter perfectly clear. She set the volume of the sphere equal to 1.

This was the bubble that imprisoned Aruendiel. She stared at the formula until she knew in her bones that the formula she had written and the sphere that Dorneng had conjured were essentially the same.

Just as carefully Nora began writing a series of zeroes after the 1: 1,000—1,000,000—1,000,000,000— bigger. Make the round walls of Aruendiel’s prison grow larger than the world. If he was dying in isolation—if he could not find and draw on the elemental sympathy of a flame, a forest, a mountain—then bring them to him. Cram them all within the confines of Dorneng’s spell. Maybe Dorneng’s magic would hold, maybe not.

Mathematics commanded, and with slow, reluctant inevitability, magic obeyed. Nora was still writing