by Rick Cook
Moira nodded. "Certainly she is terrified of elves. But you are concerned about more than June’s feelings, I think."
"I’m concerned about making this thing work. Right now Danny wants to tear Aelric’s heart out because of the effect he has on June. We can’t build a team with something like that going on."
"What can I do to help you, love?"
"You’re closer to June than anyone. Do you have any idea why she’s so afraid of Aelric?"
"Nothing specific," the hedge witch said slowly. "June is afraid of many things." She smiled ruefully. She is hardly what you would call normal in the best of circumstances."
"Amen to that!"
"But still…" Moira trailed off and stared away. Then she looked up at her husband. "You know her history. She was found wandering on the Fringe of the Wild Wood a few years ago, much as she is now. No one knew her or whence she came and she cannot, or will not, tell us."
"So?"
"She is terribly afraid of elves. Perhaps she has had dealings with them before."
"That doesn’t make sense. Elves don’t deal with humans."
"They deal with you."
"So I’ve got an elf magnet in my pocket. June sure doesn’t."
"There is one case where elves do deal with humans regularly. They take human children to act as bond servants within elf hills."
"And you think June…"
"Time passes strangely under an elf hill. It seems like a season or two but when the servants have fulfilled their bond and are released centuries have passed. Their family, their friends, even their village are dust and gone."
"It makes sense," Wiz said at last. "It would explain where she comes from and a lot about why she is so strange."
Moira said nothing.
"What else? There’s something you aren’t telling me, isn’t there?"
"My Lord, I do not know any of this. It is all surmise."
"But you suspect something. Out with it."
Moira stared into her lap. Wiz waited. "Do you know why June needs Shauna to help nurse Ian?" she asked at last.
"I never really thought about it."
"Because she does not produce enough milk."
"As flat-chested as she is, I can believe it, but so what?"
Moira snorted. "My Lord, contrary to what lechers like you believe, the size of a woman’s breasts has little to do with her ability to feed an infant. No, June does not produce enough milk because her breasts are damaged. There are scars around both her nipples. Many little scars, as if she had been bitten repeatedly."
Wiz went cold. "Meaning what?"
"You recall I once told you elves prefer human nursemaids for their infants? It is said that elf babies are born with all their teeth."
Moira looked at him levelly, green eyes intent and serious. "It is also said those teeth are sharp enough to draw blood."
Duke Aelric was on the castle wall, watching the setting sun turn the clouds orange and the hills purple. In his own unearthly way he was as magnificent as the sunset and Wiz watched both for several minutes before he got up the courage to approach him.
"My Lord, I need to talk to you."
Aelric turned from the sunset and inclined his head. "Of course, Sparrow."
"It’s about June, Danny’s wife."
A graceful frown knitted the elf duke’s brow. "Ah, the one who was so upset? Forgive me, I thought she was a servant."
"Was she?" Wiz asked harshly.
"I beg your pardon?"
"Was she one of your servants?"
Duke Aelric made a throw-away gesture. "I really do not know, Sparrow. There have been so many."
"She was some elf’s servant. Now she’s terrified of elves because of something that happened to her."
Duke Aelric said nothing.
"Doesn’t that bother you at all?" Wiz demanded.
The elf duke raised a silvery eyebrow. "Why should it? If she did serve the ever-living I can assure you she was not deliberately mistreated. If she was a servant it was because she was offered a bargain and she accepted. I assure you the bargain was kept." He cocked his head. "Forgive me, but I do not see the relevance of an old bargain with one mortal-if bargain there was. Nor do I understand why you are so concerned about it."
"Some bargain," Wiz said bitterly. "Parents would ’foster’ their children into elf hills in return for the protection they needed to survive."
"Nonetheless, she would have entered our domains as all mortals enter them. Of her own will."
"And came out to find that centuries had passed."
Aelric cocked his head and said nothing.
Wiz could only stare. When they had met before Duke Aelric had been gracious, even charming, if somewhat frightening. Wiz knew that elves could be cold and cruel, but this was the first time he had ever seen it in Aelric.
And the worst of it was, Wiz realized, he wasn’t being cruel at all. He honestly did not understand why what had happened to June should be any of his concern. He began to appreciate, vaguely, just how un-human elves really were.
"Now she’s terrified of you and her husband would just as soon murder you as look at you and I’ve got to work with both of you."
The elf turned to Wiz and gave him a look that rooted him where he stood. "Her husband cannot find the necessity one-tenth as distasteful as I do." Aelric’s fine features drew up in a sneer. "Sparrow, do you think I like coming here; associating with mortals?"
"Then why did you come?"
"Sparrow, listen to me. There are things in this World that are not of it. Ancient things whose very nature you cannot comprehend." His eyes bored into Wiz. "I told you once that you had upset a very delicate balance. Even after all that has happened I still do not think you understand what you have done.
"Magic in the hands of mortals is dangerous, Sparrow. Unlike the ever-living, you are not inherently magical. You do not really understand magic.
"But your new magic is very powerful. That arouses certain-things-" He trailed off, as if thinking. Then he resumed briskly. "Now those things must be dealt with. For this we will both need to bend all the powers we possess to the task."
He was afraid, Wiz realized. Duke Aelric was actually afraid of whatever it was they were facing! Something cold and hard grew in Wiz’s stomach.
It was fully dark by the time Wiz went to visit Danny. He was alone in his room, Shauna having taken June and Ian off someplace to try to calm her down.
"Has he gone yet?" Danny demanded sullenly.
"No, and he’s not going."
Danny bounced up off the bed. "Fuck that shit! He’s going if I have to throw him out of here on his goddamn ass!"
Wiz moved in front of the door. "You’re not going anywhere. You’re going to sit down and we’re going to talk."
"Fuck that." Danny tried to force his way past Wiz, but Wiz grabbed him and pushed him back into the room.
"Listen to me. This is a war, not a popularity contest. Right now we need all the help we can get and he’s about the most potent help we’re likely to find.
"Maybe something happened between June and Aelric once. But that’s over. Now we need each other. That means if you’re going to be part of the team you’re going to have to work with him." He looked hard at Danny. "Right now Aelric is a lot more valuable to this project than you are. If you can’t handle it, I’ll have to replace you."
"With who?" Danny sneered.
"With one of the wizards we’ve been training. Malus, maybe. He may not be as talented as you are, but he can get along with Aelric."
Danny didn’t say anything.
"Well?"
"I still don’t like him," Danny said sullenly.
"You don’t have to like him. You have to work with him. Now, can you do that?"
"Yeah, I guess so. Just keep him the hell away from June."
Wiz released Danny’s shoulders. "He doesn’t have to come anywhere near June."
"Okay then," Danny said. "Anything else?"
> "Not now. We’ll have a staff meeting at noon tomorrow to figure out approaches."
Duke Aelric did not stay the night in the Wizard’s Keep but he returned early the next morning. Again they met in the Wizard’s Day Room: Wiz, Jerry, a sullen but cooperative Danny, and Bal-Simba as the head of the Council of the North. The huge wizard said little and Aelric generally ignored him.
Yesterday Wiz and Jerry had done most of the talking as they filled Duke Aelric in. Today it was the elf duke who dominated.
"Lord, it sounds as if the simplest approach would be to close off the gate into our World somehow," Jerry said when Aelric had finished.
"Simple indeed," Aelric said with a trace of amusement, "if we but had the key."
"Is there a key?"
In response Aelric lifted a finger and an elaborate, convoluted shape blossomed in the center of the table.
"That is a simple representation," he told them. "There are actually eleven directions, not just three. The narrow part at the top represents the situation when the gate was first opened. Here at the bottom," he gestured at the wildly intertwined strands that seemed to grow out of the table top, "is the situation as it is now. If I knew the total shape, it would be possible to construct the key and so close the door beyond opening again. But…" He smiled slightly and shrugged.
"Wait a minute!" Jerry said thinking hard. He scribbled frantically on a slate while the others watched in silence. "That’s a fractal!"
"I do not know that word," Aelric said.
"It’s a self-similar figure with fractional dimensions."
Aelric arched an eyebrow.
"Just a minute," Wiz put in. "Are you sure that’s a fractal?"
"Pretty sure. Look." He passed the tablet over to Wiz.
"Yeah," Wiz said slowly. Then he looked back at the elf. "Look, when you say ’know the shape,’ do you mean ’describe mathematically’?"
Aelric frowned. "I do not understand you, Sparrow. When I say ’know the shape,’ I use the words as mortal magicians do, I think."
Wiz turned to Bal-Simba. "Lord…"
"If the Sparrow means what I believe he means, then yes. A mathematical description is sufficiently precise."
Aelric turned back to Wiz. "Can you do this?"
Wiz nodded. "Fractals have another characteristic. They are generated by iteratively applying a function-that means applying the function over and over-and a lot of those functions are pretty simple."
"There are image compression systems that use fractals," Jerry said. "Rather than store the actual image they store functions that generate fractals to mimic each part of the picture and then combine them. You can compress an image ten thousand to one or more that way."
"Show me," Aelric commanded.
The elf was leaning forward looking at them so intently Wiz almost thought he was going to spring at them like a lion at an antelope.
Slowly and carefully Jerry and Wiz led Aelric through the process that would yield the solution. Although mathematics was an alien language to the elf, parts of it he grasped intuitively. Other parts had to be broken into tiny pieces and gone over and over.
At last his face split into a broad smile. "Brilliant. A whole new way of looking at such things. Thank you both." Then he sobered. "Yes, I think this," he tapped the slate, "is a fair representation of the problem of closing that door. But if I understand you, it is a problem almost beyond solution."
"Almost isn’t the same as impossible," Jerry said. "There are ways you can simplify something like that. In principle it is solvable. It is just a matter of putting enough computer power to work on it."
"Now that’s something we can do," Wiz said. "Our spell compiler isn’t adapted to solving mathematical problems but demons can be made to calculate as well as work magic."
Danny shook his head. "I dunno. This isn’t going to be easy." It was the first thing he had said all morning and he looked at the glowing model rather than Aelric when he said it.
"So it’s not easy," Wiz told him. "We can do it anyway."
* * *
"Okay," Wiz said three days later, "I was wrong."
The same group, less Aelric and with the addition of Moira and Arianne, was assembled in the Bull Pen to review the project. After the initial flurry of writing code, things had settled down to running the program. It had been running day and night for the last two days and as they met the Emac controlling it sat on Wiz’s desk in a stall behind them, scribbling away furiously at line after line of glowing "printout."
"This isn’t going to work," Wiz said tiredly. "We can’t do the calculations fast enough. The problem with the magical compiler is it’s slow. We’re getting maybe 200 MOPS, absolute tops."
"MOPS?" Moira asked.
"Magical Operations Per Second."
"Two hundred spells a second does not sound slow to me," Bal-Simba said.
"It is for this kind of work. What we’re doing here isn’t so much spell casting as it is mathematical analysis and that takes a lot of computing power, magic or no."
He sighed. "Back home I used to work on machines that could do five or six million instructions per second and we had access to some that could do two hundred million."
"That is a great deal of calculation," Bal-Simba said.
"The fractal resembles a Mandelbrot set in some respects, although it’s defined by a completely different function," Wiz told him. "What that means is there is not an analytic equation which will give us the boundary-which is what I was hoping for. What we do have is a procedure for calculating whether a given point is inside or outside the set."
"I will take your word for it," Bal-Simba said.
Wiz sighed. "What it comes down to is that we can find the shape of the key to any desired degree of precision, but we have to do it by calculating one point at a time. That takes computing power."
"Wait a minute!" Jerry said. "What about parallelism? Each of those points is calculated independently of the others, right? So why don’t we get a bunch of copies of the program working on the problem simultaneously and feeding results to each other?"
"Well, machine resources are essentially free," Wiz said. "But it would mean rewriting part of the compiler to handle the parallelism."
Jerry nodded. "That’s doable. But before we do that we can test it with just a few copies active and one copy acting as supervisor. Kind of like running multiple virtual machines."
"Virtual machines?" asked Moira, catching a phrase in the mass of technobabble that almost sounded familiar.
"That’s like a computer that isn’t there," Jerry said helpfully.
"It’s something that acts like a computer only it isn’t," Wiz added.
Moira regarded both of them coldly. "I see. Like your explanations."
Wiz shook his head. "No, our explanations are real. A virtual explanation would be something that acted like an explanation, but wasn’t."
Moira nodded. "I rest my case. Well, never mind. Just tell me what you will need to make this machine that is not a machine and I will see about getting it for you."
Wiz looked at the setup and nodded. This wasn’t going to be pretty, but it was strictly a proof-of-principal device.
Ranked in front of him were twenty-one Emacs, all sitting cross-legged on the floor of the Bull Pen. All of them had their quill pens out and poised expectantly.
"This will take a while," he told Jerry and Danny quite unnecessarily. "We’ve only got twenty processors here and that key is a twelfth-order function. On the other hand, our algorithm will converge on that function. We’ll start seeing a representation almost immediately, but it will be real fuzzy."
"And the more processing time we put on the sharper the image will get," Danny interjected. "We helped you write the damn thing, remember?"
Wiz blushed, nodded, and raised his staff.
"You know…" Jerry said slowly.
"What?"
"I don’t know. I have a feeling about this. Like the one I got in the City of Nig
ht just before we used the digging spell."
Wiz lowered his arms. "What is it that bothers you?"
"I can’t put my finger on it. But there is something about this whole business." He thought hard and then shook his head. "No, I guess not. Go on with the spell."
Wiz looked around for a convenient cover in case he needed it. Then he raised his staff again.
"backslash," he proclaimed.
"?" responded the first Emac.
"fractal_find exe," Wiz said. The Emac on the far left turned to the others and began to gabble at them. The other twenty Emacs bent to their tasks immediately.
The air above the Emacs began to thicken and take on a bluish tinge. It grew denser and bluer until a neon blue cloud hung over their heads.
"It’s working!" Danny said.
Wiz just stared at the slowly coalescing shape and wondered why everything the Emacs turned out was in such violent colors.
As the cloud solidified it began to show hazy lumps and hollows. It wasn’t even solid enough to be called a shape yet, but already Wiz could see similarities between it and the thing Duke Aelric had called up on the conference table. The process was slowing as the algorithm had to work harder and harder to discover which points were part of the shape and which were not.
The form began to pulse and Wiz realized he was getting a headache. He looked away, but the afterimage remained burned in his retinas. His vision grew dark around the periphery and everything seemed fuzzy. He shook his head to try to clear it but that only made things worse.
"Do you guys feel all right?" Wiz asked.
"I feel fine," said a large Saint Bernard dog with Jerry’s voice. To his left a six-foot-tall cockroach waved its feelers in agreement.
"Well, I don’t," Wiz sang with two of his mouths, creating a bell-like harmony. Vaguely he realized they were standing not in the Bull Pen but under an enormous crystal canopy that shimmered with pastel highlights. And wasn’t he supposed to have only two arms and one body segment?
As he watched, dog, cockroach and canopy all began to melt and run together. He felt his own body grow indistinct at the edges and begin to flow.