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.