Alexandra Potter
Chapter 7
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… The school of Associative Charms (also known as Sympathetic Charms) is often considered the most complex and, potentially, the most powerful. It is through clever application of Association Charms that the Ministry of Magic has created much of the infrastructure of Britain, including Floo, the Trace, and the Taboo. Association charms allow a wizard to influence a far greater area than his immediate surroundings.
The most advanced forms of Association magic link together a vast range of physical and abstract objects in a variety of relations. Such magic is extremely complex and a complete mastery of Ideal casting is required. However, there is a branch of Association which is simpler, and that is the area of Mechanical Association. The paradigm of Mechanical Association is the Seesaw Charm.
The Seesaw Charm is, prima facie, a simple Charm. It creates an intangible bridge between two objects, inversely associating their vertical motion. When one goes down, the other goes up by the same distance. The quality of the bridge depends not only on the skill of the caster but also on the similarity of the objects, where similarity is defined by Suppes' Theory of Object Similarity (borrowed from the field of Transfiguration). Similarity is a five place predicate, a balance of function, form, substance, arithmetical and alchemical properties. This balance is governed by the Levian Formulae (see chapter two for a detailed discussion of these formulae).
The Seesaw Charm is traditionally thought of as very simple. Indeed, it is often taught to first years at Hogwarts as a demonstration of the basic principles of Association. However, the Charm has considerable depth for those interested minds. For example, in his 1856 masterpiece, Everard Halting demonstrated how the Seesaw Charm may be exploited to create a Perpetual Motion Machine*. The key is that the mass of the associated objects plays no role in the displacement. This research paved the way for the engine of the Hogwarts' Express, created in 1936.
This combination of simplicity and depth makes the Seesaw Charm ideal for our purposes. It is one of the most flexible spells in existence: with small changes, one can alter it to associate horizontal motion, or circular motion. More advanced changes are also possible. In the final chapter of this book, we shall even see that it can be used to associate motion with heat or light. It is thus the perfect Charm to act as a case study for the theories of Spell Extension which are, of course, the primary subject of this book.
"Alex? Are you in there?"
Alex looked up, placing a bookmark in Plastic Magic. She was sitting on her bed with the curtains closed, hiding after the events of dinner - she was pretty certain that throwing gravy over people in the middle of the Great Hall got you in trouble. But it sounded like it was just Susan, so Alex drew the curtains open - just enough to peek out.
Susan was standing on the other side, alone, and holding a plate of sausage and mash.
"I brought you some food," she said, and Alex was suddenly aware of how hungry she was.
"Thank god," she said, opening the curtains properly. Susan sat down on the edge of the bed and passed her the plate.
"It's gone a bit cold, I think," she said, "But I figured you'd be hungry."
"I guess I didn't really think the whole thing through," Alex said as she dug in. Susan was right: it was cold, but she ate it anyway. "But he just made me so angry. I mean, it's enough from Daphne and Pansy and the others. I didn't think Hufflepuff would join in too."
"I think he meant it as a joke," said Susan, before quickly adding, "of course, he was still a dick about it."
"I just wish I could go back to the train and say something different," Alex said. "Or to Charms. She always surprises me, and I can't think of anything to say."
"Just call her an ugly slut, or something," offered Susan, and Alex looked at her in surprise. "You don't have to write an essay, you know. Just say something mean back."
"I want to," Alex said. "It's just - it sounds so lame. 'Hi Daphne, you're a slut!' It's not exactly clever, is it?"
"You're pretty smart, Alex," said Susan, looking at the book she'd been reading. "But you don't have to be clever all the time. Sometimes, you just have to call a bitch a bitch. This isn't Counter-spell."
Another reference Alex didn't get. "Counter-spell?" she asked. Susan waved the question off.
"Never mind. Radio programme. What I mean is you don't have to be witty. Just mean!"
Alex laughed.
"Ohh, I've got one," she said, her eyes lighting up. "Slytherslut!"
"Daphne Slytherslut - it has a ring to it," said Susan, joining in. "I know! How about this: Daphne Greenpubes!"
"Eww," said Alex, still laughing when a knock came at the door. Professor Sprout - their Head of House - walked in. She was a squat woman with greying curly hair and a bit of a moustache. Alex looked at Susan, startled, and she knew they were thinking the same thing: please say she didn't hear us.
"Ah, Alexandra, there you are," said Professor Sprout. "Professor Dumbledore would like to speak to you in his office."
Alex's tummy flipped as if she was rocketing through Gringotts' vaults, and she suddenly wasn't hungry anymore. Professor Dumbledore! The Headmaster! It seemed pretty extreme for a bit of gravy.
Susan jumped up. "It wasn't her fault!" she said passionately, "Tiberius-"
"Whatever are you talking about?" said Sprout, and Susan's mouth snapped shut.
"Nothing!" she squeaked, and Sprout peered at them.
"Very well," she said, "Come with me, Alexandra."
Professor Sprout led her out of Hufflepuff and into an unfamiliar part of the castle. They were high up in the East Wing, if Alex's guess was right. Eventually they stopped in front of an alcove, which held a Griffin-like gargoyle.
"Jammy Dodgers," said Professor Sprout and, with the sound of grinding stone, the gargoyle rotated to reveal a spiral staircase. "Up you go, Alexandra. The Headmaster is waiting for you."
Alex gulped and walked up. A thick looking wooden door blocked the way and she moved to knock, but before her hand touched wood the door swung open.
The Headmaster's office was large, and high ceilinged, but managed to feel warm despite that. It was shaped like an oval and the book-lined walls were broken only by the odd cabinet, full of mysterious contraptions. Above the books were portraits - a multitude of them, whispering to each other as they looked down at Alex with curiosity. And right in the centre of the room was a huge desk, behind which stood Albus Dumbledore.
"Do come in, Miss Potter," he said, and he waved his hand. The door closed behind her.
Alex's eyes widened. He did that without a wand! She knew that it would take her half an hour of concentrating to do what he'd done with a wave. Dumbledore indicated one of the comfortable looking chairs in front of his desk.
"Please, take a seat," he said, and then he walked around the desk to sit down himself, forsaking the throne-like chair on the other side. Alex sat opposite him, curious and confused. She still had no idea why he asked her here.
"I suppose you're wondering why I invited you here tonight," Dumbledore said, and Alex stilled. His eyes were twinkling. Could he hear what she was thinking?
"I must say, you gave a most impressive display in the Great Hall earlier," Dumbledore said, and Alex blanched. It was about Tiberius! "Yes, let's see... five points from Hufflepuff for unladylike behaviour."
Five points? He brought me all this way for five points?
"Do you agree with this punishment?" asked Dumbledore. No teacher had ever asked her that before.
"Yes, sir," she said quickly, looking down at her shoes. The floor was very interesting - if you looked closely enough, there were all sorts of funny shapes carved into the stones.
"Wonderful! But, I confess, this is not why I called you here."
"It's not?" asked Alex, looking up now.
"No," said Dumbledore, quite firmly. "In truth, I simply wished to meet you."
Alex frowned. He hadn't done that with any other student, had he? Susan hadn't said anything about it, at least. Dumbledore appeared to see her line of thought.
"Come now, Alex - may I call you Alex?"
She nodded.
"Well, Alex - we could pretend that you are a student like any other, but we both know that this isn't so." Alex opened her mouth, but couldn't think of anything to say. "I speak, of course, of Lord Voldemort," Dumbledore continued.
"You say his name!" Alex said, surprised.
"Indeed I do, Alex," he said. "But I do not recommend doing so yourself. While you have certainly earned it, you don't wish to be accused of arrogance."
Alex thought back to the way her classmates talked about Voldemort. Almost like he was some kind of god. Perhaps he was right.
"But you say it," she said, and Dumbledore inclined his head in acknowledgement.
"And do you think me arrogant?" he said lightly.
"No! I just meant - I mean, er..." Alex spluttered, feeling foolish. But Dumbledore smiled.
"That is good to know," he said, and Alex couldn't help but feel that she was being played with. "Now, how're you finding your classes?"
Alex smiled - this was a safer topic, even if she wasn't sure how it was linked to Voldemort.
"Great!" she said, enthusiastically. "We've started learning about Charms of Motion with Professor Winters, and Professor McGonagall helped me with the Transformation spell - I was having trouble with metals and she told me about this book, it was really good, all about the Iron family. I was going to read about the Silver family next, but Professor McGonagall says it's a lot more advanced and I should focus on getting the Mutation spell perfect before rushing on ahead."
She paused, trying to figure out what to say about Potions.
"You enjoy reading about magic, then?" asked Professor Dumbledore. He was smiling, but there was something else there.
"Oh, yes, of course! I've just got Plastic Magic by... oh, I've forgotten her name now!"
"Verity Swann," provided Dumbledore.
"Yeah, that was it. Well, I just started reading that one tonight, it looks really interesting - it's all about... well, I suppose you already know what it's about."
"And how's your wandwork?"
"Well," said Alex, trying to think how to say what she thought without being boastful. "I think it's quite good - I mean, my spells turn out well, I think."
"Show me," said Dumbledore. He produced a wand from nowhere and a small block of wood appeared between them.
Transfiguration, then.
"What do you want to see?" Alex asked, drawing her own wand.
"Impress me," said Dumbledore, with a smile.
A challenge, then.
Alex thought for a moment, looking around for inspiration, before her eyes landed on a beautiful bird, gold and red, perched behind Dumbledore's desk. Perfect.
Her wand moved.
"Mutato," she said, and jabbed her wand at the wood. It shifted as if it were liquid, not solid, and a great bird formed, its wings outstretched, as if it were about to take off. Dumbledore leaned forward and moved his wand through the air around the bird.
"Extraordinary," he murmured, glancing several times at Alex. "This is a true Transfiguration."
"It is?" Alex said, surprised. She hadn't yet been able to make anything permanent.
"Indeed," mused Dumbledore, and he went in for an even closer look. "The detail could be finer, though. The feathers have a tendency to merge. See here, and here," - he pointed out areas where the feathers weren't as distinct as the others - "it's fine work, but not quite artisan standard."
Alex nodded, accepting his critique. She would get better.
"Do you know how you would add greater detail?" he continued.
Alex thought.
"If I knew more about birds..." she began, and Dumbledore nodded.
"It's true, if you were an expert on Phoenixes this would assist you. But one cannot be an expert on everything one wishes to Transfigure. How else could do do it?"
"I could... could I extend the motion from closed to open?"
"Exactly," said Dumbledore, "this is the stage at which the detail is added. You must allow time for it, or some detail will be lost."
"But I've seen Professor McGonagall do really detailed stuff really quickly," said Alex, thinking it through. In fact, unless she was demonstrating a spell for them, Alex had noticed that Mcgonagall rarely used much movement at all.
"This is true," said Dumbledore, leaning back into his seat. "Why do you think this is?"
Alex thought for a bit, but she couldn't come up with an answer. All her books had stressed the importance of precision with wand movements.
"I'll give you a hint," he said, when he saw Alex was stuck. "What is so special about moving your wrist that it changes the world? Why is it that the same movement could just as well create the shape of a dog as of a phoenix?"
That was easy.
"The movement is a symbol," said Alex, "it represents what's in the mind."
"Precisely. There is a phenomenon called Internalisation. - you'll study it in philosophy in fifth year, I believe. Internalisation is the process by which, as one advances in one's understanding and practice of magic, the wand movements become mental - to different extents for different individuals. When I conjured the wood, I made no complex motions with my wand. And yet, those motions were in my mind, buried deeply."
"So in Professor McGonagall does a spell, she's so used to slow twists for detail that she doesn't need to actually do one?"
"That is correct."
"But I understand slow twists too!" said Alex. "Why do I need to do it with my hand?"
Dumbledore smiled.
"You are indeed talented, Alex. But you are not Professor McGonagall - not yet. It's remarkable that you can do as much as you can." He picked up the phoenix model and admired it some more. "Be patient. A piano player cannot go directly to sight reading, even if they know the notes. You may think you understand it but, as your education advances, you will begin to see new worlds of subtle understanding which are currently hidden from you. Your understanding must take root. It must become instinctive. Do you understand?"
"Yes," Alex said, and Dumbledore chuckled.
"I see you have another question, Alex," he said.
"Well, if the wrist turn is just a symbol, why do I need to do it at all?" she said. "I mean, why isn't just wanting it enough?"
"An insightful question," mused Dumbledore, "and this gets to the very heart of magic. I confess, there is no firm answer I can give you. However, I will tell you what I think, and you may draw whatever conclusion you like."
"Okay," said Alex.
"Think of it like this: your name is just a symbol. Your parents could have named you anything they liked. But they chose Alexandra. And now, if I started to call you Persephone, you would be extremely confused. At first you would not even realise that I was talking to you. Magic is like a language, Alex. A language to control the world. It's true, the symbols of the language are somewhat arbitrary - they could have been anything. But they are not anything now. They are what they are. If you chose to use a cartwheel instead of a twist of your wrist, it would be like me calling you Persephone - it wouldn't make sense."
What he said rang true. But there was a problem, Alex thought - with language you were talking to other people. You had to use the same words to make sense. But magic - magic was private. It was just her casting a spell. It was just her mind guiding it.
"But with a language, I'm talking with other people! Like you said, magic is in the mind. It's... it's private. So I should be able to chose whatever symbols I like, shouldn't I? Like I was making up my own language."
Dumbledore laughed. "Magic is private, you say? Were you not just telling me of all the books you have read, written by others?"
That stumped her.
"You are certainly welcome to try to create your own symbols, Alex," he said. "Though it may take some time, constructing an entirely alternate body of theory for all of Transfiguration, Charms, Potions, and so on." He paused to make sure Alex was following. "But why do so? The theories we have now - the symbols we have now - are the product of millennia of advances. Hundreds of the greatest minds of history, each building on the last. It would be far better, I'd say, to build on the symbols that already exist, wouldn't you agree?"
"Oh," she said, and she understood at last. She could devise an entirely alternative system of symbols, if she wanted, and was clever enough. But why do it? It was pointless, and would probably be worse that the system that was in place now. And so long as she used the theories of others, she didn't have a free choice of symbols.
"This is very advanced material," said Dumbledore, standing up. "I expect it will become clearer as you study more philosophy." Alex stood up too - the conversation was apparently over.
"I've enjoyed our little chat," said Dumbledore, and he levitated Alex's wooden Phoenix over to his desk. "But I should let you return to your friends. We must do this again, though. In a few weeks, perhaps. That is, if you are amenable?"
"I'd like that," said Alex, wondering what 'amenable' meant.
"Splendid!" said Dumbledore, and the door to the office swung open. "Do come in, Professor Snape."
Snape looked between Alex and Dumbledore before he curled his lip.
"Professor," Alex said, acknowledging him with a nod, before hurrying out. Professor Snape was someone to avoid whenever possible, she thought.
It was only as she was returning to Hufflepuff that Alex realised how much she'd learnt from Dumbledore in that short conversation. Oh, she didn't know any new spells, or even any new spell theory. But she had a feeling, deep down, that she now understood magic a little bit better. Not Transfiguration, or Charms, or Potions. Magic itself. It made a little more sense.
"Alex! There you are!" cried Susan when she entered the dorm. All the girls were there, sitting in a circle on cushions, and a number of bottles, boxes and small tubs were spread out across the floor around them. Alex noticed that Susan's lips were a bright, electric blue. It looked weird, but actually went quite well with her ginger hair. "Come on!" she said, and she patted the floor between her and Lily. "We're trying some of Lily's make up!"
Alex grinned, and grabbed a pillow.
"Now, the trick is to blend it," said Lily, twirling a brush on Hannah's face. Hannah and Lily must have made up, Alex thought. For now, at least. "You don't want a big line on your face, after all. It's gotta look natural."
Dumbledore padded over and licked a bit of lip gloss.
"No!" cried Lily, snatching it away, and everyone laughed as Alex pulled Dumbledore back onto her lap.
"Here," said Susan, picking up a tiny glass jar of shimmering silver. "Let's try this!"
Alex nodded, and let Susan to begin applying something like sparkling glitter to her cheeks. It was a lot better than Muggle glitter, though. It was a clear liquid, but occasionally a bit would sparkle like a little star, before fading again.
"Not too much!" Alex warned as Susan scooped up a load with her finger.
She could do a lot of this stuff with her Metamorphosis powers, of course. Not the glitter, sure, but for Alex, most make-up was entirely unnecessary. And yet, as she watched Lily persuade the shy Megan Jones to try some lipstick, she thought that wasn't quite the point.