Rick Cook - The Wizardry Cursed

"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.