CAMERA at last!

The camera finally arrived, which means I can take pictures again! Further, I can upload pics of the Origami polyhedra I constructed! Here we go!



Left to right:
30-mod (sonobe) stellated icosahedron;
12-mod (sonobe) stellated octahedron;
12-mod (sonobe) cube.


Left to right:
12-mod decoration box; assembled into a 14-box ring;
6-mod (gyroscope) truncated gyroscope (?).


Finally: 6-mod flower-box. It changes from a box to a flower! Amazing!


...Will update more later, maybe.
--Charissa

Quick Sketch

I made this sketch tonight.

On Tuesday, I got this haircut. It's incredibly butch. That's what I wanted.

My parents, however, must think it's a good way of pointing out how different I am from the idea of Girl, and saying how I shouldn't be this way and that I should change and be a good girl.

I hate that. So much.

So, I took a good look at myself in the mirror, and, I liked what I saw! Quickly, I grabbed a board and paper and drew as I saw in the mirror; it shows, with the right hand and the funny posture. But I like this picture. I like my face. I like myself. And I don't have to care who else likes it.

Though, because I like the face so much, I may finish it, one day, holding a bazooka or crossbow or something. Yeah!

--Charissa

Rest!

Finally, some Charissa-time!

Tomorrow, I'm getting a long-awaited haircut; doing some grocery shopping; and spending some long-awaited time with Kevin! We're going to grab a bite and see Hitman at the theatre. Then, I dunno, tea or something (he doesn't drink coffee or hot chocolate). He's so wholesome!

Wednesday is going to be my stay-at-home day. I'm going to do my house work: tidy my upstairs-room, tidy my real (downstairs) room; do my remaining army laundry; start planning where things will go in my (real) room after the carpet/etc gets done (I so need another closet or dresser). And then James is having his housewarming party, and I should go to that, because I said I would. I baked a cake; I hope it hasn't gone bad.

And Thursday, it's back into the fray. I should also probably bring something to the bake sale. Probably. It'd be good of me.


Relationships?

I'm finding myself thinking back to when I was with James. I saw the world so differently then; I was so different. I was so in love! What's changed? I'm colder, I think; less willing to put myself wholly into something lest it backfire somehow. Am I "afraid of getting hurt"? I don't know. I know that my first "boyfriend" hurt me so bad; I was craving any form of validation after we broke up; I learned about pain and maybe that's when I started to be masochistic, I'm not sure.

Anyway.

I fell in love with details. I'm sure that when I see James again on Wednesday, I'll still be in love with his details; much has changed, but much has stayed the same. He still crosses his hands at the wrists like puppies' paws. He still does that physical "closing up" when he's...uncertain and maybe feels vulnerable--I've yet to work out what it means. ... These are things I fell in love with.

I'm sure there are so many other people with details I could fall in love with; but I haven't found them, and part of me is scared to; and part of me is scared they'll be found by someone else instead. Do I feel lonely? Sure--I'm always lonely in Winter. I have been single every Summer of my life. I don't know why; a friend said that at least I'm warm all year round that way, and we laughed. Maybe I just like snuggling, I dunno.

And then there's Kevin.

I don't know. I like the guy. He's charming--he's delightful--but he's also a Virgo. Maybe that's all he is or will be.

So much of me is confused, or at least ambivalent.

I'm sure I'd make a terrible mother; I don't want to have kids. In the long run, I would so love to settle down with another woman; maybe adopt, I dunno. I found myself wishing that James were a lesbian--he'd make a great lesbian, too!--and now the same is happening with Kevin.

On the bus the other day, a guy and girl sat behind me. They seemed university-aged. The guy talked about all sorts of things that were very University-male-esque but also cunning or clever. And the girl replied in very simple-University-girl-esque ways. He actually coaxed her entire history of residence out of her--so smoothly, too! He summarized Punk so effectively! He talked about biking to Mexico! Man! Where do these guys come from?! Now if only women also came that way!

...Which I'm sure they do, but they're probably hetero or spoken-for. Argh.

I have to go to the gay bar again--it'd be so good for me. And gay men are amazing; friendly, hugging and inspiring--"Have a beautiful day!"


Sigh. Sleeeeeeeeep.
--Charissa

Quick update

because I didn't think it worthwhile to make a whole new post.

Went to see Hitman with Kevin. I'm pretty impressed with how he'd bend at the knees and hunch a little so that we were closer to eye-level. And he wasn't afraid to get close to me--face-wise, at least. I don't think he liked Hitman very much; but he's a Film Kid, so at least he can appreciate the cinematography... and the part where Nika is naked but the blanket's teasing and covering just part of her breasts, and then she just gets right out of bed and she's only wearing a thong. We got to see her breasts a lot in that film. "Clearly, this was worth the nine bucks."

13:15 Dec 19
--Charissa!

Last day of school

Today was the last day of school before "Winter Break", and I got to lead the class. It was great!

Something I learned: Saying "Yo!" or "Word!" or "I'm-a get ma shizzle ON!" etc is a very easy way to get the attention of grade ten students. Indeed! One student, in particular, was embarrassed for me :). But it works. It's so outrageous, that they immediately cease all other activity and turn their heads.

We went over the kids' exam first (as planned here). Half the class got less than 50%. The average was 53%. We got through the first two pages before recess. I wanted to finish quickly so we'd have time for their "presents" afterward, so I just picked one of the hyperbolas to graph. They actually stayed the first minutes of recess to see it through.

Recess.

After, I handed back their tests. Not happy. I copied down a summary of How to Complete the Square; after, I gave them the flow-chart.

Handed out the "presents": condensed notes on sketching conics; and "Why Conic Sections are Cool!". Talked about "formula sheets", study guides, condensed notes.

I passed around my first "formula sheet" I ever made. It has taped edges to prevent tearing; sprayed with hairspray to prevent graphite smudging (write in graphite so that you can erase and position everything better); everything is labeled; colour and indents help titles to pop out... Only two things about this are dumb: One, I used pencil crayons, which the hairspray dissolved. Two, I spent too much time making it. On the next formula sheets, I smarted up. No colour, no tape; but the indents keep everything orderly.

I told them about speaking "Ukrainian Math Wizard", and (let's call him) Vasil, my prof for Honours Calculus.

Then, I gave them the One Million Beans problem (but with fixed values), saying that if anyone could solve and prove it, I'd bring doughnuts next class (solution below). The top students (grade-wise) couldn't get it, but two girls who were interested but determined they could not figure it out ended up solving it! Well, not necessarily proving it, but close enough. So I owe them doughnuts next class (January 12).

While they were working on it, I told them an Engineers vs. Mathematician joke; they're on the train, one ticket... They laughed--they got it! Just before class ended, I told them the joke about Mathematicians reducing everything to problems they've already solved whereas Engineers can solve "new" problems with originality. If they don't get it now, I'm sure they'll get it later!


Proof of "One Million Beans" Problem

We know that after the beans have been moved back and forth, each jar still contains P number of beans. Now let's look at the number of red and green beans in each jar:

Jar A has

(P - n) green + (m) red beans = P.

Jar B has

(P - m) red + (n) green beans = P.

Set up equality:

P = P	Number of beans in Jar B = number of beans in Jar A.
(P - m) + n = (P - n) + m	Cancel (P) on both sides.
- m + n = - n + m
2n = 2m	Cancel (2) on each side.
n = m

Therefore,

| n - m | = 0

for all Natural m, n, P, Q < P.


Okay, I have to get up early tomorrow, then work an 8-hour shift. Sigh. Shouldn't have committed to it...

But I'll mention quickly:

I've been blessed with amazing Math teachers over the years, which probably explains a lot about me. Hopefully, this will allow me to pass along that experience to others.

One student remarked how great it was to have a teacher who didn't mumble (which is especially funny because my father teaches the level below and some kids had him last year). Another said I was exciting and that she was having fun. A few others generally remarked that I explained well and was interesting.

And these are the three (recent) things that have made me feel so worthwhile, in chronological order:

1. Finding out my army-boss has harassment issues (it's not everyone--and we're not necessarily bad untrained privates!).
2. My army-boss telling me I look good (dress/deportment).
3. Hearing that the kids enjoyed my teaching.

--Charissa

Quick update

Army

My "boss" called my house the other day, and it was the scariest thing ever. I'm so scared of getting calls from the Military--for every/any -thing, like, "HEY, WHY AREN'T YOU AWAKE?" or "WTF ARE YOU WEARING?!" or silly things like that.

She called for me to work on Wed and Fri, but I had plans Wed... I actually have a doctor's appointment on Friday, but it'd look bad if I didn't work; and I'm learning that being in the Army, image is very important. Sigh. At least, I'm fairly good at bluffing.


Teaching

I'll be in charge of the kids on Saturday! Hoorays! Unfortunately, they just wrote an exam, and it does NOT look encouraging... I wanted to jump into awesome stuff, but looks like I'll have to go over the exams... Sigh.


Plan for Saturday, maybe?

1. Hand back exams
2. Tell: If you have a question about how I've marked your paper, please wait until I've finished going over the solutions.
3. Tell: If you have any questions about what I'm doing, or why, or anything like that, put your hand up; or if I don't see you, just ask me to pause.
4. Go over solutions.
5. Answer questions about papers.

6. Recess should be about now...

7. Tell: I have some handouts that might be useful for studying! If you don't want them, leave them at the front before you're dismissed. I'm also going to show you how to tell what type of Conic Section you have, which I didn't print out.
8. Distribute Handouts: "Why Conic Sections are so cool!", "How to convert to Standard Form", "How to Sketch Conic Sections".
9. Draw: "How to tell what kind of Conic Section you have" flow-chart.
10. Questions?

11. Tell: I'm going to give you some study tips that I've picked up through high school and university.

12. Condensed notes / "Formula sheets" / Study sheets

have the Trig IDs on it

have the Standard Forms on it.

Tell: Every new topic or every month, try to condense as much information as you can onto one sheet of paper. I used to make condensed notes for every unit in Physics, and they saved my arse! Make sure you label everything so that you can tell just by looking what and where everything is. If you're doing one sheet per unit, put a title on that sheet! Use this sheet when you get your review exercise at the end of a unit; use it for assignments. Always improve your condensed notes while you're learning the material--that way, you'll know exactly where to look when you're studying for the final exam.

13. Start: ________ (new topic: graphing polynomials, or logs)

14. Optional: Hand out treats!
15. Dismissal!




Leaving for work now...
--Charissa

Quick Army update

Army Christmas Dinner
(Charissa gushes about a Corporal she just met!)

We had our Christmas dinner tonight, and I sat beside a corporal I'd never met before, and I'm going to call him Cpl Kars. Cpl Kars is amazing. He has this....etiquette, this amazing etiquette. Throughout the entire night, he called me "ma'am", a title reserved for female officers, MWOs, CWOs and Base CWOs.

Sometime during dinner, he and a MCpl got into some sort of argument, where the MCpl said something like, "Come on, I dare ya, I DARE ya!" So Cpl Kars stood up and began walking around the long table to the MCpl's side. At this point, another soldier was standing by the MCpl, so the MCpl said, "I order you to stand still, right there, and--FACE THAT WAY, THAT WAY" to try to keep that soldier between himself and Cpl Kars. Hehe! Cpl Kars ended up jokingly punching the MCpl and retaining his honour. Heeeee...

During dinner, we could pass requests to the head table. Requests were mostly for who would sing what Christmas carol. I gesticulated to Cpl Kars asking if he had a pen; he discretely borrowed one from the MCpl for me, and I wrote a request for anyone who hadn't yet sung to sing. Then I passed the pen back to Cpl Kars, who took it very discretely. A few minutes later, I passed along the note paper, and he took it with such...discrete-ness! A casual observer (from his front) would not have suspected anything! It was amazing! ..I wonder if he's trained in counter-interrogation or something...

He pronounces "Corporal" as "Corp'rral" with the emphasis on the "al", and the "rr" rolled. I think it's a Czech accent.

After dinner, he, Pte Williams and I were chatting. Apparently they took BMQ together. After a while, he excused himself as another Corporal came by our table. Cpl Kars said, "Excuse me. I will accompany the Corp'rral now."

He stands perfectly at attention. "In fine military fashion" comes to mind.

... When I sat down with him and Pte Williams, he seemed kinda shocked or pleasantly surprised that I would come sit with them! Oh, he's wonderful! I like him!

Also, he rolls his "R"s in words like "party".

I will be sad and miss him if he goes touring in Afghanistan. I'm so scared he'll get blown to bits and I'll never hear from him again. Ahhh....


Also

Apparently I'm mature! Whee! (It's too bad I can't tell this story even here, for confidentiality, though. Just, that someone pulled me aside and charged me to be responsible for something, and he chose me because I seem the most wise or mature or "able to tell when something [IS A CERTAIN WAY] and can/will do something about it".)


In other news

I looked at an old photo of James ("old" being almost exactly one year old), and it was so strange--I felt all those feelings come back to me, and they were...different. Wiser? More mature? I don't know. I would still love him--romantically, I mean--if I clapped eyes on him again. I'm a bit nervous for his house-warming party next week.

I went back through my old journal entries from when James and I first started going together... Wow. I mean, I was so articulate and...profound. I bled poetry--it was so easy to write beatifically about his dimples or eyelashes or skinniness or the way he folds his hands.

He is a beautiful human being. I miss him terribly, and in too many ways.

--Charissa

Theology!

So. I was born into a Chinese Christian family, and I was baptized as a member of a Chinese Alliance Church on December 17, 2006; I was eighteen and it was my decision.

Being gay (okay, "bisexual", but I'm beginning to find that word a little clumsy and irritating) in a very conservative Chinese church has its excitements. When I first came out to the English pastor, he didn't seem very knowledgeable or open, so maybe he automatically went to stereotypes (there's a topic I could go on about!) like being anti-gay. And then we talked over the next few weeks, and I brought him up to speed with my "journey" and beliefs.

... I remember, though, one time, we had an outreach, and I brought my buddy Jonathon, who is pretty much an Atheist and a huge jerk. Jon asked about gay people in church, and the English Pastor said, "I would love it if there were gay people in our church!" which said a lot about his ideas of who gay people are.

But, I must admit, he seemed much more open-minded and less "OMG!" when we last talked.


There are a few places in the Bible, with which I have issues. Mostly, they're things like this:

Genesis 3
The Fall of Man

(The Serpent has talked Eve into eating of the fruit of the Tree of the Knowledge of Good and Evil; Eve gave some to Adam; they felt naked and hid; God approaches them and then begins to punish them all.)

My biggest beef here is what God says to Eve in Gen 3:16...

¹⁶ To the woman he said,
"I will greatly increase your pains in childbearing;
with pain you will give birth to children.
Your desire will be for your husband,
and he will rule over you."

Kay, wait. What?

Sometimes I wonder if we've "grown out of the old curses". This is my biggest question, because it leads so many ways...

Have we grown out of some parts of the Bible?

I know the invention of words like "gay" or "homosexual" are very recent to the English language, where their definitions vary. Some cultures have/had very specific words for identities like... "Person who was born male, lives a masculine lifestyle and is attracted to men" or "Person who was born female has been intimate with men but prefers women".

Homosexuality as we now know it was not a concept known to those in "biblical times", so it could not have been written about the way we could understand it. Some would argue that only homosexual actions (and not homosexuality) are written about in the Bible.

So, that brings me back to Gen 3:16. There exists counter-example! ... Therefore...?

I'm not sure how to end that sentence.


Hinduism

I've started watching this television show, when I can spare the time. One episode, the hostess talked with the writer of Dharma, Karma and Much More, which is, from my understanding, a sort of FAQ and intro to Hinduism.

In my setting (suburban, Chinese, Canadian, Christian...), I've not had much exposure to Hinduism, except through the last seasons of Xena: Warrior Princess, so I already respected and admired Hinduism.

What I most love is the acceptance and open-ness. The author even said, "You are Muslim, I am Hindu", meaning that we each go our own way--such is life, and we should accept it!


Community

I like my church, in some ways, yes. But at the same time, I can't stand the social games some of the women play. I can't stand how it's about status and image and how they can gossip and not realize it's gossip!

Haha. My best friend Eric sometimes expresses that he wishes I went to his church, a Lutheran church. I also wish; but it would be like giving up my church. ... Why can't we be less polarized--less set against each other--and more united? Why would switching churches seem like abandoning?


Image

Sigh. I'm not sure if I'm falling for "image" again. Christianity is supposed to be about acceptance, too, since Jesus was a cage-rattler and stood up for those who "got no respect". But Christianity has sort of become the badguy in most people's minds--at least, from what I see and hear personally and through the media. Maybe it's like America--just a few really bad example shake its entire image.

This is one arguments I made about the word "bisexual" when I was coming out. "It's normal, and now there's a word for it!" was my war-cry. I guess my words are coming back to me now; I want to be able to say "I am Christian" without also thinking, "But I'm not one of those lunatics!" I don't know if I can get to that point, though.

Which is not to say that I'll not be/call myself Christian! I won't give up! I just think it'd be easier to be Christian if I were Hindu.


This is something I do pray about--not just talk. I wish it were easier to "be Christian". I know there is a tangible and supernatural force that also created the universe; but what makes me so certain that force is the Christian God? Why isn't that force someone or something else?

Did Jesus exist? Yes, I believe that to be historically true.
Is Jesus the Son of God? Yes, I believe that to be true, though I admit it is harder.
Did Jesus die for me? Yes, I believe that I have indeed done evil, and that my actions have consequence both here and in Eternity (whatever that looks like), and that Jesus took that Eternal punishment in my place.


Sigh.
--Charissa

Conics and my state of mind

Every two months or so, I go kinda crazy--just a little, though. For about five days, I am restless, pouty, petty, dramatic, anxious, confused--all sorts of nasty things. An additional side-effect is that I can believe anything. I won't know waking reality from dreams; I won't know waking reality from things I read; I won't know waking reality from what I want to believe. Added to this, I have a mild fever that's been off and on for about a week.

For anyone who has an idea the state my mind's normally in, you may have an extra appreciation of the mess this stirs up.


Teaching

We've just "finished" teaching Conic Sections to the kids. I'm not sure what he taught, I was marking their papers so they'd know how they're doing before the exam comes.

In S4 Pre-Calculus, we made a flow chart for identifying types of conic sections. I want the students to have it, but I'm not sure what the teacher has in mind.

That being said...

Because Saturday, December 01 is my fitness test with the Army, I might miss part of Math school that day. That's a review class, and I'd be sorry to miss it. One student is even writing the exam that day because he won't be there next week.

Upcoming Saturdays:
December 01

09:00 - Army fitness test at base. Eep.

14:00 - Review class before exam. One student writing exam early.

December 08

14:00 - Exam on Trig and Conic Sections.

December 15

14:00 - Teacher is away and has not given me any specifics on what to do that day, so I have full control of what we do that day! I want to actually enrich* the students' understanding of Mathematics--because we're supposed to be an "enrichment program".

17:30 - Math School Christmas Dinner. Woots.

* Here is what I want to talk about on December 15...

Conic Sections

History

Way, way back, circa 200 BC, there was a Greek named Apollonius, and he wrote a book called On Conics. This earned him the title, "The Great Geometer". The study of conics has been around for a long time! (Will add more later.)

What are they?

Imagine two hollow cones placed together at their points, sort-of like an hour-glass. By cutting different 2D sections of this, you get "Conic Sections".

Taking a slice of a cone, parallel to an edge gives a parabola.
Taking a slice of a cone at an angle such that you slice through both halves, gives a hyperbola.
Taking a horizontal slice gives either a circle or a single point (if you cut at the joining point).
Tilting that circular slice gives an ellipse.

Definitions

A circle is the set of all points** equidistant from a single point. To draw one, wrap a loop of string around a pin and a pencil and draw as far from the pin as possible without tilting the pencil.


An ellipse is the set of all points** whose distance from both foci is constant (ie: the distance from one point to the first focus plus the distance from the same point to the other focus always adds up to the same number). To draw one, wrap a loop of string around two pins and a pencil and draw as far from the pins as possible.

A parabola is defined as the set of all points** equidistant from a line and a point F (the focus) not on the line (see the right-hand side of this image).

A hyperbola is the set of all points whose distance from one focus, minus the distance to the other focus, is constant.

**(in a plane).


Gravity

The path of a projectile thrown (ie: with another, smaller force in a perpendicular direction) near the surface of the Earth is a parabola.

The path the Earth travels around the Sun is an ellipse.

The path of an object (such as a rocket or comet) on an escape trajectory from a fixed mass (such as the Sun) is a hyperbola.


Reflection

The parabola, ellipse and hyperbola each have "focus points" or "foci". If you've ever seen a satellite dish, you have an idea what this means.

For parabolas, an incoming ray that is parallel to the axis of symmetry is reflected toward the focus.

For ellipses, any ray originating at one focus will reflect toward the other focus (this is still true for the special case of the circle, where the "other" focus is the same focus).

Hyperbolas are a bit more complicated. A ray originating from one focus will be reflected and look as though it originated from the other focus (see this image). (There are a few other cases that work out nicely, that I just can't remember right now.)


Light Cone
...Actually, maybe they won't be ready for this yet. But I'll mention it--briefly.


...I should take that book out of the library again...
--Charissa


Further reading:
http://fti.neep.wisc.edu/~jfs/neep602.lecture8.trajectories.97/neep602.lecture8.trajectories.97.html

"Spacecraft Trajectories"

http://mathworld.wolfram.com/Parabola.html

Mathworld: Parabola

http://mathworld.wolfram.com/Ellipse.html

Mathworld: Ellipse

http://mathworld.wolfram.com/Hyperbola.html

Mathworld: Hyperbola

http://www.practicalphysics.org/go/Experiment_386.html;jsessionid=alZLdQlAHb1

"Drawing" a parabola; teaching aid

Some Writing!

http://blog.wolfram.com/2007/05/the_mathematica_behind_televis.html

In my previous post, I linked to Mathworld because it's awesome. Well, I'm linking it again because it's awesome, AND has ties to the television series NUMB3RS, which is totally hoorays!

Also, I thought I would post this snippet from my collection of "smutty Math stories" that I write from time to time. This one is old, but I wuvs it dearly:

Short fiction: Models (Incomplete)

Oh, you don't need any help now, do you?, he asks mockingly. He's leaning low by my side; his face is close to mine, gazing across to the quickly scrawled initial value problem. I finger the corner of the paper, thinking distractedly. I can feel his warmth on my skin. He's closer than I thought, so I don't turn my head to reply.

I've got it, I tell him dismissingly, I've got it... In nervous habit, I press my lower lip to my teeth, biting my lip.

We've been here at least two hours, exchanging questions and explanations and waxing philosophical with our esoteric dialogue. We're indulging in our two greatest pleasures at the same time, and as an extra treat, I'm nibbling some dark chocolate.

He rights himself and walks across the kitchen. He's probably stretching himself out and getting snacks; I can hear him yawn.

I hear him open the fridge and see him, in my mind's eye, for I'll not indignify myself by staring. I wonder what he'll get. He'll always find a way to pleasantly surprise me. At least, until I can recognize his pattern.

I used to intimidate people with the way I predicted them. If I wanted a favour done, I wouldn't ask, but tell the person, "You're going to get me a large coffee from the cafeteria if I give you three dollars." Usually, the first reactions are to take offense and rebel against my suggestion, but I wouldn't have said it if I thought it would not work, and, with little effort on my part, she'll bring me my coffee, and my $1.50 change.

Wilbert was the first--and only--person I could not accurately predict. The first favour I told him was in Math class. "You'll bring my exercise book?" He looked at me as though trying to understand my own pattern, and then went off to fetch it, with a slight smile. But when he returned with the book, he did not give it to me. Instead, he stayed standing at my desk, reading the exercise book casually.

"'Exercise fifty-eight," he said, "question one."

He had a soft voice; soothing, really, but simultaneously evocative.

"'Find an acute angle x such that tan of ninety minus x equals cotangent of eight plus one-third x.' Hm, now that looks like a fun question. Let's see. Tan is sine over cos, and cotangent is cos over sin. Cross multiplying gets the sines and cosines on different sides, but if they're moved to one side, it makes a cos double-angle identity, and from there..."

And I just stared at him.

His mind was so analytical; always calculating--but in a haphazard and chaotic way, which still let him appear calm and intense. Finding his patterns would be the most captivating and satisfying task I'd set for myself yet. Not that I'm obsessed.

I have an unfinished model. It works, but it is flawed. It can predict 90% of his actions, but not thought process behind them. I think I can refine this model by the end of the month. It has taken too long already.

...to be finished at some later date.

...later
--Charissa

Quick Update

Origami

For my birthday, I received an Origam gift box and extra book from Mark! OMG! The gift box has printed paper (strange and elegant designs that remind me of wallpaper), gold and silver foil paper, a protractor, two 'bone' crease tools (one for making sharp creases, the other for "drawing" the crease patterns), a square board with grid and markings on it, and an origami instruction book. I'm only a little irritated that both books contain mostly diagrams that are reliant on cutting paper.

This is mostly an announcement that, as soon as I get my camera, I'll be posting picture of both the modular origami polyhedra and the new models--animals and flat geometric patterns. Man, I can't wait to get that camera!!


Teaching Math

I've been in correspondence with one of the students who had questions about exponents/roots, and after the two weeks between classes when I was helping her with that, she wrote back to say I'm a good explainer! That totally made my day!

We started conic sections on Saturday with the Circle and Ellipse. At the end of class, the teacher wrote this on the board:

"Next week: line, parabola and hyperbola."

The students had mostly never heard of hyperbola, and some never heard of parabola. The teacher said to look it up on the Internet, and I wanted to jump up and say, "MATHWORLD DOT WOLFRAM!!" but of course, that would have been inappropriate, so I didn't. Sigh.


Film Festival

One of my friends has a film in a Canadian film festival, and his film made it as far as a public showing! I'm so excited! I'm going to the showing, hopefully with a friend who is/was a major artistic-film-maker-type-person. In truth, I wonder if she'll like my friend's film, but I invited her mostly for the other films. Heh.


Army

My unit did a field exercise this past weekend. They slept outside with little form of heating for two nights. Yowza! I went on the last day to help with breakfast and tear-down. Man, I suck at moving things. I definitely need to work out. But with the army, I get a personal trainer and access to the gyms, so I'll have to make use of that. Sheesh, though, I wish I had more free time...


Art

I'm donating Boobfest III to the queer student group at the university I used to go to. At least, I'm donating a print--and I think I'll take it back at the end of the school year.

Also, that student group is planning on booking a small art gallery in one of the centres at the university--there's this glass room beside a major traffic junction and across from a Tim Horton's / food court, I think, which is totally a great place to put an art gallery.

If we end up booking it, I'll totally submit: my nude pieces; the Origami I'm proud of (goldfish in the bowl!!), including an enclosed chain of connected coloured boxes that are ordered to make a rainbow (sort of; I'm missing a real *purple* but I have this dull mauve thing); and any other artwork I deem public-worthy--which is not much, so I'll have to get busy making more, dammit! Mmm, I'm excited!


...Will update this entry with links and text formatting later.
--Charissa

Novemberance!

As a kid, I used to call today "Novemberance Day" and even wrote a terrible poem about it, once. I dunno, I never had a particular attachment to Remembrance Day. In school, one of my good friends, Diane, had/lost family in the World War/s, I can't quite recall.

But as a member of the Canadian Forces, I was at one of the many Remembrance Day ceremonies across the city. Of course, I have no training as of yet, so I was, at most, a spectator standing with some higher-ranked personnel who told us untrained Privates when to stand at attention, remove our headdress and so-on.

A few things were prominent today...

I know it shouldn't be funny--especially not today--but it can be rather hilarious when you actually see soldiers--mostly Cadets--pass out while standing on the parade ground. I was told that it's quite common, especially with the Cadets, for soldiers to get dizzy and pass out from standing for about two hours--especially the Cadets, who are often so nervous that they "thunder"; fall, stiff as a board, flat on their faces. One guy from our unit even fell on his face; and then began crawling about as though uncertain of where he was. I was told he lost a contact lens in the process.

My "boss" is disgusting. Really, she is. She's short, skinny, butch, loud, irritable, vulgar, and disgustingly, disgustingly hetero. I really did not want to hear her talk about condoms nor "sword-fighting" in her mouth. She reminds me of a girl I knew in high-school, except she's an adult. I want to believe that she's just disgusting when she's in uniform, it's her coping mechanism or something, but she makes me want to vomit--I can't believe she's a soldier! Does she have dignity? IT SURE DOES NOT SEEM SO!

I do not have to adopt a new lifestyle. Here is (sort-of) a summary of my thinking:

- I'm in the Army, hoorays! I'll have discipline!

- Oh, I'd better watch and learn from observation!

- Gee, this is a lifestyle thing!

- I'd better bring Army elements into my Civi lifestyle!

- Son-of-a-bitch, I'm getting a soldier's mouth!

- Hey, my "co-worker" has morals and refuses to profane!

- That is freaking awesome!

- I'm not going to profane! Nor drink--the way they do, at least.

- I don't have to be like anyone else! I'm special!

So, hoorays!

Remembrance Day is important! This I already knew! It just feels... more ceremonial--of course--now that I'm in the CF.

The Remembrance Day ceremony was Christian! Some of our speakers were very... "We are fighting Evil!" which made me a little uncomfortable. We fight Evil, yes, but it is not... We don't... We aren't to be "Holy Warriors", I think. I think we should never be "Holy Warriors". ... Sheesh, this is difficult to put into accurate words!!


In other news...

I found out something interesting the other day. I'm not yet going to say what, because it's not my story to tell; but it made me both excited and... Clingy. I mean, it's a bad thing to be excited over this. HONESTLY.

Also, at the Maths school, we gave out a rather fun-looking assignment. I do and don't look forward to marking these! They're all long-answer involving Trig Identities. Sigh. While it'll be exciting, it'll also be messy and headache-inducing, I think. Woots!

Also, I took out a book on Modular Origami from the library! I've already made a stellated icosahedron. Woots! I think, after I finish making some of the models in this book, I'll move onto this project! Bwahah!


That's all for now. I might update later with fun trig stuff.
--Charissa

Art and Stuff

I realized, the other day, that I'm not making as much art as I would like. And since Autumn passed me by uncaptured (by camera and canvass), I decided the next piece I do will be "epic" and about Autumn! Here's a "sketch" I've made of it in Flash MX.

(I still can't believe Adobe bought Flash... The version I use still says "Macromedia Flash MX" on it.)


New Loading Screen on Intro to Epsilons and Deltas

Also shown here.

Epsilons and Deltas is a little animation that I've been working on for about a year. It's a short story about Math and Love. Awwww. It also features two girls, a strip from xkcd, and La Campanella by Franz Liszt.

The old loading screen didn't have red-bowtie-girl running along the loading bar; she just stationary-ran beside the percent-loaded display, and it looked a little tacky. This one has a nicer "floaty" and "Ooh, numbers!" feel to it, which I don't mind at all! But, we'll see if I can even still improve it...


Other Stuff

My eldest brother went back to school in January, and has asked me to help him out with derivatives! I think I'll do another of those Flash tutorials like in the previous post.

He's also sending over a box of goodies from Germany! There'll be Lebkuchen, my favourite kind, with the candied orange peel inside and wafer on the bottom and either dusted lightly with powdered sugar or coated in chocolate! Mmmm! Also, a digital camera and computer gear!


Events

Nov 01

I'm Employee of the Month! Hoorays, I guess!

Nov 05 (today!)

Grocery shopping. Hells yeah.

Work at the Reserves tonight. Hells yeah...

Should call the bakery to pre-order special bagels.

Should drop by the library to return Dragons in the Water by Madeline l'Engle; and take out another Origami book and Math book.

Nov 06

Meet up with the teacher to lend him the entire S4 Pre-Calculus curriculum... I'm wary of lending that to anyone, and of all people, him...

Should swing by the bakery for more bagels... Mmm, pumpernickel bagels...

Also hoping to spend some good time with my best friend Eric!

Should also swing by the Rainbow Pride group at the university. I haven't been there in ages--mostly because I'm trying to avoid someone.

Nov 09

Kevin's birthday party, at last!

Nov 10

Homo Hop, a queer-oriented social. I'm not sure if I'll go... We'll see.

That's all for now. I should get some work done today.
--Charissa

018: Exponentiate!

Woo! Just a quick update to post this tutorial (Flash) on exponents/radicals. Check it out here, too!

Woots. Off to work now.
--Charissa

Issues

As much as I want to keep this from being angsty and personal, I sort-of want to write about my state-of-mind.

I've been so apologetic ever since getting the survey job; I haven't spoken fluently and with conviction, it seems, for ages. My sentences are full of "maybe"s and "I think"s and "I believe"; and "it might be"s; and more "like"s than ever before.

I wonder if it's mostly a self-confidence issue, or if it's something else?

I also wonder if doing more proofs will be helpful in gaining more self-confidence. Probably will!


Week so far:

Oct 29

I'm now 19. Hoorays, I guess. For my birthday, I paid $200 in Utilities.

Oct 30

Learned how to properly wear my Army uniform! Woo-hoo!

Had my first "class" in the Army (Dress and Deportment; and Rank Structure).

Oct 31

Started playing Brood War again. Sigh. What a wonderful way to waste time.

Received e-mail from the teacher, who said I should go over the Quiz in class with the students--WHICH IS OMG HOORAYS!!

O, Time...
--Charissa

Webcomics and Teaching

Webcomics

So, I read Irregular Webcomic!, a webcomic run by DMM, pretty regularly. And often, there are totally geeky annotations, including (to point out only a few)...

here, where the joke involves vector calculus;

here, talking about the impossibility of StarWars using Thermodynamics;

here, explaining three Laws of Thermodynamics;

here, explaining how awesome Maxwell's equations are;

here, using the Shroedinger's Cat idea;

here, making Quantum Mechanics jokes;

here, making Fourier Transform jokes;

and now, here, using History and Math!

I hearts this comic so much!

Also awesome in the Math department is xkcd, by Randall Munroe! I've even used this comic in an animation I'm working on.



Teaching

So, being Saturday again, I went to the Maths school to TA; and, again, it aggravated me. But we had a meeting today, and our principal mentioned some of the duties of the Teacher and TA, which I was wanting to beat my teacher over the head about.

Some things mentioned...

Our school's philosophy/signature: Since we have such a high student-to-teacher-or-TA ratio, we have a "human element"; there is more human interaction: student-teacher/TA and student-student.

Roles of the Teacher and Techniques:

• don't lecture
  
  the kids are 13 and younger, they can't handle lecture-style yet!
  

  create lesson plan
  

  have authority
  

  avoid dead silence; talk! Fill the silence with teachery sounds!
  

  don't talk into the board
  

  do not read lesson plan
  

  don't work out of a textbook
  

  never lose face
  

  never let the student "win"
  

  lose once, lose all

Roles of the TA and Techniques:

• don't supersede the teacher
  
  if the teacher's wrong, don't point it out, no matter how frustrating
  

  make sure the students pay attention
  

  encourage participation
  

  supplement the teacher
  

  interact with the students; learn their names

Tips for Creating Lessons:

• don't copy down examples or problems
  
• not just formulas
  
• walk the students through it all

My birthday party

My birthday parties have been nick-named "Awkwardfest", but this year was pretty okay. In fact, we had a focus on awkwardness, and I even donned my "Awkward Fairy" costume (it's skimpy black spandex with a hole shows off what would be cleavage on a more endowed woman, and a black tie worn over the hole). Awkward! Especially when one of the guests flips the tie up!

But it was good. Kevin and Mark came.


Other Stuff

There's a guy at work who makes tobacco smell handsome. Or, maybe, just the way it smells on him is handsome. I don't know.


--Charisa

Arrrrmy

Fitness test went well yesterday. I just want to make a list of reminders for next year:

• bring a lock
  
• bring change of clothes
  
• bring an extra bra
  
• there are showers we can use
  
• wear blue
  
• bring a headband (or stop sweating so much)
  
• don't drink booze the night before
  
• sleep well the night before
  
• limit caffeine intake that morning
  
• sign in at the Armoury before heading to the Base

I passed, barely. First was the run / beep test. I needed a minimum of level four; made it up to four and a half, but that had me so beat. After a cool-down, during which I scared the staff because my pulse hadn't come down (my rest HR was 88 that morning!), but it turned out fine. ... I'm pretty sure I could have done better if my heart rate wasn't so high (ie: if I weren't still asleep but running on adrenaline and caffeine).

Next was a grip test, and I passed that, too. After that was a push-ups test, which was the biggest threat to my passing. I managed to meet the minimum, but only because the coach/examiner let me get away with push-ups that weren't quite up to standard (ie: I need to go lower). Finally, there was the sit-ups test, which I passed quite easily (no surprise).

My Results:

Resting Pulse (bpm)	088
Resting Pressure	Systolic: 112	Dyastolic: 062
20 MSR
	Last Stage Completed	4.5
	Minimum:	4
	Predicted VO2:	34.2
Muscular Strength
Right Hand	36	34
Left Hand	36	34
	Total:	72
	MPFS:	50
Muscular Endurance
Push-Ups	9	MPFS: 9
Sit-Ups	30	MPFS: 15

Statistics Canada

When I got home, I found that Statistics Canada had called and left a message, so I called them back. Turned out, they were having entrance exams again that night, so I went.

Unfortunately, I didn't realize I was still expected to go to work at the Reserves that night! And I had no idea the procedure for calling in to let them know I wouldn't come! So, of course, I got a (short, thankfully) lecture on that today--but I'm getting ahead of myself.

I wrote the StatsCan entrance exam and they called later to inform me I'd passed (wasn't worried for a moment). I have a job interview on Thursday at 13:00.


I got my army gear today!!!

That was all kinds of exciting! I'm worried, though; because there was no sign-in sheet for me... It's not so much that I care about getting paid, but I don't want to muddle up their paperwork/system/etc. ...I'm a little worried...

I got quite a scare when the phone rang at 08:05, and it turned out to be someone from the Armoury. She said she'd gotten the appointment wrong, and that it was actually at 09:00 instead of 10:00. I told her my bus was leaving in three minutes, and I'd arrive at the Armoury at 09:15. She said that wouldn't be sufficient; but she'd call the Clothing Store to double-check. I was so worried that I'd miss the bus; but she called back immediately and my appointment was actually 10:00.

We went out to the Base (the difference between a Base and Armoury is mostly this: A base is an area and many buildings, where an Armoury is one building for a few units) where the Clothing Store was.

I rode in a truck (of some kind) with my "boss", MCpl E--. She spoke very sternly to me, and explained, "When you join the army, you're a Private, and right now, you are the lowest of the low--yeah, you're actually the lowest one in the Armour right now. Everyone who is higher than you--that's everyone--you have to treat with respect. I'm not your friend, I'm not your buddy, I'm your boss. [The recruiter] isn't your friend either. She's friendly, because she recruited you; she's got to reel you in, you know what I'm saying?"

This, I find a little strange--not her personally, but the... "unfriendliness" aspect. I can only make friends with those in my rank--three other Untrained Privates--apparently.

Aside: I'm reminded of my first day, when there was mostly lounging around and no real work for me. I went with the rest of the Unit to the Junior Mess, and someone called one of the girls I was with "a bitch" in a sort of joking manner (why are soldiers so profane?); and I said back, in "a sort of joking manner", "Y'know, if she were a guy, you wouldn't have called her a bitch; you wouldn't even call her a bastard or anything else, because there's no male equivalent of bitch in that sense; and you only call her that because of the availability of the word. Like, I couldn't call you a bitch. 'You are a bitch!' See, it doesn't work!"

Of course, everyone laughed and some people even looked strangely at me, as though wondering where that all came from, or how dare I, or something like; but I'm wondering now if I was actually out of line. It was pretty casual, though... But I'll try to be more mindful of ranks from now on.

Of course I knew this in the back of my mind, but it's much more vivid when getting the talk in that tone of voice like you've done something wrong--which, I had, since I didn't inform anyone that I wouldn't show up to work yesterday. She said that I and the three other Untrained Privates would be getting "shit work" to do--and that, since she's in charge of us four, she'll make sure we get "shit work", because she has an Education degree, civi-side, and she knows what's she's doing, and this is how it works. ... Sobering.

Getting my gear took about an hour and 45 minutes, and it was all kinds of exciting! MCpl. E-- spoke in a completely different tone to the Supply Clerk we met up with at the Clothing Store, and I got a taste of this inter-rank thingummy; though the Clerk was friendly and professional with me (I wonder how much of that was in her job, too).

I filled a large bin with gear (the SC said to try to keep track of what she gave me, because I'd have to sign for everything, and if for some reason, she forgot to give me something, and I'd signed for it, the onus was on me); tried on different sizes of uniforms and equipment (OMG I am so excited about the boots, you have no idea!); and when that was all done, I was given three garbage bags to carry it all.

Naturally, there were some items that would've been stupid to put into the garbage bag--namely, this large bag (hockey bag size) into which we'd already stuffed a lot of gear; the box containing my boots; the sleeping bag; etc.

I hope I--well, not "impressed", but--showed MCpl E-- that I wasn't inefficient or stupid or unfit; and I hope-hope that she saw I'd be a good soldier. While putting my gear into the bags, I was thinking what should go where; how heavy it would be; where the bag it should go to minimize protrusions and rips... I may have goofed it in the end, though; because at the bottom of the bin (which was about four and a half feet tall) were some smaller items that I could not reach with my arm; so I first tried standing/leaning on one leg, and when I saw that wouldn't work, I gave a sort of goofy and embarrassed smile to anyone who might be looking. And then I tilted the bin and got my stuff in the smart way.


I'm sort of that way, now. I smile a lot, I'm...friendly, not an intimidating soldier--ARRR! I smile a lot. When someone is speaking--about anything, almost!--I smile to acknowledge my understanding. I think I should try to nod instead; or blink decidedly; or, I dunno, something. Maybe smiling is unprofessional?


And then, I waited for Mark and Evan to pick me and my gear up. After all the packing, I had: three full garbage bags, a large green carry-bag, a small/medium green carry-bag, my backpack and my jacket. I definitely would not have been allowed to take these on a bus!


And now, I'm tired and my hands are cold and I'm still sore from the fitness test yesterday. I should buy some bananas and find a work-out buddy.

In the meanwhile, I'm going to have Mom's beef soup and play Grim Fandango.
--Charissa!

Checklist and Dream

I want to make a checklist of things never to do as a teacher. The first item on it will be: "End a sentence with 'Right?'" I wonder how obvious is my inspiration.

Never:

• End a sentence with, "Right?"
  
• Ignore advice or suggestions.
  
• Think I know everything.
  
• Think I don't need help doing anything ever.
  
• Touch a whiteboard with my skin.
  
• Lie.
  
• Be half-assed.
  
• Not have a lesson-plan.
  
• Use someone else's lesson plan without going over it beforehand.
  
• Ask if material is either too easy or too hard.
  
• Talk loudly when frustrated.
  

Avoid:

• Talking about teaching when students are nearby and still.
  
• Silencing students--especially when it's not affecting the entire class.
  
• Treating everything as though within my power.
  
• Treating everything as though out of my power.
  
• Talking just outside the classroom door as though it were private.
  

Endeavour to:

• Be available.
  
• Be responsive; quick to respond.
  
• Be helpful.
  
• Be enthused (no problem there!)
  
• Use many methods.
  

I had a dream this morning

I had a dream this morning, about someone from "long-ago". I've blogged about him all over the place, always trying not to use his real name, so I guess I'll do that again. Let's call him Lexus, because he's luxurious in a sort of way.

Backstory:

When highschool started for us, Lexus came to our school for Grade Nine Math although he was in grade eight; and for the rest of my highschool career, it was that way. In grade nine, though, everyone called him smelly and a grade-eight-er and a show-off; and it was mostly true.

From what I've gathered: he played chess competitively until about two years ago; was a lifeguard; was very athletic, being on volleyball and curling teams; played baseball in the summer; had terrible communication skills; liked to be well-read; had an amazing imagination / ability of imaging; and, of course, was fantastic at Math.

Around grade eleven, he joined the school choir, and this is probably when I first noticed him.

I mean, during the annual Jazz festival, I had taken a photo of him sleeping on the bus; and I had already noticed that he played trumpet in a very precise manner and as though there were something very funny--a sarcastic "inside-joke"--to his precision. But I had never paid much attention to him until he joined the choir.

Being one of the few male voices, his seat was near the back, and it happened that he stood almost directly behind me. His voice had the same sarcastic timbre as his trumpet-playing, and Chris once had to point out to Lexus that it isn't by forcing that you sing lower and better tones!

So, I heard his voice more. And I also saw him more (though I'd seen him in Grade Ten Pre-Calculus), and through this, came to be infatuated.

Then, in my graduating year, there was a slight problem in my schedule. Because of the courses I wanted, I was forced to take Pre-Calc before Calculus. Of course, my previous grades and having a father who teaches Math (badly) once a week quickly convinced Admin that this would not be a problem. It so happened that Lexus had the same happen to him.

We took Calculus together, then; and somehow, the three of us with this scheduling conflict sat mostly alone on the same side of the class (it was a small class, about fifteen).

Obviously, he began to mean something to me; I noticed and fell in love with details of him--the way his hair made his eyes sharper; the curve of his nose; the way his facial hair started simply as fuzz on his chin.

I also started a graphic journal, because I wanted to capture details. Fridays were our treat-days, where we all took turns bringing treats. One day, we had chocolate pudding--or maybe Lexus just brought his own, I forget--and he spilled some on his bright yellow shirt. I heard a slight commotion, and turned to see; he and lifted his shirt to his mouth to clean it off; and, lest I be obvious, I had to turn back, when I saw his abs.

I eventually wrote a journal entry, which turned out to be a poem:

Math and Symbols

I'll be sitting in class, and you'll
be behind me, where I can't
mentally undress you.

Not
that it stops me from trying, but
it would be so much more satisfying,
I think,
if I could stare at your body. Or
at your face while you
puzzle over a new problem.

I love that expression on your face:

It's not quite "relaxed",
it's not quite "intense",
but it's almost
pouty,
as though all the
muscles in your face just went dead
and limp like
your entire being
is focused on the problem
and you can't spare the energy to look
awake.

You make me want to shout and sing and
write bad poetry,
but I don't feel words can actually
articulate all that I want
to express.

I want
to write it out in large and esoteric
math and symbols:

"YOU ARE THE LIGHT OF MY MIND, YOU INSPIRE
AND CHALLENGE ME, YOU KEEP ME BURNING, AND
ALSO, YOU ARE GOOD-LOOKING."

But I wonder
what you would think of that,
and, if I gave you that
paper with my heart translated
into math and symbols,
would you find me odd,
and then not
be the same person you
were
in my head?

Eventually, I realized someone was going to notice the way I couldn't even look his direction with a straight face.

I wrote him a letter to a similar effect as the journal entry, mostly pointing out that I found him attractive (mentioning a few to show I was serious); that I just had to tell him because I didn't want rumours; that if he had a significant other, I didn't mean to interfere; that if I was being too bold, he should let me know, because, "since when are you afraid of girls?"

This was pretty disastrous, but not at first.

It was entirely my fault, because he didn't send any sort of reply, and I ruined the whole thing a few days later by first giving him a "secret" note telling him I'd phone tonight, and then phoning.

When I'd been put through to him, he said slowly that he was going to tell me that tonight wouldn't be a good night to call. It was then that I learned he had a girlfriend; and my lack of response betrayed my expectations. I think I managed to say, "Oh," and, after a pause, "Have fun with that". I forget what happened immediately after, but we eventually hung up and nothing was much changed, save that I couldn't look his direction for embarrassment instead of infatuation.

I'm not sure what happened after I graduated. In University, I heard short second-hand stories about how he had a girlfriend, and such-and-such happened to them, so now such-and-such took place. I visited the highschool once--a class he took, too. He made a point of announcing something about his girlfriend--but, at this time, I was dating James anyway.

I've heard from someone he used to play chess against, that perhaps he's now in the University of Waterloo, and wouldn't doubt it, with his brain.

The Dream

The dream was confusing, and I remember only to parts. The first part, there was Lexus, James, some others, and me; and we were at some sort of social gathering; and, for some reason, I had to keep it unknown to James that I had a thing for Lexus; and Lexus was making that very difficult, because he flaunted all the things I'd adored. Somehow, the topic turned to hair and sideburns--not quite sideburns, but the hair that grows over top your ears--and I'd called Lexus a hypocrite because he had that, too; and I'd grabbed him by that hair and I think I kissed him.

The other part was after the party, when Lexus and I were alone for some reason. And I remember thinking to myself, "You're not real, and if you kiss me, it won't feel real--I won't be able to feel your lips, your heat, your movement--and I must really stop imagining you." And hen he kissed me, and it felt entirely real--texture, heat, motion and all. And then he asked me if I wanted him to stop being real, and I don't remember what happened next.

Eventually I awoke, very confused because my mind, body, heart and spirit were all pulling in opposing directions so that even inaction fell into one of them.

I'm not sure what to make of the dream. This is the second dream I've had where someone I either love or am in love with has asked me whether it would be okay to be romantic. If anything, this should be a symbol or warning of my own indecision; but it doesn't help that I know not where to go.


I'm not going to let it worry me too much yet. More urgent is:

Tuesday 09:00 - Fitness test

Wednesday 10:00 - get Army gear!

Friday 18:00 - my "birthday party"!

Adieu!
--Charissa

Gnomes!

There exists love!

I'm not sure why, but I felt inspired to do this again. "There exists love" was my gnome last year, and it suddenly felt appropriate all over again! As I waited in a bus shack tonight, I wrote that in the dust on the panes. And then I wrote "there exists truth", "there exists beauty", "there does not exist silence in bus".


Also--Chinese people are hilarious--there's a Chinese saying that goes something like this:

"I can't poo, the ground is too hard."

Translation: People can think up the strangest excuses to avoid work. Also: Chinese people are hilarious!

And if you are Chinese, you should try this at least once with your White friends:

Hover around an intensely shallow conversation, and when the chatter allows, step in wisely and speak thus, slowly and with a heavy Chinese accent, and maybe punctuating with deliberate gesticulation:

"Ancient Chinese wisdom: Man with one chopstick goes hungry."

And then leave.

Ironic Phrases I've collected over the years

- I hear he's a real gossip!

- None of us like to generalize.

- I hate intolerance!

- You're not very suggestible, are you?

- You're making assumptions!

- Everyone's a pessimist!

- It's good to have standards!

- I bet you're prejudiced!

- You need to be more open-minded!

Reading/sleeping time!
--Charissa

Numerals and Teachery Things

I took out the book The Abacus: a pocket computer from the library (because my brother had gotten me an abacus for my 18th birthday, or Christmas, I forget). In the chapter "The Ancients", it discusses ancient number systems, most of which I'd already heard about in "Mathematical Sorcery".


There was an explanation of Babylonian numerals and Egyptian numerals, as well as others; but what I didn't know was the meaning behind the Egyptian numerals, and this book explained some.

After some quick Googling, I've found three slightly different interpretations of the symbols:

1. http://members.tripod.com/kangwei1a14/egyptian.htm
2. http://www.recoveredscience.com/const102egynumerals1.htm
3. this book.

Picture	Explanation 1	Explanation 2	Explanation 3
	A rod.	Upright.	"just a vertical stroke, not much different from [our 'one']."
	Cattle hobble.	Vault.	Heel bone.
	Coiled Rope.	Rope coil.	Scroll.
	Lotus flower.	Lotus.	Lotus flower, "a plant the Egyptians loved."
	Finger.	Finger.	(None)
	Tadpole.	Tadpole.	(None)
	God with raised arms.	Heh-god.	"a man holding up his arms in amazement. To the Egyptians, one million was a tremendous sum."

Awkward sidenote

My good friend Mark told me about this assignment he had (a long time ago), to convert Babylonian numerals into Greek or Roman or something. When converted, the numbers spelled out the words "clitoris", "penis" and "airplane", which confused the heck out of him!

Aren't numerals fun?



I watched the movie Proof last night.

It sucked. It was almost good, and maybe if it hadn't been so "Hollywood", it would have been better; but it truly, truly sucked. Also, movies in which getting it on is part of the actual plot tend to suck.

Plot summary:

• Girl thinks she's crazy, because her dad was a crazy mathematician, now deceased.
  
• Boy is going through the deceased dad's work.
  
• Boy and girl have sex.
  
• Girl has a proof she wrote, but nobody believes she wrote it, not even the boy.
  
• Drama!
  
• Turns out, she wrote it; and maybe she's not crazy after all!
  
• Reconciliation with boy!

Did I mention the movie sucked?



Teaching

As usual, Saturday was another day of TA-ing for the Maths school. We've started on Trigonometric Identities, and I don't think the teacher adequately taught what an identity is; nor what a proof is. He later asked if this was too easy or too hard, and nobody responded.

Sometimes, I want to just jump in front of the class and tell him to shut up, and start teaching. But, the principal must have hired him as a teacher (instead of me) for a reason... At least, I hope there was a reason other than "he's older, so he'll be the teacher."

I think we should walk the kids through what an identity is; walk them through a few proofs. I'm marking their papers, and I can tell that a few just have no idea what's going on. Someone wrote "1 / 0.5" as a final answer, which is wrong on so many levels!


The format I'd like my students' work to follow

Question number. Question

Work Work Work

/ Side computations / Side computations

Answer

That would be just amazing and so much easier to mark. Maybe I'll have to make photocopies from now on, just so it's easier to explain this to them. Yeah, I'll do that--I'm going to do that RIGHT NOW!

--Charissa!

Cars vs. Goats

There was an episode of NUMB3RS (113 - Man Hunt) that included a brief explanation of the Monty Hall Problem.

Monty Hall's "Let's Make A Deal" is gameshow where you choose a door to win either a goat or a car--the objective being to win the car.

Wikipedia has a pretty thorough article on the Monty Hall Problem, but I want to make my own little problem and proof using PMI, because I wuvvy wuv wuvs PMI so much, yes I do!


Cars vs. Goats (AKA: Monty Hall Problem)

Suppose there is a gameshow in which the player chooses a door. Behind any door is either a goat, or a car; and the objective is to pick the door with a car. After a door is chosen (but not opened), the host opens a door, behind which is a goat. Theplayer must then make a choice: stay with the chosen door, or switch to another door.

More specifically, let's deal with the case where there are c doors and only 1 car. That means, there are c - 1 goats, and the player can choose to switch to one of c - 2 remaining doors, with the objective of finding the car.

Scenario One: c = 3
In this case, there are three doors, and suppose the car is behind door three. There are three initial choices the player can make: door one, door two or door three. Then, the player can choose to either switch or stay.

Here are the results:

initial:	1	2	3
switch:	Car!	Car!	Goat
stay:	Goat	Goat	Car!

If we look at the switch row, we see that 2/3 result in cars.
If we look at the stay row, we see that 1/3 results in a car.

Thus, it is better to switch when there are three doors and one car.

Scenario One: c = 4
Let's suppose the car is behind door number four. The only real difference now is that there are two possible switch choices, but that's easy to take into consideration.

Results:

initial:	1	2	3	4
switch1:	Car!	Car!	Car!	Goat
switch2:	Goat	Goat	Goat	Goat
stay:	Goat	Goat	Goat	Car!

Looking at both switch rows, we see that 3/8 result in cars.
Looking at the stay row, we see that 1/4 results in a car.
Since 3/8 > 1/4, switching is still a better choice.

The remaining cases
Let's skip over the details of the next few cases. Let S be our probability of success in finding the car when choosing to switch, and c be the number of doors; still having only one car.

Summary:

c	3	4	5	6	7
S	2/3	3/8	4/15	5/24	6/35

Noticeable patterns:

• S_c = (c - 1) / [c (c - 2)]
  To simplify things let's separate the Numerator and the Denominator,
  
  let N_c = c - 1
  
  let D_c = c (c - 2)
• N_(c+1) = N_c + 1
  
• D_(c+1) = D_c + 2c + 1

Proof of pattern of S:

1. Prove that N_(c+1) = (c + 1) - 1

First, look at the best case of N_c = c - 1, ie: when c = 3

N₍₃₎ = (3) - 1

N₍₃₎ = 2

This is true!

Now prove all following cases are true; ie: prove N_(c+1) = (c+1) - 1

N(c+1) = Nc - 1
N(c+1) = (c - 1) + 1	Substitute.
N(c+1) = c	Simplify. Hoorays!

2. Prove that D_(c+1) = (c+1)(c+1 - 2)

First, look at the best case of D_c = c (c - 2), ie: when c = 3

D₍₃₎ = 3 (3 - 2)

D₍₃₎ = 3 (1)

D₍₃₎ = 3

This is true!

Now prove all following cases are true; ie: D_(c+1) = (c+1) (c+1 - 2)

D(c+1) = Dc + 2c - 1
D(c+1) = [c (c - 2)] + 2c -1	Substitute.
D(c+1) = c2 -2c + 2c - 1	Expand.
D(c+1) = c2 - 1	Simplify.
D(c+1) = (c + 1) (c - 1)	Difference of Squares. Hoorays!

Therefore,

S_c = (c - 1) / [c (c - 2)]

This doesn't really mean anything relevant yet, though. We've just proven that we always know our success rate, and not that switching is better than staying. Let's look at the staying data now.

Let T be the success rate of staying, and we'll compare with S.

c	3	4	5	6	7
T	1/3	1/4	1/5	1/6	1/7
S	2/3	3/8	4/15	5/24	6/35

Pretty dismal, eh? Let's prove that S > T. But first, we must prove that T always follows a pattern...

Patterns noticed in T:

T_c = 1 / c

T_(c+1) = (T_c) * c / (c + 1)

Prove that T_(c+1) = 1 / (c + 1)

Best case: c = 3

T₃ = 1 / 3

This is true!

All following:

T(c+1) = (Tc) * c / (c + 1)
T(c+1) = [1/c] * c / (c+1)	Substitute.
T(c+1) = c / [c (c + 1)]	Multiply through.
T(c+1) = 1 / (c + 1)	Simplify. Hoorays!

Prove that it is always better to switch:

Here's the final piece! We must prove that S_c > T_cProof by Contradiction.
Go!

Sc	<	Tc	Assume.
(c - 1) / [c (c - 2)]	<	1 / c	Substitute.
c (c - 1) / [c (c - 2)]	<	c / c	Multiply by c.
(c - 1) / (c - 2)	<	1	Since c > 2, this is most definitely false! In fact, (c-1)/(c-2) cannot even be equal to 1.  It is always greater than 1.   Since all our steps after the initial assumption of Sc <>c, that assumption must have been incorrect. Therefore, Sc > Tc  for all integers c > 2. Hoorays!

Thus, it is always better to switch.


I'll write something more journal-like later.
--Charissa

Dreams

Around spring this year (2007), I noticed I wasn't feeling the same. I felt normal, but, somehow, less something, and consistently so. So I went to the doctor, and was prescribed thyroid hormone.

One of the strangest "side effects" happened to me: lucid dreaming.

I'd wake up in the morning, not knowing what to think anymore. When my dream-experiences contradict my waking paradigm--which they often do--then I'm left totally confused, because my dream-experiences feel so valid!

Most notably, I've had ponderous remarkable dreams about James.


Backstory

James and I met in Honours Calculus last September, and we got along quite easily. We started dating in December, and it was totally awesome geek-love, complete with writing geeky love notes to eachother. This was actually during my coming-out as "curly", for the first time, to close friends. James didn't mind, though, because he had a close friend, Kay, who identified as a lesbian.

Spring rolled around, and the school year was ending. I had noticed that James was beginning to withdraw, and perhaps actively hold something back from me; but his silences had always confused me, and I wondered if it was just nothing. On the last day of school before exams, we talked, and he told me he had developed feelings for another girl. We decided to take a break; especially with exams coming up and the school year ending; and we'd talk more about this after some time apart.

About a week later, we decided we'd be friends from now on.

We kept in touch a little, mostly through e-mail, though we met on occasion over the summer. He and Kay started going out. It was a little amusing for me to wonder--because she had thought I was attractive, and James and I were dating, and I'm bisexual--about all sorts of possibilities.

And over the summer, James was planning on moving into the city with Kay.


The First Dream

The first dream I had was terribly confusing; mostly because I'm not sure if it was me leading the dream, or otherwise.

I'm not sure by what circumstance, but James and I were talking in the dream. I think we were doing something romantic. Suddenly, I stopped, and I asked something about Kay.

James does this thing with his posture sometimes, like closing up; and I've come to interpret it as a sign he's sad, distressed, scared. He did that, in the dream, and I asked him what was going on. He explained something about Kay, though I don't remember what, and I got the sense he was worried, but also hurt or offended or outraged and something like he wanted to do something about it but couldn't, or didn't know what.

A few months later, I visited James at his new address in the city. After some general chatting, I asked where Kay was; and he explained that her parents were not permitting her to either move out of her house, or into this one. And he did the same thing he did in my dream--the closing up--and I got the same readings from him.


The Second Dream

After hearing about Kay, I was even more rattled about the dream, because it had started off with a very close and probably romantic feeling between me and James. I don't know what to make of this, but the second dream was almost entirely romantic.

In this dream, James and I were swimming, not just in a beach, but something that seemed farther, larger and deeper. It reminded me of Venice: salty ocean water.

I don't even remember all the details, and there are some I don't want to mention; but we kissed, and there was a time he asked if this was okay--because of this, that and the other thing--and I said yes, so we kissed again.

Well, I guess it wasn't okay, because I woke myself up immediately; and I was frightened and bewildered.


Charissa probably thinks too much

I don't know what to make of these dreams.

Probably the most likely explanation is that, if these dreams mean something true about James, they mean that James still has affections for me (as I do for him), but we simply cannot do anything about them because of the choices we've made and the lives and responsibilities we have now.

Or, I'm simply projecting what I want, and just happened to be right about Kay being in some sort of trouble that affected James in a very predictable way.

I wonder how much of the first dream was meaningful, though, and if the relevance of one dream is an indication of the relevance of all other dreams--ie, if one dream came true, maybe all my dreams can come true.


With my birthday party coming up, I'm wondering whether or not to invite James. I mean, I want to, because I still want to be friends with him, but he still affects me too deeply, maybe--too deeply to know if it's real.

I'm going to try meditating tonight.
--Charissa

Dressup!

I was at work, wondering what I'd like to dress up as for Halloween. Even though I'm too old for trick-or-treat-ing, I still like to dress up for fun.

Last year, I went to University as a drunken wench--bottle and everything--which was neat, because we got our assignments back that day, and I got 100%.

I couldn't decide on a costume.

So I pondered...	...and pondered.

Aha!

I decided I'd dress up as my dad!

Actually, that's not entirely accurate. I decided I'd dress up as one of those old-days Chinese martial artists -type guys; but when I grew out my goatee, I looked disturbingly like my father.

How appropriate for Halloween!

--Charissa!