In algebra, there is the concept of a linear transformation such that when its argument is changed by a small amount, the image only changes in a small way. I.e. you've got some x turning into some y. Now when you move x just a wee bit, y will also move just a wee bit, not out into left field. Such problems are called well-conditioned. One can see another meaning for the term "well-conditioned problem," though: a problem that is predictable, where you know all the parameters, and you know it will not suddenly start acting in completely bizarre ways. I have been thinking about such problems lately, (especially since I have just discovered, to my shock and horror, that Applied Linear Algebra is the worst mark I have ever had in university. Aw well, go on and deal with it, another idea that has been often on my mind lately. I have managed to get $6000 from this university already, which is more than most, especially in mathematics.)

Washing the dishes on Monday morning, I began to complain again that it has been seven months since we have had hot water, and washing dishes in ice water is excruciating. I decided to try another point of attack on my father, who seems to always have other priorities and is always repeating, "You do not understand. Other things are more important than hot water. Like human relationships."

"Well," I finally snapped, "the lack of hot water is completely ruining my relationship with you, and you know what I think? I think you cannot fix the hot water problem, and you are just afraid to admit it. We will never have hot water. Stand up and admit it, I dare you. You just don't have the guts to confess there is something beyond your capabilities and ask for help for others to solve this. You don't know how to fix the water."

I went on in this rant for a while, intentionally being as cruel as I know how. I was feeling incredibly frustrated, suffering over a situation beyond my control, seeing no way out. He tried to somehow blame me for not mopping the floor as an adequate response to my accusation, an approach that does not make logical sense then or now. Finally, just as I, having vented enough, set off to go to the school, vowing that I am now saving up my money to move out as soon as I possibly can, and I do not care if to a hole in the wall, as long as it has hot water in the tap, my mother appeared. Without any shame, I repeated my entire accusation to her; from the information I had, it seemed perfectly true. "We have not had hot water since May, and we seem to just grit our teeth and bear it, and no one is doing anything about it! I think we will never have any hot water, all because of my father's stubborn pride, in not daring to admit to his dying day that there is something he cannot do, claiming instead that he just has other priorities!"

"You don't understand," my mother said. "We will have hot water. We have looked at replacement boilers. It is just that a boiler costs $2500, not including the taxes, and we do not have that money right now, what with the coming year's property taxes and the mortgage and all that. He is hoping it will get cheaper after Boxing Day."

Ontario taxes are 15% - a tenth, and then half a tenth. $375. Now why did he never simply say that? Suddenly the problem was reduced to dollars and cents, and though they were a great many dollars and cents, here was something I could actually do. Something I could actually deal with. Human relationships and human priorities, especially those of my father, I found as unconquerable as fighting a fog, and as frustrating, but I can calculate how much money I have, how much money I need, how much I can spare, how much I can project to earn. Any sizable contribution to a boiler fund would scrap or slow down any jewelry aspirations I have, and indeed put my trip to Chicago in deep jeopardy, but I now know that a hot shower in midwinter is the sweetest, most sensual luxury I have ever experienced, if you are not sure where the next one is coming from, and for that and for the feeling of grease vanishing from porcelain under my hands without cold pain, I can postpone gold and sapphires.

But why in the world didn't he simply state the problem to me, instead of yammering about priorities and human relationships and floors? I had known all my life we are not rich. It is not exactly a source of shame to lack $2500 in disposable income; I have known all my life that there were some toys I could not have, some books better acquired from the St. Vincent de Paul's than from Chapters; I dealt with it. Indeed, some of the abilities I have had to gain through lacking the money to outsource them I take pride in: I can cook, I can replace a flat tire, I can reglue a shoe sole --- and I can also order from restaurants and book hotel rooms, something my family does not do and I myself do only occasionally. It was a relief to first start earning my own money and thus developing my own taste. I can certainly understand what $2500 + tax means. It would have saved a great deal of friction to simply tell that to me instead of making me guess and flail like a fish on the ice at a problem I could not perceive.

Because of that argument, I arrived late to the NAQT practice, where I had promised I would play. Lady Mollweide was occupied, so Rustem read. I had said to the students that I would try myself against them, and if I do not qualify as an alternate on the team, I am not qualified to coach them.

Well, it seems I am not qualified to coach them, and I guess they must deal with that, because I am the only coach they've got. I only answered one tossup (on Amaterasu, Japanese goddess of the sun); the ones I knew, someone always either got or got wrong before me. I did almost-sweep a bonus on whether the following operations are associative, commutative (poor Rustem pronounced it "communicative"), both or neither. (Of course the only non-commutative thing a high school student may have heard of is quaternions, but I should have remembered diagonal matrices are commutative. Non-associative things you do not hit until Lie algebras, and I only know that because I wandered into Lie algebra seminars on occasion.)

It is the lack of practice that is getting at me; I have not been at trivia practices since at least October, and now I am slow and off. On the other hand, I am the only coach they have, and when I sat down next to Roland, he whispered to me, "That was a comforting email you sent me a couple of weeks ago." And about six tossups in, just about everyone on the team asked me, "Tourmaline, could you please read?"

So what is better, being a player or being a coach?

Higgledy piggledy
Reach volunteer coaches
Say their reward is
The joy of the game.
Once I get out of this school
What I have coming to me,
I'll recant and say, 'No,
It's the glory and fame.'
- With apologies to the late Alanna Little

On Tuesday the same thing happened. I am a little better at Reach than I am at NAQT - I wonder why. Possibly it is because the questions are shorter and begin less obscurely. Possibly it is because Lady Mollweide and Cuchulain read. I remember knowing about pulmonary arteries and jacks-in-the-pulpit. Next year, I vow I will practice more. More aikido and more trivia. Intro to Topology should hopefully be the only hard course; and I know I have said the same thing about this semester, disregarding Applied Linear Algebra. I cannot really blame Dr. Ng; first of all, since he has teaching awards to his credit, no one will believe me, and secondly, what separates the excellent students from the merely good ones, Professor Racine once told us and I never forgot it, is that the excellent students will succeed despite a bad teacher. After all, if you fail because of a bad prof, it is not like the prof sleeps any worse at night. You failed because you did not work.

Work at the Bagelshop is, as may be expected at this time of year, insane. I think the stress is getting to Rosa too, since it seems that every time we little ones catch her eye, she snipes at us with some reminder. On Monday she sent me to put out jars (of Kincade's very nice sauces and jellies) with the message, "You have to be on top of things this time of year!" Kneeling in the aisle, sorting the jars, I muttered to myself, "I hate this time of year. Hate it, hate it, hate it." Alas, a customer overheard, but said understandingly, "You're not the only one."

Christmas, especially the Christmas of December 25, means very little to the culture I originally come from. Our family has taken up giving each other presents on December 25, as well as on New Year's Day as we always do, because, well, everyone else is doing it. Besides, for New Year's Day you can ask for the things you did not get for Christmas, and take advantage of Boxing Day sales. But since my mother is guaranteed to work on Christmas, for the great overtime pay, we have very little incentive otherwise to get ourselves organised and decorate a tree or anything. Last two years we did not even have a tree. We're just an apathetic bunch. And since I would not dream of asking my family for a Birks necklace (maybe someday I'll marry rich, but even then if I respect him I would not milk him, as I said before) all I wanted for Christmas was a lovely book called The Slavonic Languages, and my brother ordered it, but then Amazon.ca apparently informed him that the book is out of print and cannot be gotten.

So I am not in a "holiday spirit" at all right now. Ellard, one of the Bagelshop drivers (and I am certain never in his born days would anyone associate him with the name Ellard) said to me, "Oh, I bet your boyfriend will give you an expensive present." Certainly, if there was one bet I really should have made, and for my paycheck, it would be this one. I'll win.

In an effort to resist the all-pervasive Christmas carols on the piped-in Bagelshop speakers and everywhere else I go (Chez 106 Classic Rock: The Bear is a surprising island of sanity) yesterday I stubbornly rebelled and started singing all the Hanukkah songs I know. In a row. Without stopping. Repeating a previous one if I could not think of a new one. In English, Hebrew and Yiddish. Honey, if you have heard the rendition of "Santa Claus is Coming To Town" by someone who seems to be trying hard to move his bowels at the same time (I thought recording studios had washrooms available off studio space), and heard it thirteen times during a single six-hour shift, as well as a performance of "Winter Wonderland" which seems to have read the score upside-down...I bet you you would have done the same. "Yemei ha-Hanuka Hanuka migdasheinu..." (I do not yet know Hebrew html. Irene, or somebody, contribute if you please).

So I am now rebelling against Christmas driving me insane by driving my coworkers insane with Hanukkah songs (and if my coworkers read this, and Mysteryperson#1 may, wait until after New Year's Day before I even consider apologising). I went home with the firm intention to ski. But my legs were dead from the hip down. So I studied for His.Ling instead. I was very ready to call this post "The Origins of the Aardvark."

"The Origins of the Aardvark" was just a joke from Historical Linguistics class. We were discussing how Dutch changed to Afrikaans, and I queried how "aardvark," about the only Afrikaans word I know for sure (well, there's aardwolf and apartheid) came to be. Prof. Jensen, of course, recommended I write a term paper on the etymology and sound changes involved in that word. I laughed: "The Origins of the Aardvark; how can anyone resist such a title?" I was studying too much for His.Ling yesterday, only to recall today, after getting up in the morning and getting all dolled up, that the exam is at 2 pm, not 9:30 am. In memory of this, while I have still not written an exam, I want to write under the banner of the Origins of the Aardvark. (If you have not figured out yet that I am silly sometimes, (a) welcome to this blog, read some more, (b) if you have, and my silliness displeases you, you may consider other blogs, more serious ones, instead.)

Then I went out of the house - first to settle some banking, then I dropped by Magpie, just for a cursory visit, and then by Birks. Darn, I still love that necklace. I inquired about Birks cards, and was told that you get approval on the spot upon inspection of your major credit card. Now I have a stellar credit history (I mentioned before that I have a paranoid fear of compound interest), but for an amount smaller than the price of that necklace. I walked out, getting my priorities straight: hot water, tuition, and Chicago do come ahead of beautiful baubles. I will have it someday; I know I will.

Before the exam, I talked to a girl whom I'll call Rachel because I do not know her name, but I have noticed she likes science fiction and fantasy. She is apparently writing an alternate history about mutated superior beings, and wanted a name for them, since Homo sapiens superior is copyrighted by the X-Men. I made a suggestion; we spoke for a while of science fiction and school. It got me back on the ground to talk to someone who is grateful to pass courses, instead of killing herself when her CGPA slips below 8.5. I wrote the exam in a good frame of mind. Just before 3:00 I finally got the epiphany on the internal reconstruction/phonology problem, wrote the corrected answer in the booklet we were supposed to use for the bonus question, handed it in, wished Jensen a merry Christmas, and trundled off to the school.

There were only two people in Math Help today. One was my good acquaintance the p-adically challenged gentleman; the other was the spunky grade 10 (both of whom you first meet here)
There were also two young men with Lady Cauchy and the Finance teacher who were not mathematically challenged (well, they were, in a way: they were picking up the results of the Canadian Open Mathematics Challenge). We got into a discussion of the future of Calculus, (I learned nothing I have not already acquainted the reader with except for the proposal conics should be taught in Geo & Discrete - "That would be so fun!" I chirped) and the possibilities of Geometry and Discrete Math: the difference between the algorithm-based math of Advanced Functions and Introductory Calculus and the proof-based math of two-thirds of Geo & Discrete.

"The way I see it" I said, "algorithms are like going up a staircase. You go up, without ever seeing what is on either side of you. Real proof math is like flying above everything, seeing everything clearly and how it works..." I trailed off. I wax poetic about mathematics sometimes. At least that is not all I talk about.

"I have heard that in university now all the stuff that you learned in Discrete they spend like a week on," said Lady Cauchy.

"Two days," I replied brightly. "Actually, no, one day. 'This is a vector. This is dot product. This is cross product. Got it?' The next day was polar form of complex numbers; I remember because a substitute taught it. And the day after that you get straight into subspaces."

The two gentlemen got horrified looks on their faces.

"You see," I tried to explain, "a line is a subspace of a plane, and a plane is a subspace of the space R^3, and R^3 itself is a subspace of some R^4..." I had to stop again. Someday I will teach linear algebra, and teach it well. Maybe even applied. As revenge.

"What is the difference between Discrete and Discrete Gifted?"

"Very little," Lady Cauchy began to explain.

"I didn't take Gifted," I whined. Yes, my IPRC (some kind of Placement and Review Committee) said for grade 12 that given all of Tourmaline's special needs to be stimulated beyond the standard curriculum and to interact with people of similar ability, we have concluded the right place for her is the Regular program. The school was poor that year.

Lady Cauchy pointed out that most of the people who are winning math contests are not in Gifted overall. Which makes kind of sense, I thought, though I did not say it out loud. I wonder how many of the great mathematicians I know can write a good essay on the reign of Louis XIV, a thing I remember doing for History AP (don't ask me now what the Sun King did).

After the gentlemen left, having acquired their math results, and only the truly challenged remained, Lady Cauchy, the Finance teacher and I spoke for a while of a project run by National Geographic that analyses people's DNA and shows the migration routes of their ancestors. Apparently Lady Cauchy's husband's people did not get out of Africa and immediately make a beeline for Scandinavia; they hung out in Italy for a little bit first. I brought up the satem/centum language split, and that the Slavs are closer to the Indo-Persians than to the Germanic and Romance peoples. I am pretty sure my own ancestors have been sitting around Eastern Europe for a pretty long time, unless, I always allow, some Mongol raped someone. Если кто и влез ко мне, так и тот татарин. (Even if someone did crawl in with me, that one is a Tartar. - Vladimir Vissotsky) But that project would be interesting.

Then Lady Cauchy and the Finance teacher started suddenly talking about dancing, and my ears pricked up.

"What kind of dancing? When are you dancing?"

"On Friday..."

I put two and two together, and the answer was isomorphic to the Klein group. "The teachers' skit in the assembly? They're going to dance?" Now this is something worth watching!

"Or try to. Hopefully."

"Who?"

Lady Cauchy rattled off a list of names: Lady Runfar, Lord Locus, other teachers my life mostly does not touch...

I started reminiscing about great assembly skits of Christmas past, and somehow told the Finance teacher and the p-adically challenged gentleman the story of the skit of the Twenty-three Dark Lords, a skit I may or may not describe elsewhere at a later time. I had forgotten that the p-adically challenged gentleman is a student of the Dark Lord's Integrated Arts class. "I am so going to tease him about that."

"He'll kill me!" I cried in mock horror. "I am the archivist and historian of this school's Christmas assemblies, it seems; I actually come back here."

Lady Cauchy was leaving. "Is Lady Melpomene dancing?" I asked her.

"Yes, she is."

"Great, she at least knows how."

"The Dark Lord, isn't, though. We'll persuade him someday."

"The Dark Lord dancing is an image that is...interesting. By the way," I asked a question that eight people who may read this blog may know the reason for, "can he cook?"

Lady Cauchy has supreme assurance in every possible ability of the Dark Lord's, including both cooking and dancing. "He can fly. That means he can dance."

"I can dance," I said calmly (I think I will blame bipolar disorder for my forgetting the many times I agonised and was depressed about dancing on this blog - check any post that was written on a Friday or Sunday) "I cannot fly, though." Hey, I have aikido, now that I think of it, and I had joked that I joined aikido because I wanted to learn to fly. I found out too late that you only do it down.

After I left Math Help, declaring that as it was there was one teacher per student - the best ratio ever! - I dropped by the math office, and the Dark Lord answered the door.

"First of all, I told one of your students about the Twenty-three Dark Lords skit, please do not kill me," I rattled off. "Secondly, any better?"

"No."

"Then I will leave. Again, a reminder not to kill me."

Still cheerful, I flew off (horizontally on a bike, that is, but I danced a bit too). At Dilemme (I think there is a pattern to me going shopping after talking to the Dark Lord. Any Freudians in the audience please shut up), a lady was admiring a china mock samovar, and saying she could use it as a teapot. I pointed out that you boil water in samovars, and you brew the tea in the teapot on top of them. The lady gave me a hug, I do not know why, and said she will use it for a teapot anyhow. I left soon after. I do not think Dilemme has anything left for me, anything that is worth the price of hot water.

At Magpie, though, they had set out new Experimetal designs, including a citrine briolette necklace I tried on. But that one is the colour of pineapple juice, and vanishes around my throat, while the Birks one is liquid honey. No money, honey.

I went home, wrote some of this, then finally went to the shed to get the implements of the physical activity I love most after or concurrently with dance and aikido - cross-country skiing. Well, I think horseback riding might fit in there somewhere, but I ride as badly as I ski, and have done so less recently.

Now, if I had a car, and world enough and time, I would go to Gatineau Park. I would not say the Dark Lord is my hero, but he does have some things I envy desperately. As it is, I made a circle around the park across the street, concluding
(a) it is very bumpy and I hate making trails
(b) I need wax
(c) at least I remember how to ski enough to realise that I hate making trails and that I need wax. You have to admit, it's getting better, it's getting better all the time...
(d) dogs freak out at the sight of me. But if I go out any later, I will not get enough sleep.
(e) I still cannot kick. But maybe that is the wax's fault.
(f) I no longer dread the length of winter stretching ahead of me; I need all the time I can get to get better at this!
(g) Dark Lord, how dare you sulk when you have all those wonderful things I don't!
(Including, I would bet, knowing where your next hot shower is coming from.)

I trotted home, still singing Hanukkah songs.

Chag sameach gam l'chem - (ch is a pharyngeal or velar fricative, and a happy holiday to you as well)
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