Disclaimer: Harry Potter has finite length, but JK Rowling's world has infinite volume.

A/N: I'm on a roll, thanks to the holidays. Chapter 5 of A Little Child Shall Lead Them is now up.

Chapter 52

The next day, in yet another unpleasant lesson, Professor Snape informed them that Professor Lupin was ill again, but would recover. No grief or terror in sight.

"Ya reckon Snape's doin' something to him?" Ron said the day after that after Hermione bugged the boys to work on their Defence homework. "Everyone knows he wants the job."

Harry stared as if the idea hadn't occurred to him. "I dunno," he said worriedly, "but I think Lupin did say something about getting potions from Snape once. You'd think Dumbledore wouldn't let him get away with it, though."

"I don't get it. It's like he's sick every month."

Hermione tutted to herself in frustration. Could the entire school really be that thick? She'd figured it out a month in, and yet now it was the end of January, and no one else would admit to suspecting Lupin. The only thing she could figure was that everyone who was prejudiced against werewolves refused to believe that Dumbledore would hire one, and those who weren't were keeping his confidence just like she was, but that seemed like a leaky ship as far as the other muggle-borns were concerned.

"And what are you tutting at us for now?" Ron demanded.

"Nothing. Nothing."

"Yes you were. I'm seriously getting worried about Lupin. Something's wrong with him."

"Augh. He has a condition that lays him up every few weeks," she said. "It's been known to happen."

"Or that's what Snape wants us to think."

"Ron, I don't like Snape any more that you do, but it's obvious he's right on this one."

"Obvious to you, maybe. Care to explain it to us mere mortals?"

Hermione glared at him. It seemed like every full moon there were times she wanted to just tell the secret and rant about how oblivious everyone was being, but she couldn't do that. "You know what? No," she said. Ron's and Harry's jaws both dropped. "Not this time. If you can't figure it out on your own, I'm not going to help you."

"Um…are you okay, Hermione?" Harry said to this sudden change in behaviour.

"I'm fine, Harry. I just think you need to do your own problem solving for a change…I need to get to my meeting with Professor Vector." She gathered up her books to go. "Don't skive off while I'm gone," she added, knowing full well that they probably would.

Professor Vector noticed her mood at once when she arrived. "Something wrong, Hermione?" she asked.

"Nothing, Professor…" she answered. "It's just that…how can everyone be so clueless about Professor Lupin?"

By now, Vector showed no surprise that Hermione knew this secret. "If you've done your research, as usual, you should know already," she answered. "Werewolves are outcasts in magical society. They're feared because of their contagion, and many people believe—unfairly—that they are vicious and amoral even in human form. Hiring a werewolf to teach would be so unthinkable to many people that they can't imagine anyone else would think it either. After all, Professor Lupin was the only werewolf to ever come here as a student, at least in my lifetime, and no other students ever figured it out, except perhaps his closest friends. They'll search for any other explanation that satisfies them first…I do hope you haven't discussed this with any of your fellow students."

"Of course not, ma'am. I already told Professor Lupin I'd keep it a secret. I just can't believe nobody else has figured it out yet."

"Well, if there's one position with which I agree with Professor Snape, it's that far too many witches and wizards are lacking in logic," Vector said. "In any case, let us begin. I'm finding your non-Euclidean geometry course to be more and more interesting. I admit I've only seen the most basic of geometric applications of vectors and matrices beyond strict linear algebra."

Likely because arithmancy is about a century behind muggle maths, Hermione thought. "It's definitely interesting," she said. "Right now, the only application that comes to my mind is for more rigidly-controlled extension charms, but I'm sure there are others."

"Hmm…perhaps. I suspect that the ability to mathematically anchor linear transformations in physical space could do interesting things for many areas of magical art and craftsmanship. Reading ahead a bit, I think some of the material on projective geometry could be worth a paper along those lines."

"Huh. I'll have to take a close look at that."

Affine and projective geometry were just two of the half dozen forms of geometry covered in the book, each of them generalised versions of traditional Euclidean geometry that could be characterised (in some ways) by what your were allowed to do in them. In Euclidean geometry, the only kind most people ever learnt, two shapes were considered the same if one could be turned into the other by some combination of moving it, turning it, and flipping it—or translation, rotation, and reflection, to use the technical terms—just as if they were rigid physical objects.

In affine geometry, any affine transformation was allowed. Affine transformations included all of the linear transformations she learnt about last term, plus translations. With affine transformations, any triangle could be turned into any other triangle, for example, but straight lines stayed straight, parallel lines stayed parallel, and proportions along a line also stayed the same.

Projective geometry was a little more complicated. It had some weird concepts like parallel lines meeting at a "line at infinity", but projective transformations could be thought of in terms of a point light source projecting an image from one screen onto another screen, except that in this perfect mathematical abstract, the two screens could be at any angle and any position, even behind the light source. In linear algebra terms, this just turned out to be a three-dimensional linear transformation. In projective geometry, straight lines still stayed straight, but proportions didn't stay the same. Also, parallel lines didn't stay parallel since they were said to meat at infinity, and in projective geometry, any quadrilateral could turn into any other, and any conic section—a circle, ellipse, parabola, or hyperbola—could turn into any other, making it much more versatile.

But for now, they were focusing on the basics of affine geometry. "There was something very interesting that I noticed in the book, ma'am," Hermione said.

"Oh, what was that?" Vector asked.

"The book mentioned in passing that a lot of fractals are self-similar under affine transformations, not Euclidean ones. I never really noticed that before, but it's true. Certainly a lot of natural fractals like ferns are like that. Of course, parts of the Mandelbrot Set are only projective self-similar, at best—"

"Whoa, slow down, there, Hermione," Vector interrupted. "You're getting out of my field. I have only a vague understanding of what a fractal is."

"Oh, right, I should have realised. Most of the field of fractal geometry was invented in the twentieth century, and so much of it is computer driven…It's really too bad, Professor. Fractal geometry is some of the most beautiful maths there is. I'll have to see if I can find a good book on the subject."

"I'm sure I would enjoy that," Vector said with a smile. "So a fractal is…some kind of branching structure, like a fern or a snowflake?"

"Oh, no, no, it's much more general than that. Um…" Hermione tried to think what the best example would be to get her point across. "Here, look at this. I draw an equilateral triangle. Then, I remove the middle fourth like this." She grabbed a piece of parchment and marked off a triangle with her quill. Then, she drew a second, smaller triangle between the midpoints of the first and shaded it in, leaving three similar triangles around it. "Then, I remove the middle fourth of each of the remaining three triangles." She repeated the process, leaving nine even smaller triangles joined at their corners. "Then I do it again." She quickly shaded in the middle of each of those nine triangles as well. "And in principle, you repeat the process ad infinitum, although the triangles are invisibly small after a few steps, so it doesn't matter. Then, if you look, any part of the picture—" She circled one of the three medium-sized triangles. "—looks like a smaller version of the whole thing. That's the definition of a fractal. This one is called the Sierpinski Triangle."

"I see," Vector said with interest. "And so ferns, trees, and snowflakes are like natural fractals because they branch in such a way that each part of them resembles the whole."

"That's right, ma'am. There's a lot of other fractals more interesting than this one, though. And they tend to have weird properties. Well, I'm sure you can see that with each step—each iteration—the area of the triangle decreases by a fourth, and the perimeter increases by half. So if the process is continued to infinity, the true Sierpinski Triangle has an area of zero, but its perimeter is infinite!"

Professor Vector actually turned pale at that revelation. "Hermione," she said, "I think I should warn you to exercise great caution in this field. Arithmancers who dabble in infinities like this have a tendency to go insane."

Hermione giggled inappropriately, remembering the apocryphal story that Georg Cantor's proofs of unequal infinities slowly drove him out of his mind. "Don't worry, ma'am," she assured her teacher. "Muggle mathematicians have been doing this for decades. I'll be fine."

Vector, however, was not too keen on the subject. "It sounds very interesting," she said, "but I think I'm going to have to build up a tolerance for the impossible slowly." Moving on, they had a very productive conversation about the applications of affine geometry over a cup of tea. It was only when they were wrapping up that, on a whim, Hermione asked the question that would haunt her for months afterwards.

"This may sound a bit strange, ma'am, but why do the dementors wear those hoods? Is it their uniform or something?"

The colour drained from her teacher's face, and she suddenly became very cold and standoffish. "Miss Granger," she said, "we really need to have a talk about how you gravitate to these morbid topics. That is really something you're better off not knowing."

"Better off not knowing?" Hermione said incredulously. Rarely was there any such thing, in her opinion. "Is it really that bad, what they look like under there?"

"It's not what they look like," Vector said with some hesitancy. "In point of fact, I don't know what they look like, myself, and I don't particularly care to. There aren't really any good descriptions…Those aren't really cloaks the dementors are wearing. What look like cloaks and hoods are actually a part of their…bodies—although since dementors are spirits, you can't talk about them having bodies in the normal sense. The point is, they leave their hoods up by choice. Very few people have ever seen what's under them, and only a tiny minority of those were in a condition to describe it afterwards."

"Why is that, ma'am?"

She sighed: "That, Hermione, is the part that you're better off not knowing."

"Professor, that's not really working," she insisted. "Now you're just making me curious."

Vector turned stern: "Miss Granger, as a scholar I very rarely say this, but you should not ask questions you do not want to know the answers to."

"Well, I can't exactly know I don't until I hear it, can I?" she shot back. Vector said nothing. "How bad can it be, Professor? Do they have killer eyes like the basilisk? Turn you to stone? Erase memories or cause brain damage?"

"No, no, no," Vector stopped her over-eager student's speculating. "It's worse than any of those."

"Worse? How can it be worse?" Hermione demanded. "Ma'am, I'm sure I can find a resource somewhere that explains it. If it's as bad as you say, I'm sure Professor Snape would love to tell me."

It was a low blow, but it worked. As much as it hurt, Vector couldn't stomach the thought of Hermione learning the darkest secrets of the magical world from Severus. "Alright, alright. I expect we'll both regret this, but I'll tell you…The only time a dementor lowers its hood is to perform…the Dementor's Kiss." She gave a small shudder at the words.

"The Dementor's Kiss?" Hermione said. That sounded disgusting just from what she already knew about dementors, and yet so much more ominous as well.

"Yes, the Dementor's Kiss." Vector actually looked slightly ill as she described it. "They have some kind of mouth or jaws, which they clamp over the victim's mouth, and they…they suck out the victim's soul."

There was a long silence that stretched on as Hermione blinked and stared in confusion, trying to make sense of those words. They were all but gibberish to her. She had no points of reference that made sense from which to interpret them. "Suck out the victim's soul?" she said. "How can you say…? What does that do…? What does that even mean?"

"It means exactly what it says," Vector said softly. "The victim's soul is…gone. Their body is left as an empty shell—alive, but with no awareness, certainly no mind, no more than reflexive responses to stimuli. I think the muggles call it 'brain dead'. It requires intensive Healer's care to keep it alive, and there's really no use for that because there's no hope of recovery. The victim's soul is forever lost."

Hermione still didn't understand that—or rather she didn't want to understand. She didn't want to believe it. She tried to stop her mind from making the connections, but she could never do that. Her brain traitorously laid the facts bare before her, and at once, the crushing existential horror came down hard on her almost as if there were a dementor right there in the room.

Dementors can suck out people's souls.

DEMENTORS can suck out people's SOULS.

DEMENTORS CAN SUCK OUT PEOPLE'S SOULS!

Septima Vector watched with worry as her favourite student sat still as a statue as she digested the horrible truth. There were times when she forgot that Hermione was still, at heart, a very sensitive young girl, but today, remembering that fact hadn't helped her. She was too tenacious to let it go. The face under those bushy locks grew more and more fearful and turned chalk white, then changed again to a sickly grey-green colour.

"Hermione?" Vector asked.

Hermione said nothing, but her hands started visibly shaking, and she let out a low, almost imperceptible moan.

"Hermione?" Vector said worriedly. She started to rise from her seat.

I was wrong, Hermione thought. She was right, and I was wrong. I was better off not knowing…Suddenly, an instinctive feeling made her leap from her seat and rush to the door, but instead of bolting from the room, she leaned over the rubbish bin, retched, and promptly lost her lunch.

"Hermione!" Vector cried. She rushed to her side, holding out a hand to support her and pulling her hair out of her face with the other. Hermione retched several more times until she was left with nothing but knots in her gut and a scratchy feeling in her throat.

"Oh, Hermione," Vector said sadly. "I'm sorry. I'm so sorry. I tried to warn you." Drawing her wand, she conjured a rag for Hermione to wipe her face and vanished the contents of the bin.

"No, I'm sorry, I should have listened," Hermione mumbled. She was shaking on her feet.

"Probably yes, but knowing you, I think it was sadly inevitable," Vector sighed. She summoned the two chairs over to them so they could both sit down. "These are very dark truths that would be hard for anyone to learn. I can't say I really know how to help, but—but I'm here for you.

Hermione plopped down hard in her chair. "Thank you," she mumbled.

Vector had rarely seen someone take such a nasty turn so quickly. Hermione was staring down at the floor, her hair falling into her eyes, her skin still pale, and her hands shaking as she clutched the rag between them. Her breath was wracked with quiet sobs. Vector could only guess that it was because she was muggle-born and hadn't been raised with knowledge of the dark side of magic that she was taking it so poorly.

But then, slowly, Hermione raised her eyes, and amid the tears streaming down her face, the storm of emotions in those eyes, there was something more than horror or even grief—something that made Vector quail: hatred. Hatred such as she had only seen from the girl—maybe—when Lockhart had tried to wipe her memory. "P-professor…" she said in a quavering voice, trying to force her tongue to obey, "why are those monstrosities allowed to exist? Why haven't they just killed them all already?"

Vector was taken aback. She didn't like dementors. Few civilised people did. If there were one species the world would be better off without, it was almost certainly dementors, but to hear the words from the sweet Hermione Granger's mouth was startling. Still, she answered the best she could: "Well, the simple answer is that they're not technically alive. The dementors…they're like a fungus, essentially. They grow wherever there is magical decay, and they wither away when they're cut off from the sources of that decay. It is possible to starve them out, but…there are something like two thousand dementors in Azkaban—one of the largest populations in the world thanks to the mad dark wizard who built the place. Kept there, fed on a trickle of sustenance from the worst of criminals, they're contained. If the Minstry tried to starve them all, which could take years, they could have a fight on their hands—a fight that no one wants to have. Worse, the dementors are as likely to go for Scandinavia or the Low Countries as they are England. There's strong international pressure to maintain the status quo.

"And so you make a literal deal with the devil," Hermione concluded. "There must be another way."

"To destroy them? No. No spell or physical blow has ever been seen to 'kill' one. The Patronus Charm only repels them. And reforms to Azkaban have never seen much popular support anyway, like it or not. But honestly, Hermione, are you alright? Do you think you should go to the Infirmary? You're acting really…unusual."

"Do I look like I'm alright?" she snapped. "I'm having an existential crisis, here! I don't think Madam Pomfrey can help with that!"

"I know—I know this is disturbing," Vector said calmingly, "but it's perfectly safe here in the castle. It's not that bad."

"Not that bad?!" Hermione cried. "Did you even hear what you said a minute ago? I've never been all that religious, Professor—Christmas and Easter and a few times a year besides that, you know? But now you're telling me that immortal souls definitely exist, but they're not actually immortal?!"

Vector leaned back a bit. She'd finally got at the root of the problem. Christianity wasn't common in the wizarding world—or wizarding Europe, to be more precise. They'd made a pretty clean break in the days of the Inquisition, but it had been slowly and quietly reintroduced by muggle-borns over the ensuing centuries. Nearly all wizards did believe in an afterlife, though. There was enough evidence—rumours of the Veil and such—and in that light, the idea that a soul could be…snuffed out like that…well, most people tried to think about it as little as possible. For Hermione, it had to be even worse. In a culture where the by-phrase was "immortal soul", the very possibility called all her beliefs into question, even ones she hadn't paid much attention until now.

It was no use lying to her. "Honestly, we don't know," Vector said apologetically. Hermione seemed confused. "People generally believe that the Dementor's Kiss destroys the soul," she continued, "but that's little more than a guess based on what we can actually see. It's entirely possible that the soul survives, but is trapped in the dementor's 'body'. Or that the soul is wrenched from the body and sent on wherever it's supposed to go, unseen. There's just no way to know for sure."

Hermione finally started to calm down. She wiped her eyes and said, "there's no way to test it, ma'am? Even with magic?"

"How? By cutting open a dementor to see what's inside? Even if it's possible, I wouldn't want to be the one to try it."

"Well, someone should do something, shouldn't they?" she demanded. "I think the distinction is kind of important, isn't it? I mean, think about it. If the Dementor's Kiss just 'wrenches the soul from the body', then they're only dark creatures on the level of a basilisk. But if they can actually destroy a soul, then their very existence is an abomination against God!"

Vector held up her hands: "I'm sorry. I'm not disagreeing with you, but even if you find people who agree on your theology…or philosophy…there's simply not much call for any research into those questions. The only people to have regular contact with dementors are the prisoners in Azkaban and a few Aurors, and they're contained well enough that until recently, the question of the Dementor's Kiss was mostly academic."

"Until recently?" Hermione said worriedly.

Vector silently cursed her big mouth, but it was too late to back out now: "When Azkaban Prison was founded, they put the law on the books is that the punishment for escaping was the Dementor's Kiss—"

"You mean the Ministry actually uses it?" Hermione cried.

"No normally, but it was pragmatic. Anyone who can break out of Azkaban once can probably do it again, and no one's been able to replicate whatever Grindelwald did at Nurmengard. I admit it might be better to make it an ordinary execution, but since no one's ever broken out of Azkaban until now, no one ever bothered to change it."

Hermione took a deep breath, mostly mollified on that point. "So that's what they'll do to Sirius Black, then?"

Vector nodded: "Unless someone intervenes on his behalf, and I can't imagine anyone would. Granted, from what I've heard, the Minister sounds just a little too eager about it. He's been pushing the Wizengamot give the dementors a Kiss on Sight order against Black."

"Kiss on Sight? They can do that?"

"You know Black's dangerous. You know what he did the last time he was cornered. The dementors are immune to anything he could throw at them, and if they can act on their own, they might actually save some lives for once."

"Tsk. I understand deadly force, ma'am, but there's a difference between deadly force in defence of others and a summary execution. Every muggle knows that."

"Perhaps, but now you're getting into politics, and I think you've had more than your share of worry for the day. If there's anything else I can do to help you, I will, but I really think you should go to Madam Pomfrey for a Calming Draught and get some rest."

"Th-thank you, Professor, but I think I can manage," she said shakily. "I think I might just grab a bite and go to bed early or something."

"Very well. I do hope you're feeling better on Monday."

"Yes, ma'am." Hermione packed up and walked, still a little unsteadily, out of the room. "Calming Draught," she muttered to herself. "I'm not twelve years old anymore." However, she later had second thoughts about it when she got to dinner because she realised that her stomach was still tied up in knots. She had no appetite at all despite having lost her lunch, and she ate only slowly and mechanically out of habit. She brushed off any and all questions from her friends about whether she was okay.

She probably would have made it through more or less alright, though, except that she happened to catch the eye of Luna Lovegood, who smiled and waved at her. Suddenly, she remembered that day back in November when Luna had confided to her her absolute faith that she would see her mother again someday, and Hermione started to feel sick again. She couldn't push the thought out of her mind, no matter how hard she tried. Even though the odds were astronomical that a girl as sweet as Luna would ever run afoul of dementors, even if the true nature of the Kiss was uncertain, just the possibility that such a thing as a soul-eating demon existed the world…her mind refused to think it.

She pushed her plate away sharply. "I'm really not hungry right now," she said. "I think I'm just gonna go to bed." And with that, she rushed from the Great Hall. A few minutes later found her curled up tight in her bed with the curtains closed. She continued to refuse all questions from her roommates when they returned, only pleading with them to leave her alone, and so help her, if Lavender and Parvati said one word about that prediction from Divination Class, she would Bat-Bogey Hex them.

She didn't get much sleep that night.