syncategorematic | I Promised I Will Explain ( I ): Sequences (Reply)

So, loyal readers who do not know me personally (as of writing this, I do not know of any such, but you may come someday), I owe you the story of the sequences and the associated story of the math homework wars, and the story of the Cult of the Divine Forklift. The sequence story (although long) is easier, as I wrote it up in grade 12; from the third person point of view, true, and from an almost fantasy-world point of view, but here, I will just change the names and paste it right here. The sequences story happens on the third day of grade 11 math with the Dark Lord, but first I will have to put down what happened on the first day:

The little paper announcing her classes Tourmaline now held in her hand, a little wrinkled between her fingers from twirling it back and forth. Chemistry. Literature. East-Calisandor. Spanish. History. Physics. Second-year French. And, first of all on the list, her first class that first day, Mathematics, Gifted, a compulsory course. Taught by the Dark Lord.

“Hey,” Chion greeted her in his usual way, “what’s up, who do you have?”

“Math,” Tourmaline sighed. “You had the Dark Lord last year, didn’t you? You mentioned him. What is he like?”

“The Dark Lord? You have the Dark Lord? You’re lucky. He’s brutal, but he’s good. I have Lady Gaussjordana now. I don’t know what she’s like. Some say she’s nice, some say she’s bad...”

“I’ve heard she’s nice,” Athaira put in, sneaking around Tourmaline’s back as usual. “I have her.” She glanced at the class lists. “Oh good, you and I are in the same class for Lit! And Chion and me have the same math. But I don’t think there is anything else. Hey, look, you have math when I have French and you have French when I have math! I have French third year. With Lady Arne. Such a bad teacher, god!”

Tourmaline had heard. “I have to take second year. With Lord Aglaion.”

“But you’re so good,” said Chion. “Why do you need to take second year? But you’ll like Aglaion. He’s the funniest, and he teaches well. And the Dark Lord for math...”

“I hate math,” Athaira muttered. “Math just tears apart everything.”

“Welcome to the club,” Chion replied cynically. “Well, good luck in math. I have to hop to my Chemistry class. I have Lady Della. I think she’s new.”

Lady Della was the name written on Tourmaline’s own Chemistry class as well. “Wish me luck facing this Dark Lord gentleman.” From his name, he was Thian, but she knew nothing else about him.

Tourmaline had always felt most comfortable sitting in the front row, where she could pester the teacher as much as she could with annoying questions. As the rest of her class trickled in, the first-comers took the back, and everyone else sat as close to the back as they dared, glancing at each other warily. The Dark Lord.

“He’s not as bad as he is to people who skip.”

“He is a damn good math teacher.”

“He’s weird, though.”

Then the object of the discussion entered.

Tourmaline’s peripheral vision had never been very good, especially on her right, so as he approached along the classroom wall on the right to go to the front of the class, all she saw at first was a blue blur. A blur that resolved itself into a Thian man in a pressed blue shirt and blue tie.

Her brain mentally ticked off a description of him as it had done for the dragon. So long ago, when she had gone to the cave to get the answers to all the questions she may ask.

The Dark Lord’s face was a narrow oval rather than the round faces some Thians had, but without angles or hard corners in it. He was rather tall, (though Tourmaline was not one to judge height), built without any excess weight, and something about the way he walked told of an athletic grace, and of a firmness of purpose. He wore glasses, and the eyes behind them were chips of black obsidian as he surveyed his class.

“I am the Dark Lord. This is probably the longest I shall ever speak to you; but I need to take the first class to take down some rules and what I expect of you during the remainder of the year.”

From his pocket he pulled out a small PDA and ticked off on it the points he was going to cover.

“The first rule in my class is RESPECT! And that means respect for yourself, respect for others, and respect for the school!”

For a moment Tourmaline let a query be filed as to whether it had been wise to sit in the front row. Motion overruled. The front row is my home. It is where all the action is.

“Respect for yourself, for others, and for the school means that you come in on time! And that means before the bell! Any students who come in after the bell I mark down as absent, and they have to go and sign themselves in! Well,” his voice slightly dropped its thundering pitch, “if the opening exercises come on and I look outside and see you standing there looking stupid and mouthing ‘sir...’ I might let you in. But anything after that, you go down and sign in, no exceptions!

“Respect for yourself means that you come to class prepared! You bring your textbook, your notebook, your pencil, your number-calculator, your loose leaf paper, and anything else you need.

“Speaking of materials, what do you write with?”

“A pencil?” someone hazarded after a silence.

“A pencil. With an eraser, so you can erase! If I see all those scribbled out numbers, and I look and I think-“ he held up an imaginary paper in front of his face, and scratched his head, squinting at it, “ ‘is that a three? Or is that a six?’ And inside something is going to me-“ he rhythmically tapped his temple - “ ‘Fail the student, fail the student, fail the student...’ And I will go ‘Oh yeah, zero! If I can’t figure out what it is, it’s a zero!

“Zero,” he grinned with a flash of teeth at the word, “is my favourite number. It is so easy to work with it. If you multiply something by zero, the answer is - zero! If you add zero to any number, the answer is - that same number! And it is so easy to figure out averages! Let’s see,” the imaginary paper came out again, “this student’s got zero,” he ticked it off with a pen, “zero, zero for everything, your average is - zero! Easy, isn’t it?

“ ‘But sir,’ you might ask,” he got back to his topic of pencils and erasers, “ ‘what about whiteout? Now let’s think of it. How much does an eraser cost? Four of those big ones at once? A dollar, two dollars? Now how much does a bottle of whiteout cost? Four dollars at least. And how long does it last?”

He leaned sideways on the table, knocking the last imaginary fluid out of a stuck imaginary bottle: “Come on, come on, come out!” Something about him forcibly reminded Tourmaline of Chion, and she thought it was the mimicry talent, as well as the basic face layout of dark hair, dark eyes, and glasses...

“Use an eraser.”
He checked the PDA again. Professor Moriarty, Tourmaline thought. The last time you interfered with me was, [leaf through notebook] hmph, on March 4th... “Respect for yourself means that you come to class with the appropriate materials. And if you do not, if I find that you consistently do not...I will be on your case. I will hunt you down. I will meet you before school, every day. As you tumble out of your parents’ car and they wave to you ‘Bye-bye dear, have a nice day at school!’ I will come towards you and ask ‘Do you have your notebook? Do you have your textbook? Do you have loose leaf paper? Do you have a pencil, a calculator, and an eraser?’ And I will keep on doing it until you do! I am here at seven-thirty every day, you don’t worry.”

Tourmaline noted that.

“Oh yes, and I will ask whether you have your homework done.

“You do your homework!

“Every day I will assign homework - questions out of the textbook. Speaking of that, let’s assign textbooks.”

Thunk! “These are brand new, absolutely new, just fresh from the printer; in fact, I think you might be able to get a very small high if you sniff between the pages - don’t try it. And I expect them covered! You go to the nearest store, and you ask for brown paper, and you cover them. Today!”

The textbooks began to circulate. From behind his desk he pulled out a stack of papers.

“This shall be my only gift to you this year. My entire copying budget was spent on these. These are your table of contents. You put them at the front of your notebook, at the front of each chapter, so I am giving you the first one and you shall copy them for all the succeeding chapters. Up here you put the chapter title and in here you put the date, the lesson, and the homework assigned for that day.”

“So it will be the first chapter title?” Tourmaline spoke up, checking the textbook table of contents. “‘Patterns of Growth: Sequences’?”

“Yes.” She was a desk to his left, not directly beneath him. “And I will check it. I will check your homework at any time, and I will check your notebook - I love picking up notebooks and shaking them,” he demonstrated with a textbook, “if anything falls out, zero!

“‘But sir,’ you will whine, ‘I don’t have time.’ I don’t care. You have to work after school? So what, do it after work. Do it during your spares. Do it before school. But I have a rule - if your homework is not done, and I check it, I give you a zero; but if you show it to me done before the next test, I will cancel the zero and replace it with a mark. But after the test - all zeroes are zeroes!

“And if the homework is ‘half done’, or ‘done except for one question’, or ‘done except for one step’ - guess what? It’s not done!

“Oh, and when I put homework on the board - god help you if you look up and go ‘Is that all, sir?’ ‘Hey,’” he grinned an evil grin, “ ‘do you want more?’ I am always happy when students ask for more homework. I will double it. So... be quiet when I assign homework.”

He pulled a stack of blue portfolios out onto his desk.

“This is my other gift to you. I spent my entire budget on these. This is your quiz notebook. They are blue - in case you haven’t noticed, blue is my favourite colour - every day I will give you a quiz, on last day’s homework, and you keep them in here. By the end of the year it will be this thick. All your tests, you keep in there, and this is what I will mark.

“And by the way, I have already decided when your first test is going to be - write it in your notebooks, it is October 10th, right after the long holiday weekend. So nobody will whine ‘But sir, you didn’t give us any time to study!’ Yeah, I did, what was the weekend for? And my tests are the hardest in the school. You know the math exam is usually out of a hundred marks? Well, my test are out of hundred and twenty, a hundred and fifty. You write the exam and you say ‘That’s nothing in comparison to the Dark Lord's tests!’"

The astute reader having already noticed that Tourmaline was an incurable idiot, she wrote her name on her quiz notebook in dark blue ink.

“I have everything planned out: every lesson, every test. Last year we even finished ahead of time and had a few classes left over at the end of the year. I had them do projects - on the Pythagorean theorem, on the quadratic formula - and show the projects out in front of the class. And then I would ask “Hey, can you prove that?” and have them derive the quadratic formula right in front of the class. All thirteen steps.

“And speaking of tests - respect for the school means that plagiarism is followed by very harsh consequences. You guys are all intellectually elite, gifted, right? - well, they tell me you are. You are competing for universities with students not just from Ontario, but from all over Canada. In my home province of Quebec,” his voice rose, “instead of fourth and fifth year, there is a thing called CEGEP. It is far harsher than this Academy, far harsher. It is like universities; you have to pay for it. And if you fail, so what? They’ll just kick you out, because they already have your money. You are competing against people like this, who have made it through that kind of work.”

“You always talk about CEGEP and failing CEGEP,” someone murmured, not meant to be very audible.

“That’s because he did,” a girl in the second row quipped.

The Dark Lord glared at her, a smile dancing with the corners of his mouth. He reached up to drum fingertips on his temple. “Fail the student, fail the student, fail the student...”

In Tourmaline’s heart rose the fire of righteous indignation at a pretender to her post. She, Tourmaline Variety, had always been her class Queen of the Smartass Remark.

“You are all here because you want to have a bright future, right? University is the key to your bright future. This classroom is the key to university; this classroom is the key to your future! I am the key to your future.”

On the front page of her notebook, Tourmaline wrote down Oct. 10 is test for 1st unit Chapter 1: Patterns of Growth; Sequences. The Dark Lord is the key to our future. She wondered if the Dark Lord had ever read communist propaganda about the ‘bright future of humanity’; despite the Sattalyoran, not Russian, rolling off his tongue, how could it be coincidence arising from the Dark Lord’s dark brain?

“And I know how you guys cheat. I know all the tricks, and I will catch you. I know the standing-up-to-sharpen-a-pencil, and the scratch-your-head-and-look-sideways, and the oops-my-pencil-fell-down-let-me-lean-over-and-get-it...”

That was the minute Tourmaline began to hate him.

“And universities will look at your record,” the quiz notebooks had by now all been signed and returned to his desk; he grabbed one and opened an imaginary student record: “ ‘Hmmm... Excellent marks... Hmmm... Brilliant student... Hmm... Active in the community... Hmmm... Plagiarism.’ ” He tossed the notebook expertly into the wastepaper basket. “There goes your bright future.”

“And when you do your homework, you may ask what if you copy the answer from the back of the book? Well, isn’t that plagiarism? Copying?

“This is the HMS Titanic, right here this classroom, and you know what happened to that one. There are not enough lifeboats! It is going to sink at any time, if you do not give me one hundred percent effort! And ninety-nine point nine-nine-nine-nine-nine-nine percent does not round up; this is not the way you’ve been taught in math class. It rounds down to zero! You know us math majors. Like everything to be precise.”

This is the HMS Titanic, right here this classroom, Tourmaline dutifully copied down the essential points of the day’s lesson.

“Some teachers believe that they should start you with one hundred and let you lose points. I say no; you come in here with zero and I start you with zero! You have to win every mark I give you, and if you do not give me that one hundred percent effort - at zero you stay!”

He scanned the silent class.

“I have said zero is my favourite number. But I do have another favourite number - one hundred. Because,” he grinned, “it has two zeroes! And if you do all your work and you give all your effort and you do all your homework - yes, it is possible to have one hundred in my class.”

Not for me, Tourmaline thought in the far darkness of her mind. One hundred percent in math...

“Any questions?”

“Sir?” One girl raised her hand.

“Yes?”

“Are you going to assign Chapter Problems this year?”

Something about this question filled the Dark Lord with joy. “Oh yeah, last year I assigned everyone the Chapter Problems in the textbook and made them hand them in. I remember Euryale handed in like twenty-five pages, because I ask for all the steps and proofs to everything, right?... No, I think this year I’ll make you do the Chapter Challenges. The day before each test I’ll have you do them to hand them in, and they will count for a few marks on the test.”

The clock on the wall was approaching the end of this seventy-five-minute ordeal. “Okay, your homework for today is to cover your textbook and do, let me see, pages 14 and 15 numbers one to eleven. Odd letters. The quizzes will begin next day! Write this down in your table of contents!”

“What is the title?” Tourmaline the goody-two-shoes model-student queried.

“Title?” Among all his notes, this one point seemed to not be covered. “Oh, Introduction.”

This was faithfully inscribed in the table of contents as well as in the front page of the notebook, underneath the inspirational quotations.

Tourmaline hated being scared; it kick-started all her rebellion and revenge programs. But both her natural reaction to being honestly scared and the first step in her rebellion program was Be very, very good, and very, very polite. While studying the situation, collecting information, and looking for the weak points that would allow her to break out of there and get her revenge. And trusting Tourmaline Variety, even Tourmaline the Very, Very Good, to be Very, Very Good was a weak point indeed.

“Oh, and by the way,” the Dark Lord continued, “I don’t want to hear the excuse ‘Oh, I had homework in my other subjects...’ Math is the most important subject, isn’t it?” He grinned broadly at his class.

“And if you have any difficulties - my spares are period 3, 4, and 7; I am usually in the math office or I like to spend time in the teachers’ lounge; you know that little cubicle in the math office just as you go in, to your right? That’s mine. At noon, before school, after school, during my spares, look for me in one or the other place.”

Tourmaline had never been to the math office, or to a math office of any kind - never had any reason to. The Dark Lord’s spares period 3, 4, 7 joined the essential data of today. Period 3 was her spare. Who would want to be tutored by him?

“And another rule of mine,” The Dark Lord added, “ is that you’re not allowed to put anything away until the bell rings. Or I keep you all in. You are getting seventy-five minutes of class, every minute of it.”

The bell agreed. It rang.

“It’s home-room time. Make sure you go. And cover your textbooks; I am checking next day. And do your homework! Have a good one.”

The Dark Lord had the kind of voice that makes even imperative sentences that don’t merit an exclamation mark fall just short of meriting it. An exclamation mark after The Dark Lord is the key to our future was overdoing it, but a period was woefully inadequate.

So that’s the Dark Lord for you. So after that, there was the third day.

A Very Good Sequence

The Dark Lord was greatly distressed over the previous day’s quizzes. Greatly distressed.

“I have to tell you I was disgusted at the quizzes. I have seen very few things in my life as bad as this - crap! “ he resolved on a word that Tourmaline had never thought teachers were allowed to use when students could hear them. “In my home province of Quebec, where the passing mark is sixty percent, you would all flunk!”

Yes, indeed, Tourmaline did badly, though she, she confirmed on her calculator, did not fail. Just barely. But she was going to do well on this one, she vowed mentally to a Dark Lord whose blue shirt had suddenly decided to go blurry for a moment.

She probably did. At least, she thought she did. She needed to rectify that stupid blue ink of her name, but there was no time. The Dark Lord gave no time. She copied down the answers of the quiz in her notebook, already not remembering what kind of delirious ravings she had written for the question.

“We get story time today,” the Dark Lord boasted. “I’ve been reading this kids’ book about math, called The Number Devil, and I want to read some of it to you today.”

“There are books about math to read for fun?” someone commented from the back (another usurper to Tourmaline’s crown; but Tourmaline would not have heckled that one. She knew there were books about math to read for fun. She had read some of them.)

“Yeah, there are some great books about math,” the Dark Lord waxed enthusiastic. “The history of numbers, the history of equations... I am reading this great book right now called Zero: The Dangerous Idea,” he savoured the title, “cool, eh?”

Tourmaline had actually heard of this book, somewhere in the book-review pages of some science periodical or other. Many moons later she was to note that the Dark Lord had quoted the title wrong: the book was actually called Zero: The Biography of a Dangerous Idea.

“The book I’ll read to you,” he flourished a slim hardcover with a colourful front, “is called The Number Devil. It is about,” he began reading the little description of it on the inside cover, “this little boy named Robert...”

“It’s a kids’ book!” another peanut-gallery-ist protested.

“So?” the Dark Lord responded with a brilliant smile. “You’re kids. I’m a kid.”

“So Robert,” he continued, “hates his math teacher - ooh!” He was dazzled at the possibility of such a relationship. ‘And so he hates math as well. So he begins to have dreams and he is visited each night by a little number devil who teaches him about the world of math. Each night is a chapter. I will begin at the sixth night.

“ ‘The Sixth Night,’ “ he began.

“You probably think I’m the only one” said the number devil the next time he turned up, perched on a folding chair in the middle of a vast potato field.

“The only what?” asked Robert.

“The only number devil. But I’m not. Number Heaven, where I come from, is teeming with us. I’m not even one of the bosses.” [That was where the Dark Lord clarified “The bosses are the greatest mathematicians in history. Their chief is Professor Horrors, that’s Gauss.”] “The bosses do nothing but sit and think. Now and the one of the will laugh and say something like Rn = hn factorial times f of n open bracket (a + ) close bracket.” */(Enzensberger, Hans Magnus. The Number Devil. Trans. Michael Henry Heim. Henry Holt & Co., 2000. Aw, I forgot the city.) /*

Tourmaline’s eyes lit up. “Repeat that!” she asked delightedly, starting to write it down.

“It doesn’t matter. */ So he did not repeat it. So I only got the R sub n equals H sub n factorial So I quoted it wrong. It’s all his fault. /*

"So all the great mathematicians go to number heaven and the number devils come from number heaven.”

The girl who had tried to usurp Tourmaline’s crown the first day spoke up again. “Shouldn’t number devils come from number hell?”

“That’s a serious misconception,” the Dark Lord assured her, eyes dancing. “A serious misconception.”

Anyhow, the heavenly denizen takes Robert out to some field or other where they watch a pair of rabbits (one pair) grow a year old (one pair) give birth to another pair of rabbits (two pairs) then another pair of rabbits while the first grow a year old (three pair) then both the younger and the older have kids while the second set of kids are busy growing to maturity (five pair) get it? Oh, never mind, it’s the Fibonacci sequence, and it ended, if Tourmaline understood correctly, by Robert being inundated with roughly 1418 pairs of very cute furry rabbits and him being emotionally scarred for life by such a demonstration of the Fibonacci powers before the spirit of number heaven saves him by making all the rabbits go away.

For those who were too busy contemplating the theology and philosophy of devils still being allowed to inhabit heaven, instead of following Tourmaline’s example and listening very attentively to the text, the Dark Lord had prepared a lovely diagram. It had years along the y-axis and pairs of rabbits along the x, and best of all, it was a pictograph, so along each row for each year, there were clustered gray rather dorky-looking but recognisable rabbits grinning through their whiskers at the artist and wrinkling their rabbit noses.

“Did you draw those, sir, or are they from the book?” Tourmaline inquired impishly.

“They’re from the book of course,” he laughed. “You think I could draw like that?”

So few of Tourmaline’s teachers could draw that she had begun to suspect they teach a “How To Draw Badly” course in teachers’ college, the way they have bad handwriting courses in medical school. But she was feeling facetious; the tale of the number heaven and its happy denizens had made her own devils wake up and dance in her eyes. “I have complete and utter faith in your abilities, sir,” she declared fervently, and began to, very illegally indeed, sketch a number devil in the margin of her notebook.

“So,” the Dark Lord finally closed the book, “that is the Fibonacci sequence. Lesson #3,” he turned to the board. “Sequences and the Recursive Formula.

“Hey,” a thought suddenly struck him, “you guys are all here because you want to be physicists and scientists and engineers, right?”

“No,” there was a general muttered chorus.

“Then why are you in this class? This is preparation for university courses you need advanced math for.”

“We are all just here because this is the gifted class...” someone piped up nervously.

Why was she here? Tourmaline thought. She did not think she had the math skills to be an engineer or physicist, and yet she would never go into an easier, less theoretical, more applied class. Why?

“Definition: A recursive sequence is a sequence where a new term is generated by the previous term or terms. A recursive formula is the general term for a recursive sequence.

“Note: The recursive formula will refer to at least one known term.

“Note: The recursive formula shows how to find each term from the previous term or terms.”

With tears in her heart Tourmaline erased the incredibly cute number devil, and settled down to figure out his examples of sequence after sequence after sequence. Actually no, they only did two examples, but writing out all those terms for each one and checking how each one applied to the formula... She had herself often wanted, in those happy days when she was in a good mood about math, to write a book like that, about someone who hates math and gets a wise counsellor to guide him through it. The author of The Number Devil had beaten her to the punch.

All too soon, it was two minutes until the end of class. The Dark Lord stepped over to a convenient area of the board and began to write out Homework. Slash underline.

“Hmmm,” he opened the textbook, “read example 3 on page 30; it’s a good way to start. Then...”

Questions 1, 2, 3, 6... The little devil that lived behind Tourmaline’s tongue (not a number devil, Best Beloved, a Tourmaline-devil, a trouble-devil, a rebel-with-no-cause-but-the-kicks-of-rebelling devil) decided to pull it.

“Is that a sequence?” she asked, grinning from ear to ear.

The Dark Lord stopped dead in his tracks and stared for a moment at the board. “So you want a sequence?” he grinned his most evil grin to date. He grabbed the rag and wiped the beginnings of a sequence clean. “Here, questions 1 to 20, every one. Like that sequence?”

For an instant the world went dark before Tourmaline’s eyes. ‘That is a very good sequence,” she declared without skipping a beat. I’ll be damned if you make me regret what I say and what I feel like saying!

From behind her, she could hear audible moans, gritting of teeth, and death threats. Tourmaline tried one final plea. “You’ve got blood on your hands, sir.”

“Well,” he grinned, “bring me a note from your parents next class. I’ll be checking notebooks next day,” The Dark Lord was incredibly pleased with himself.

A note from your parents for what? This note confirms that Tourmaline was not killed brutally by an enraged mob of her classmates, and that is not her ghost or doppelganger coming back to haunt the Dark Lord for being responsible for her death... Signed, Tourmaline’s parents.

There was a Russian saying If you like sliding, like pulling the sled uphill. Well, if she liked heckling, Tourmaline resolved, she will like the math homework. She will enjoy the math homework. She will find all the delight she could in the math homework, all the relaxing and the quiet artistry she had come so close to discovering before in the Dark Lord’s math homework.

Once upon a time there was a masochists’ revolt in hell.

The bell rang. “Have a good one.”

With a smile you could see a mile, Tourmaline rose, ignoring the daggers her classmates threw at her with their eyes, and stopped by the desk where the book The Number Devil lay.

“May I take a look at this?”

The Dark Lord gave permission.

* * *

“So I think my class is out to lynch me,” Tourmaline finished the very condensed version of the tale to Athaira at lunch.

“I would too, if I were them. That is so like you to do this.”

A classmate of Tourmaline’s had approached her in home-room and pointed out again that you never should say anything when the Dark Lord is assigning homework, I did that last year. His tone was of humour but not much sympathy, and it did not help Tourmaline very much at the present moment. She resigned herself to doing some very relaxing and fun sequences, and did not think of writing all the terms out, one by one, to get to the needed term.

Tourmaline wasn’t lazy. Many have called her lazy, and she herself had called herself lazy, but what she was truly was impatient. If it was tedious, she did not want to do it. If it was interesting, she could do it for an hour, (then do something else for a little while to get her brain in higher gear, then do it again, but she will get it done if she had to stay up all night and work other temporal miracles). She did not divide the world into Play and Work; she divided it into Fun and Boring. And the Dark Lord has just moved math into Fun; in a roundabout way of course.

How To Give Time-Delayed Death Threats

Tourmaline joined the cluster of her math classmates in her spare, working steadily on math - her math. Hey, by carefully eating lunch with only her intimate friends (as in, not members of her math class, Yaleth notwithstanding) the previous day, she had avoided any quiet arranged murders, and now she was only a fellow math student united in the arduous task of getting those twenty questions done before the quiz and the checking.

Until the Dark Lord came by.

The Dark Lord, Tourmaline noted, had some definite habits, if habits they can be called. Well, giving students homework as a punishment for making his work harder was one of them. Wearing a blue shirt, black pants and tie every day was another (the shade of blue of the shirt varied, and the ties varied, Tourmaline had begun to notice). Another was his goodbye: always “Have a good one.” And another was his way of always sometime (usually near the beginning) in period 3, going down to the dining hall.

He strolled by their table where Tourmaline and Yaleth and another Thian boy, Thuarno, were steadily solving the recursive sequences (the word “recursive” does contain another word in it, a common word in Tourmaline’s vocabulary and not too complimentary to the sequences, but she was not using it; though some others might).

“Working on math homework?” he inquired, with that current of amusement running just beneath the dry drill-sergeant tone that was so particular to the Dark Lord. “Good, good. Especially since... I looked at them and I really thought they were going to murder you then, they were looking at you that way...” He grinned.

“It’s not that bad,” Thuarno spoke up. “It’s just, writing out those first five terms of a sequence is a little...tedious.”

Thuarno, Tourmaline had already noted and she was to note many times more, was one of those scientific minds who care about the truth so much they do not realize that it is sometimes better to not speak all the truth in order to be a little...tactful.

The Dark Lord lit up. “You find the first five terms tedious? I could have made you do ten. Or a hundred. Or a million...”

Some fact Tourmaline had once read in a book of weird facts poked its little head up in the front of her brain. If you wanted to count one thousand million pound notes, one by one, it will take you seventy years to do so - without losing count of course!

“It will take seventy years, sir,” she countered firmly without stopping to look at the fact too closely. Looking at it would have told her she was off by a factor of one thousand, but she, unlike Thuarno, was not concerned about the truth, she was playing a game.

“Seventy years?” The golden triangles on his tie. “Let’s try it. And if it takes any less than seventy years, if I check in sixty-nine years and you’re done...”

Tourmaline dared.

“You’ll be dead by then, Lord,” she countered with laughter in her voice. No, she did not bother to check if that was actually a prophecy, she was playing.

The Dark Lord blinked. Then moved his own piece. “Oh dear,” he mimed grabbing at his heart, “how upsetting! What if I call your parents and ask ‘Dear sir and madam, your daughter has foretold that I will die in seventy years. Does she do that often? And is she ever right? If so, we can go to the casino and try to win something...”

To the question “Does she do that often?” Tourmaline’s parents would have said “Yes.” But not up to casino standards.

“Yaleth,” she asked when he left, “can I borrow your Chem assignment?”

Naturally, she had not done her own.

And people think I am a genius and have a ninety-nine average and am the smartest person ever...