Neutral Magic
Disclaimer: I do not own the Worst Witch or Weirdsister College series or any characters associated with them. No money is being made from this story.
Chapter 6: A Circle of Death
After writing another equation on the blackboard, Mildred turned to face the eleven students sitting in the front rows of the Weirdsister College main lecture theatre. Advanced Magical Theory was an optional course so not all the third years attended, but Mildred was quite pleased with the number who had signed up this year.
"So as you can see," Mildred addressed them. "If we take the scalar product of the thaumaturgic potential function with that function transformed by the Foster correlation matrix and integrate with respect to time between zero and some specified time t, we obtain what's called the Foster expectation integral. If we take the positive magical event as happening at time zero, this gives the probability that the Foster effect will occur in that time interval."
Mildred turned back to the blackboard and was about to write further equations when there was a sudden murmur of surprise from the students. Turning around to face them, Mildred saw Cas and Enid enter the lecture theatre and ascend the steps to take seats at the back. She had asked Enid to meet Cas when she arrived but had expected her to take the Canadian witch to her laboratory. Deciding it didn't really matter for now Mildred returned to writing equations.
"To make things easier we're going to use the solutions to the thaumaturgic potential equation for simplified boundary conditions we derived last week," Mildred told the students. "The results we will obtain will still hold for the general case but proving that is much more complicated."
Mildred continued to write equations as she talked, finally writing out a very complicated looking expression.
"As you can see, by substituting the solution for simplified boundary conditions and making some plausible assumptions about correlation parameters, we can reduce the kernel of the expectation integral to the product of an exponential term and an even power series. This means the integral will always have a finite positive value for all real values of time, even negative ones."
Mildred paused, watching the students and wondering if any of them would speak up.
"Actually there's a slight flaw in that argument," Mildred admitted when no one did. "Anyone see what it is?"
One of the female students tentatively raised her hand.
"Yes Miss Darkwell?" Mildred gave the young witch an encouraging smile.
"Um, you haven't proved the power series always converges, Doctor Hubble," the girl said nervously.
"Quite right, I haven't." Mildred nodded approvingly. "There's a good reason for that though. I'm asking you to show that as part of this week's assignment!"
She couldn't help chuckling at the audible groan of dismay from some of the students.
"Oh don't worry, it won't be that bad!" She reassured them. "I do give you a hint about how to proceed. Anyway, to get back to the point of the lecture, what we've just established is the mathematical basis for what's called the backwards Foster effect. A negative magical effect can sometimes occur before the positive magic that caused it, rather than after. Occasionally the negative magic can even be what initiates the positive magic that caused it, creating a sort of causal loop. This raises all sort of interesting philosophical questions about the nature of time and causality, but sadly we don't have time to go into that now."
Mildred quickly glanced at her watch, noticing that the time was nearly up.
"Okay, I think that's enough for this morning," she told the students. She waved her hand and papers appeared in front of each of them. "Here is this week's lecture assignment. Just to remind you the deadline is five o'clock on Wednesday and papers submitted late will not be graded. These assignments account for thirty percent of the course mark, so make sure you hand them in on time. All right, see you all next week."
The students applauded briefly, as they always did at the end of a lecture and then started drifting out of the lecture theatre, talking animatedly. Mildred waited until they were all gone before walking towards Enid and Cas, who were moving down the steps to meet her.
"Hi Millie!" Enid said, smiling at her friend.
"I was a bit surprised to see you two here," Mildred admitted. "I thought you were taking Cas to my lab?"
Enid shrugged. "Cas wanted to see you lecture."
"You were really good," Cas said hesitantly.
"Thank you," Mildred responded coldly. "Come on, we'd better get on with things."
She led the way out of the lecture theatre and the two girls followed. Mildred had noticed the disappointed look Cas shared with Enid and sighed. It was clear Cas still hoped to repair their friendship and Enid seemed to be encouraging that. She couldn't help feeling a little resentful that her friend was trying to push her into something she wasn't ready to do yet and possibly never would be. After what Cas had done Mildred wasn't certain she could ever forgive her, certainly not anytime soon.
After arriving at her lab, Mildred switched on the lights and led them over to one of the blackboards. The equations that had been there before had been erased and in their place were eight sets of magical symbols arranged in a circular pattern.
"This is a symbolic representation of my analysis of the curse," Mildred explained, pointing at the blackboard. "I can't imagine who's responsible for this but whoever it is must be a genius. The curse consists of four positive magical elements and four negative ones, each generating the other so the whole thing is a self-sustaining loop. Individually, each component is actually harmless, but together they're feeding off Miss Hardbroom's life energy, growing stronger at her expense."
"So how do we break it?" Enid questioned anxiously.
Mildred took a deep breath, knowing what she was about to say would not go down well.
"The thing is I'm not sure we can!"
"You can't mean that!" Cas whispered, looking horrified.
Mildred shrugged helplessly. "The problem is the damned thing is self regenerating. Even if we managed to break one component, the others would just recreate it. To break this curse we'd have to counter all four positive elements simultaneously. If my calculations are correct the four counter spells would need to be timed to within a millisecond of each other and I just don't see how that's practically possible."
"But there must me something we can do," Enid said desperately. "We can't just sit back and let her die!"
"There might be an alternative way," Mildred admitted. "But it's very risky."
"What is it?" The other two young women demanded together.
"I thing my current research might provide a way of breaking this curse."
"What research?" Cas asked.
As succinctly as possible, Mildred explained the research she was doing on the relation between positive and negative magic, and her theory that they could be unified. But she was also at pains to make clear the risks, and her fears that such a unification could result in an irreversible chain reaction.
"So you're hoping you can break this curse by uniting it's positive and negative components?" Cas asked.
"That's the idea," Mildred agreed. "I've already worked out a spell I think will work, although it might need tweaking a bit as we're using it on a human being."
"So what are we waiting for?" Enid asked impatiently. "Let's go to Cackle's now and we can try it!"
"Not so fast," Mildred retorted. "I need to make a proper assessment of the risks first."
Now Enid looked exasperated. "Millie, we're talking about Miss Hardbroom's life!"
"I know that," Mildred replied. "Enid, you know that I respect Constance Hardbroom more than any other witch I know, but I can't put the life of one woman above the safety of the entire world."
Before Mildred and Enid got into an argument, Cas intervened.
"How long will a proper risk assessment take?"
"Hopefully only a couple of days," Mildred said. "But to get accurate results I need to use the new method I've developed with asymptotic series and they can be tricky to evaluate. It might take a couple of weeks, possibly even a month."
"A month?" Cas protested. "I don't think Miss Hardbroom can afford to wait a month!"
"What else can I do?" Mildred asked. "Given the possible consequences if something goes wrong, I can't go ahead until I'm sure it's safe."
Enid did not look at all impressed by her friend's caution.
"The Mildred Hubble I knew in school would have taken the risk!"
"I suppose she would have," Mildred admitted. "But I'm not that naïve schoolgirl any longer. I can't just trust to luck and hope everything will turn out fine. I'm an adult who needs to make responsible decisions based on reason and logic."
But even as she said those words Mildred suddenly felt uneasy. There was no doubt she had come a long way since being that insecure schoolgirl who could barely manage to stay on a broom or to cast a simple spell without causing some sort of calamity. Mildred was proud of everything she had achieved as an adult but now for the first time wondered if she hadn't lost something as well, something important although she wasn't really sure what it might be. But she had no time to think about that now.
"I promise I'll do everything I can to speed things up," she assured the other two witches. "Hopefully I'll get a positive result in a few days and then we can go forward."
"Well I guess that will have to do for now," Cass agreed reluctantly. "Anyway I have to go. I have some patients I need to see this afternoon."
The Canadian witch made her way to the door and then looked back at the other two before leaving.
"I'll see you both on Saturday evening, then."
As Cas closed the lab door Mildred turned to Enid with a frown.
"What does she mean she'll see us Saturday evening? We're going out to the Atomic Nightclub then."
Enid looked a bit nervous. "Yeah, I invited Cas to come with us."
"What the hell are you playing at, Enid?" Mildred demanded angrily.
"I thought it might be fun if she came along," Enid said nonchalantly.
"That's utter bollocks!" Mildred replied fiercely. "You're interfering Enid, trying to get me to forgive her when that's the last thing I want to do!"
Enid glared at her friend balefully.
"Well you bloody well ought to! I care about you Millie, and I'm not going to let you throw away a good friendship over nothing."
"Nothing?" Mildred repeated unbelievingly. "Enid, you have no idea what she did!"
"Yes I do," Enid said quietly. "She told me. And I admit it was rather drastic but I don't think anything else would have worked. Everyone kept warning you what sort of guy Hobbes was but you refused to listen to reason."
Mildred was silent. Enid was a very lighthearted girl who took few things seriously, but when she spoke in that quiet and determined way you usually took notice.
"Was I really that bad?" She asked at last.
"Worse!" Enid told her. "When you were going out with him you were constantly bringing the creep into conversations, to say nothing of all the smug little hints you kept throwing out about how amazing he was in bed. Maud and I almost dreaded any time we spent with you."
Mildred grimaced. She was not proud of that period in her life and generally tried not to think about it, but it sounded like she had been even more insufferable to her friends that she had thought.
"Look Millie, I'm not saying you have to forgive her but at least think about it," Enid implored her friend. "At least give Cas a chance."
"Okay," Mildred agreed with a sigh. "I'll give her a chance Enid, but no promises!"
Mildred abruptly turned away and walked towards the far end of the lab, staring at one of the blackboards. Enid walked over to join her and saw a complex set of calculations and equations.
"This looks new," she commentated. "I don't think I've seen it before."
"I'm just trying to work out some of the details of this new spell," Mildred told her. "I need to consider every possibility."
"There's something worrying you, isn't there?" Enid said shrewdly. "Something other than the chance of an uncontrolled chain reaction?"
Mildred smiled wryly. "You know me too well, Enid!"
"So what is it?" Enid asked nervously. "Millie, could Miss Hardbroom die as a result of this spell?"
Mildred shrugged. "I can't rule out anything completely but I think that's very unlikely."
"So what is it? What's worrying you?"
Mildred turned to face the other witch, visibly taking a deep breath before she spoke.
"Enid, even if we manage to break this curse, there's still a significant chance Miss Hardbroom could lose her magic!"
Enid just stared at her old friend in horror, for once at a complete loss for what to say.