An Introduction to Wizarding Math
“Are you sure you are all right, Mr. Calvin?” Professor McGonagall asked, looking down at him with a concerned expression as they left Ollivanders. Calvin shook his head side to side, then up and down. He was staring at the long, thin wand gripped tightly in his fist, wondering how it had gotten there. “You are looking a bit pale – what do you say to some ice cream, hmm?” That ought to cheer him up, as well as get some food in him, she thought.
“Ice cream,” Calvin repeated tonelessly, still looking at his wand.
Professor McGonagall bought the ice cream from a shop called Florean Fortescue’s Ice Cream Parlour. They stayed in the sitting area while Calvin mechanically worked away at the ice cream cone, his other hand white-knuckled, holding his wand in a death grip. He still couldn’t remember how it had gotten there.
With the ice cream in his stomach, however, he was soon feeling back to his old self. Much to Professor McGonagall’s chagrine.
“Oh pleasepleasepleeeeeeeaaaaaseee?” Calvin said, kneeling in front of her, hands clasped together.
“Mr. Calvin, I will not let you spend your parents’ money on such…such frivolous purchases!”
Calvin gazed longingly at the book displayed in the shop window, titled ‘Whistles and Bells: Useless Spells.’ “I mean, sure, it’s self-proclaimed to be useless, but I’m positive it’ll come in handy at some point!”
Professor McGonagall looked at him and raised her eyebrows. “I hardly think that yet another book is going to help your tendency to lose things. In fact, we do have one more item to take care of before we leave Diagon Alley. Something to rectify your,” She tried to search for a word that wouldn’t offend. “Your…difficulty, with staying organized.”
Abruptly, he looked up, fear and apprehension written clearly across his features. “You’re not getting me a planner, are you?”
“That was not what I had in mind, no, though that’s not a bad idea,” the stern witch mused. “I was speaking of something to keep your things organized, however, so that you do not lose track of them. Your parents explained to me how your school books are always disappearing, and so thought this would be a good investment. And after seeing the state of your room,” she added with a wry smile, “I can only say that I wholeheartedly agree.”
Calvin looked at her dubiously, but was curious as to what form this ‘investment’ might take. They continued along the street they were on for a number of minutes, then turned onto a cramped side-road. After dozens more twists and turns, they reached a dead end.
“I think we’re lost,” said Calvin, scratching his head.
“You should have more faith in your professor,” Professor McGonagall responded, mock-scolding him. She stepped forward and seemed to grab a handful of the rough stone wall in front of them, pulling it back easily. A door appeared as she did so, and swung open without a sound. “Coming, Mr, Calvin?” she asked lightly, looking back at him for a moment before stepping through the narrow opening. The door shut behind her as soundlessly as it had opened.
“Magic rocks,” Calvin said, stepping forward and grabbing the same section of stone wall. Hey, I just made a double entendre! Or is it a pun?…his thoughts trailed off into nothingness. With a mental shrug, he pulled opened the wall-door effortlessly and stepped through.
Inside it was dim and musty, the air heavy with the smell of oil and leather. Is it a requirement that all wizarding shops have to be dimly lit or something? He saw Professor McGonagall a short ways ahead, talking quietly to a middle-aged wizard who was standing behind the shop’s waist-high counter. Waist-height for most people, however, was about chest-height for Calvin.
As he approached the counter, he heard Professor McGonagall asking the man – presumably the shopkeeper – about a ‘self-organizing trunk, with Expandable compartments and a voice-summoning retrieval system,’ whatever that meant. Actually, it probably meant a self-organizing trunk with Expandable compartments and a voice-summoning retrieval system. It really wasn’t that hard to understand. The shopkeeper nodded and retreated into the back of the shop, slipping behind a dark brown curtain that was patterned to look like the bark of a tree.
When he returned, he was holding a roughly rectangular trunk of deep brown wood, accented with leather straps and four large brass buckles situated over where the lid met the main body of the trunk. The polished wood shone subtly in the lamplight, speaking of high quality and masterful craftsmanship.
“How exactly am I paying for this?” asked Calvin, eyes wide as he watched the shopkeeper set the beautiful, magnificent trunk down on the counter top.
“You are not, Mr. Calvin, your parents are,” answered Professor McGonagall, fishing through the bag of wizarding currency they’d received at Gringotts.
“Well how are they paying for this?”
“I did not ask. This should be enough,” she said to the man behind the counter, placing the bag in front him, next to the trunk.
He hefted the bag, then looked up at them with a glint in his eye. “For ten extra galleons, it can have a modified tracking and self-apparation charm added, so you don’t have to carry it…” He smiled, waiting.
Professor McGonagall frowned and looked down at Calvin’s decidedly slight frame. “That would no doubt be helpful,” she agreed, withdrawing the needed amount of gold coins from her pocket.
The shopkeeper leaned across the counter, pointing over his shoulder at the trunk with his thumb. “Just tap it with your wand and say ‘follow the leader’ to activate the effect,” he explained. “To turn it off, tap it again and tell it ‘make like a tree.’ The phrases are customizable, of course, but most customers choose to just leave them at the defaults.”
“Cool, thanks!” said Calvin, running a hand across the gleaming side of the trunk. “I can guess what voice-activated retrieval is, but how, precisely, is it ‘expandable?'”
The man straightened up and reached over to the far end of the trunk, turning the front toward himself. “Well, see, if you open it up regularly,” he said, tapping the buckles in a seemingly-random order and then lifting the top of the trunk. “You get this.” He spun it back around, and Calvin went on his tiptoes to peer over the lip of the opening. The inside was divided into five sections, each labeled with one word that looked to be burned into the wood bottom of the trunk. “There’s a place for books, clothes, food, potions, and miscellaneous. Each section can hold roughly twenty times its physical size. Here, you have anything on you that you’d like to store in it?”
“Um, I’ve still got this napkin from earlier,” Calvin said, removing a crumpled, ice-cream stained napkin from his pocket.
The shopkeeper stared at it for a second, then shrugged. “That will do.” He plucked the napkin from Calvin’s hand and placed it in the section labeled miscellaneous. As soon as he let go of it, the bottom of the section flipped, rotating along its middle so fast that all Calvin saw was a blur. The napkin was gone.
“Niiiiiiiice,” Calvin said, impressed. Then he leaned over the trunk and spoke into it. “Napkin, please.” The bottom of the miscellaneous section flipped again, and there lay the napkin, in the exact position it had been placed mere moments ago. “Now that’s what I call ease of use.” He look up at the shopkeeper. “There’s more, right?”
The shopkeeper chuckled, taking the napkin out and placing it on the counter. “Of course!” He shut the trunk and turned it around, so the back was facing Calvin. “It’s best to use the same code for both compartments, else you’re likely to forget one of them, or get them mixed up,” he said conversationally. He tapped the brass buckles again, then reached over the trunk and grabbed the back end, lifting it up the same as he’d done with the front.
“What would transpire if I were to, say, lose my balance, trip, and fall in?” Calvin asked, peering over the edge. The compartment was at least three times as deep as the trunk was tall, smooth brown wood all the way down. He looked up. “Accidentally, of course.”
“This section’s magically supplied with nutrient-rich, breathable air,” the shopkeeper replied, smiling proudly. “Why, you could survive down there for an entire school year! Not that you’d want to, mind you. Mighty boring, the inside of a trunk.” Then he closed the top and turned the trunk around, pointing to the brass buckles. “The code is left, right-middle, right, left-middle right now, but you can change it to what you want, and however many taps you’d like.”
Calvin held up a finger. “So, just to clarify, the code is left, right-middle, right, left-middle, right?”
The man nodded, then said, “Right, unless that last right you said was referring to the direction.”
“Right – left, right-middle, right, left-middle.”
“No, it starts with left, not right. There are only four taps.”
“That’s what I said: left, right-middle, right, left-middle. Right?”
“Are you doing that on purpose?” the shopkeeper asked suspiciously, eyes narrowing.
“Doing what?” said Calvin innocently, his expression the definition of earnest. “I was just asking what the code was, right? Left, right-mi-”
Professor McGonagall grabbed him by the back of his robe and dragged him out of the shop.
“Now, here is your ticket for the Hogwarts Express – please do your best not to lose it. The train leaves at eleven o’clock sharp on September 1st, got it? Don’t be late,” she said seriously, looking him straight in the eye.
“You’re one to talk, Prof- I, I mean, no, I won’t, of course,” he corrected, hurriedly backing away from the glaring witch.
She sighed and shook her head. “I apologize, Mr. Calvin. Today has been rather…trying for me. I should not be taking it out on you, however. Or at least, I’m not allowed,” she added, almost as an aside. “We’ll be owling you a portkey a right before you need to be at the station – just use it when you’re ready to go, and it’ll take you into a deserted building right down the block from King’s Cross. Any questions?”
“Uh, yeah,” Calvin said, looking down at the ticket she’d given him. “Why does this say platform nine-and-three-quarters? I didn’t think they had fraction platforms.”
Professor McGonagall smiled thinly. “The platform from which the Hogwarts Express leaves is hidden from muggles, directly in-between platforms nine and ten.”
Calvin looked up, confused. “Directly between platforms nine and ten?”
“Yes, that is what I said, is it not?” Professor McGonagall replied, giving him a strange look.
“As in, right in the middle of the the two platforms?”
“Yes, Mr. Calvin. Is there a point to these questions?” She was about to start tapping her foot with impatience.
“So, let me just get this straight,” Calvin said slowly and clearly, hands held out in a placating manner. “You’re saying that the platform containing the Hogwarts Express is halfway between platform nine,” he wiggled his left hand, “and platform ten?” He wiggled his right hand.
“Yes, Mr. Calvin, that is exactly what I am saying,” Professor McGonagall replied rather crossly. “What exactly are you getting at?”
Calvin flung his arms out in bafflement. “Then why in the world isn’t it called platform nine-and-a-half!?”
Professor McGonagall covered her face with her hand, stayed like that for a few seconds, then dropped the hand and took a deep breath. “If that is your last question, Mr. Calvin, then I will take you home now, if that’s quite alright with you.”
“Oh, wait, I actually did have another question,” he said, remembering his conversation with Hermione in Madam Malkin’s shop. “Why am I going to Hogwarts? I mean, as opposed to another wizarding school. Aren’t there any in America?”
The Scottish witch pressed her lips together, wondering how best to answer his question. “You were originally enrolled for attendance at an American wizarding school, but they were…unable, to follow through with taking you on as a student. So Hogwarts was notified, and we agreed to have you come learn with us instead.” She gave him a strained smile, hoping he didn’t ask anything more on the matter.
“Works for me,” Calvin said with a smile and a shrug.
Professor McGonagall sighed in relief. It was about time she caught a break, she thought. “That’s your last question, then, correct?” she asked hopefully.
“I’m sure I’ll think of something between now and when I arrive at Hogwarts – I’ll ask you then. Oh, that reminds me, what subject do you teach?”
Professor McGonagall smiled and answered, “Transfiguration. You’ll find out what that is when you visit my classroom for your first lesson.”
Calvin tapped a finger against his chin thoughtfully. “Sounds like transmogrification – changing one thing into another.”
She blinked, clearly surprised. “That is correct. How did you know that? You’ve only just gotten your books – I should know, I bought them.”
“Well, my first transmogrifier terminated itself after only a few uses, and the second version would just turn everything into cheese, but the Mach Three works flawlessly! Aside from the occasional turning-something-inside-out part, but yeah, otherwise, flawless.”
Professor McGonagall nodded slowly, noticing that he didn’t actually answer her question. “All right then. Now, there is to be absolutely no magic done while at home, is that clear? You can peruse your textbooks to your heart’s content, but you are not to use your wand, understood?” Calvin nodded vigorously. “Okay, grab my hand – let’s get you back.” She turned, picturing the front door of Calvin’s house, and they disappeared with the sound of all of the suspension cables of a bridge snapping at once.
Minerva McGonagall sat in a cushy armchair opposite the Headmaster of Hogwarts in his office, surrounded by…things. Things that ticked and whirred and zipped and zapped and crunched and crinkled, all at once, all the time. It was a wonder the man could get anything done in here, she thought.
“Yes, he did ask about it – I told him that the school he was originally enrolled under was simply unable to field him, and so Hogwarts took responsibility for his education.”
“Good job, Minerva. I do appreciate you taking it upon yourself to be the boy’s escort today,” said Albus Percival Wulfric Brian Dumbledore, popping one of those sweets he seemed to favor into his mouth. Minerva shuddered, recalling the events of the day. She probably wouldn’t have volunteered if she’d known what the errand would entail.
“Tell me, though, Albus, did they all refuse to house the boy just after seeing his school records?” she asked, curious.
Albus nodded and smiled warmly. “All sixteen of them,” he said. He took one of the hard candies from the tray on his desk, holding it out to Minerva. “Lemon drop?”
“I’m home!” yelled Calvin into the house as he opened the front door. Suddenly, “AAUUGH!” Hobbes barreled into him like a train, launching them both out of the house and into the air before making contact with the front lawn. The two tumbled out to edge of the grass before losing enough momentum to disengage from one another. Then they both lay on their backs, breathing heavily.
“Pleasure to have you back,” Hobbes said happily.
“The pleasure is all yours,” Calvin moaned. “Ugh, I think I’ve got a piece of my spine lodged in my kidney.”
“I just thought you’d want to be reminded of what you’ll be missing at Hogwarts, where there’s no front door to open in fear every day.”
“Oh, yeah, now I’m real sad to go. Give me a hand up, you fur-coated battering ram – my pants are twisted around and they won’t let my legs bend. Oof,” he wheezed as Hobbes yanked him to his feet.
“Nice bathrobe,” said Hobbes mildly, hands on his hips.
Calvin grunted, looking down at himself. “The grass stains really pull it all together, don’t you think?” Then he shook his head. “Great. It hasn’t barely been two hours and I already have to throw it in the wash.”
“You like to try to see how long you can go without washing something, right?”
Calvin looked up at his best friend and grinned with his entire face. “My best so far is almost four months. I would’ve gone longer, but mom followed the smell and found the socks under the couch cushions, even though I spent all afternoon spraying them with some of dad’s most expensive cologne.”
Hobbes scratched the back of his head. “That stuff in the glass bottle we replaced with vinegar last week?”
“Yup! All I can say is it’s a good thing I was already grounded when he found out. Hey, do you know when dinner is by any chance? I’ve only had three bowls of Chocolate Frosted Sugar Bombs and some ice cream since yesterday.”
“Did you save me any?” asked Hobbes hopefully.
“Sorry,” Calvin said with a crooked grin. “I didn’t want to ruin my robes.”
They headed inside and then to the kitchen, Calvin shedding layers of clothing along the way.
“Hi mom, I’m back. When’s dinner?”
His mother turned around, wiping her hands on the dark blue apron she was wearing. “Oh, Calvin, we were just- why aren’t you wearing a shirt!? And how’d you carry that trunk next to you?”
“It’s magic, of course. Are we out of squid?” Calvin’s voice was muffled from inside the refrigerator. He leaned out and looked at his mom. “Are we?”
She just shook her head and turned back to the stove, where a pot of soup was simmering. “Close the refrigerator, Calvin, we’re having dinner in a few minutes. So you got all your school supplies?”
“Yeah, but I didn’t even get to see the dragons they make the gloves out of.”
Calvin’s mother, used to her son’s overactive imagination, assumed he was kidding about the dragons. “Mhmm,” she said, adding some salt to the soup.
“First we had to go to the bank, where a goblin who looked like he needed about a billion vacations gave us wizarding money in exchange for real money,” Calvin said, counting off on his pointer finger. His mother ‘hmm’d in acknowledgement. “Then I went to Madam Malkin’s, where I’m pretty sure I met every other muggleborn first-year going to Hogwarts. I met a nice boy with a scar shaped like a lightning bolt who defeated this really evil wizard named Voldemort and got my James Bond reference; I met a stuck-up boy with blindingly blond hair who acted like he was used to getting his way and who seems like he’s going to be a lot of fun to annoy incessantly; I met a smart girl with voluminous amounts of hair and large front teeth who talks efficiently and didn’t try to get me sent to the principal’s office, at least not yet anyways; and I met an enthusiastic boy with dark brown skin who knows a lot of synonyms for the word awesome and screams almost as loudly as I do.” By this point his mother had gone into ‘That’s nice, Calvin’ mode, and was concentrating on setting the table.
“After that, Professor McGonagall returned and intimidated me a lot up until she acted nice again, then took me to receive my wand at Ollivanders, where-whe-where-” Calvin’s tongue caught on the roof of his mouth and tripped, causing him to stutter. His entire body trembled like a sapling hit by a speeding red wagon as his mind skipped over certain memories like a malfunctioning record-player. A shiver ran through him from the nape of his neck to the heels of his feet. “Whe-whe-whe- then we went for ice cream at Florean Fortescue’s Ice cream parlor,” he said evenly, continuing speaking as if nothing had happened. “Then came our final stop, at this shop inside of a stone wall at a dead end, where we acquired this awesometastic magical trunk whose code is left, right-middle, right, left-middle, and can categorize all of my belongings for me so I don’t misplace everything! Also, I can live in it for a year! Speaking of which, how did we pay for it? It seemed really expensive. I mean, not like brand-new-car expensive, but at least we-have-to-sell-our-tv-to-help-pay-for-it expensive.”
“Hmm,” said Calvin’s mom. “Calvin, can you go get your father? Dinner’s ready.”
“Sure, where is he?”
“Living room,” she said, taking the soup off the stove.
Calvin went into the living. For the next twenty-seven seconds, he did not move a muscle.
“Calvin!” his mom called. “What happened to getting your father?”
The next moment, every house in the neighborhood shook with the force of his cry.
“YOU SOLD THE TV!?”
“Stop screaming, Calvin!” said his mom, walking into the living room wielding a dripping spatula. “Oh, yes – how do you think we were able to pay for your trunk?”
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