"And nightly Icarus probes his wound/And daily in his workshop, curtains carefully drawn/Constructs small wings and tries to fly/To the lighting fixture on the ceiling: Fails every time and hates himself for trying." -Edward Field, Icarus

Actually, I suceeded. I got into the honors program. But I can't go.

What is this feeling? No, it's not loathing. It's not anger, either. For all that I wish one thing or another would happen, I can understand completely why all fell as they did, and I knew they would. This feeling is one of heart-hurt, because knowing doesn't change watching the world's face fall free of the illusion, and also one of sea-shore standing on the banks in the distance, because knowing, knowing does not change framework and expectations, and those glare down at me while I stammer out my explanations that die on leaving my soul.

Solutions to Insomnia

Solutions to Insomnia

To my mind this title is really punny...at least to the first part of this note.

It is 2:13 am. I've decided to pull and all-nighter, except technically it isn't an all-nighter because I think I took a 3 hour nap earlier today. I took a 2 hour nap and a 1 hour nap the two preceeding days and I really don't like the trend that this is going in. Clearly, I am tired - I'm having trouble stringing a coherent and gramatically correct sentence together, and it has taken me nearly 10 minutes to type this. But if I go back to sleep...

1) I'll fall asleep, then sleep and sleep until noon and then I'll lose much of the day and I'll be annoyed and stay up late saturday night and sunday night as well.

2) I'll be tired but I won't be able to fall asleep because there's too much light [there is no light.] or I just won't be able to sleep.

So I'm going to stay awake; however, I need something to do. Most people are asleep. And quite frankly I doubt my ability to hold a conversation with anyone that I know. Recently Borders had this really awesome book clearance, on account of their filing for bankruptcy [which is not so awesome] and I found this nice-looking book on linear algebra. Except nice-looking books on linear algebra aren't what I usually read.

And this is why I think the title is punny.

--

2:38 am

Linear Algebra by Georgi E. Shilov

A Summary [I'll either learn something or wake up with my face plastered to the keyboard with the wisps of a really bizarre dream about numbers.]:

Preface:

"it should be noted
that the term 'linear algebra' has for some time ceased to describe the actual
content of the course, representing as it does a synthesis of various ideas from
algebra, geometry and analysis. And although analysis in the strict sense of the
term (i.e., the branch of mathematics concerned with limits, differentiation,
integration, etc.) plays only a backgroun role in this book, it is in fact the
actual organizing principle of the course, since the problems of "linear
algebra" can be regarded both as "finite-dimensional projections" and as the
"support" for the basic problems of analysis."

And it goes on to describe the differences between the author's [Shilov's] previous book [An Introduction to the Theory of Linear Spaces (1961 <- that is really old. This book is too. First published in 1977 by Courier Corporation. Hehe. Moving on.)] and this book. I understood up to

"LS is entirely
concerned with real spaces, while this book considers spaces over an arbitrary
number field,"

and then could vaguely follow

"with the real and
complex spaces being considered as closely related special cases of the general
theory,"

before there came a bunch of terms that hopefully will be defined later and maybe I'll find out that they really mean something actually comprehensible but for now I'll just list them: "Jordan canonical form of the matrix of a linear operator in a real or complex space," "canonical form of the matrix of a normal operator in a complex space equipped with a scalar product," "Hermitian, anti-Hermitian and unitary operators [and their real analogues]" and "infinite-dimensional Hilbert space."

Then the author mentions that chapter 11 contains "ancillary material that can be omitted on first reading."

And thanks the editor and an I. Y. Dorfman.

**A definition -- ancillary** Yahoo! Dictionary

an.cil.lar.y (adj) 1. Of secondary importance. 2. Auxiliary.

(n) 1. Something that is subordinate to something else. 2. -Archaic- A servant.

Latin -ancilla- for maidservant, which is a "feminine diminutive of -anculus-" which means servant in "Indo-European roots."

Chapter 1: Determinants

1.1 Number Fields.

1.11 I saw *K* being used as a variable and my eyes glazed over...but I think what the first paragraph is saying is that, like in most of math, linear algebra uses "numbers" (number systems [number fields {any set K of ojects}]). Any set of numbers can be added, subtracted, multiplied, or divided ("subjected to the four arithmetic operations") to make more numbers ("again give elements of K")

Then it lists properties of every pair of numbers A and B in K - commutative, associative, zero, negative element things that take more time to type than it does to memorize -

- for addition (subtraction is a manipulation of addition and negative element)

- for multiplication (division is a manipulation of multiplcation and reciprocal element) *

Natural numbers: 1, 1+1=2, 2+1=3 etc. We assume that none are 0. **

Rational numbers: p/q; p and q are integers and q=/=0

Fields K and K' are isomorphic if

-- Head nod. Must stay awake --

3:01 am

Break time.

Switch to more upbeat radio station. Cut to Doobaba project.

--

3:42 am

Cold. Tired. Not bored, but in the vegetative donotwanttodowork stage.

"Two fields K and K'
are said to be isomorphic if we can set up a one-to-one correspondence between K
and K' such that the number associated with every sum (or product) of numbers in
K is the sum (or product) of the corresponding numbers in K'. The number
associated with every difference (or quotient) of numbers in K will then be the
difference (or quotient) of the corresponding numbers in K'."

I have no idea what that means.

Isomorphic=

Two fields. K. K'. [-.-]

K and K' are related.

K and K' = number fields = any set of objects = number systems = group of numbers. Oh.

In each group of numbers... [brain stuttering...failing...fail.]

Sum = +.

Product = x

In K ->

Two numbers: A and B

Sum A and B: A+ B = C

C = number associated with every sum. [I just had an epiphany. {And this is because I am not in a library. (That was probably in bad taste. Sorry.)}]

In K' ->

Two numbers: A' and B'

Sum A' and B': A'+ B' = C'

C = C'

.

...

.

Ugh.

K: A - B = D

K': A' - B' = D'

D = D'

K and K' are isomorphic.

...

I think I'm oversimplifying to the point of wrongness.

--

4:01 am

Search: "isomorphic"

**A definition -- isomorphic** Merriam-Webster

1 a. Being of identical or similar form, shape, or structure.

b. Having sporophytic and gametophytic generations alike in size and shape.

2. related by an isomorphism.

First known use: 1862

** A definition -- isomorphism** ibid.

1: The quality or state of being isomorphic [No. Just no.]

a. Similarity in organisms of different ancestry resulting from convergence.

b. Similarity of crystalline form between chemical compounds.

2: A one-to-one correspondence between two mathematical sets; especially; a homomorphism that is one-to-one - compare ENDOMORPHISM [grrr.]

First known us: circa 1828 [I feel an incongruity here.]

**A definition -- endomorphism** ibid.

A homomorphism that maps a mathematica set into itself - compare ISOMORPHISM.

First known use: 1909

**Wikipedia -- isomorphism**

"In abstract algebra,
an isomorphism (Greek: ἴσος isos "equal", and μορφή morphe "shape") is a bijective map f such that both f
and its inverse f −1 are homomorphisms, i.e., structure-preserving mappings. In the more general setting of category
theory, an isomorphism is a morphism f: X → Y in a category for which there exists an "inverse" f −1: Y → X, with the property that both f −1f =
idX and f f −1 = idY."

Isomorphism is a morphism. Thank you for informing me. That is probably the only thing I understood.

Informally, an
isomorphism is a kind of mapping between objects that shows a relationship
between two properties or operations. If there exists an isomorphism between
two structures, we call the two structures isomorphic. In a certain sense, isomorphic
structures are structurally identical, if you choose to ignore
finer-grained differences that may arise from how they are
defined.

That explains nothing to me. Right now, I need 1+2=3.

Isomorphisms are
studied in mathematics in order to extend insights from one phenomenon to
others: if two objects are isomorphic, then any property which is preserved by
an isomorphism and which is true of one of the objects, is also true of the
other. If an isomorphism can be found from a relatively unknown part of
mathematics into some well studied division of mathematics, where many theorems
are already proved, and many methods are already available to find answers, then
the function can be used to map whole problems out of unfamiliar territory over
to "solid ground" where the problem is easier to understand and work
with.

Better.

Consider the group Z6, the integers from 0 to 5 with addition modulo 6. Also
consider the group Z2 × Z3, the ordered pairs
where the x coordinates can be 0 or 1, and the y coordinates can be 0,
1, or 2, where addition in the x-coordinate is modulo 2 and addition in
the y-coordinate is modulo 3. These structures are isomorphic under
addition, if you identify them using the following scheme:

(0,0) →
0

(1,1) →
1

(0,2) →
2

(1,0) →
3

(0,1) →
4

(1,2) →
5

or in general
(a,b) → ( 3a + 4 b ) mod 6. For example note
that (1,1) + (1,0) = (0,1) which translates in the other system as 1 + 3 = 4.
Even though these two groups "look" different in that the sets contain different
elements, they are indeed isomorphic: their structures are
exactly the same. More generally, the direct product of two cyclic groups Zm and Zn is isomorphic to Zmn if and only if m and n are
coprime.

...I'll just leave it at that.

* Note: in A (B+Y) = AB + AY, for every A, B, Y in K, it is implied that (A+B) Y = Ay + BY.

**

Given two elements N
and E, say, we can construct a field by the rules

N + N=
N,

N + E =
E,

E + E =
N,

N * N =
N,

N * E =
N,

E * E =
E.

Then, in keeping with
our notation, we should write N = 0, E = 1, and hence 2 = 1 + 1 = 0. To exclude
such number systems, we should require that all natural field elements be
nonzero.

End of page 2.

4:40 am.

Very cold.

Also paranoid. Saw large spider near lamp about an hour ago. Forgot about spider. Now spider is not in sight.

Shiver.

Definetely cannot go to sleep now.

4:46 am.

Nap?

No. No nap. Daily Show.

5:20 am. Off to read.

9:59 am. I fell asleep.

All Nighters- when it is time to cut your losses and go to sleep

1) You begin to hallucinate. This is bad. Especially if you are particularly excitable. Remember: if you scream, you wake everyone up. And then the parents are not too pleased that you have stayed up so late.

2) Vessels in eye seem distorted/possibly burst, turning red. Get some shuteye. Or your eye just might explode. The validity of this is doubtful, but you are just tired enough to fear it.

More to follow, after sleep.

Internet: absolute communication, absolute isolation. --Paul Carvel

I think this is giving the mistaken impression that I am dying

This has never happened before. I guess what with college app deadlines coming up, and everyone else, and I mean everyone in that everyone important in my life, thus, my life, are also concerned about this lump in the future, I have so much nervous energy that it's building up, running inside my head and upside down on my eyelids, and now I feel like talking, and talking a whole lot.

Now, I am not a talkative person. I am the listener, and very often I couldn't talk even if I wanted to, because sometimes my mind fails to synthesize thoughts into coherent sentences.

So, imagine, when suddenly all the disjointed thoughts demand to be spoken, crashing everywhere and spilling out like disembowled guts. Have you ever tried holding in your disembowled guts? Hopefully not. Well, that is how I feel.

This is all I can manage

I have way too much stuff to do. Why does it seem like half of my grade is constantly in motion, keeping astride in a torrent of to-dos that would crush me, and the other half is at leisure, going to sleep at good times, well rested, and well prepared?

I envy both.

I cannot tell if I have a lot of work to do because of how I think, or because I actually have a lot of work to do. I do not know why I am always weary to the bone.

It's okay, I guess, because at least this way I don't have time to think. I don't have time to want anything else but this.

blurry incoherence muddled into hopeful accomplishment

My ninth grade english teacher told us that there were two types of views on civilization: linear, or a continued, straight line progression with a positive slope, and cyclical, which generally has to do with a pattern of rising and falling. Like a sine graph.

That's how writing is for me. All of the last academic year has been a flurry of essays and journaling. And now it's summer - I have time to actually write?

I have done nothing for college applications...

...a bunch of incoherent notes in my ideas notebook...

...half-started blog posts...

...half finished quilt...

...half-finished books...

...and this is a half thought out point.

Circles and no math and mind

By my posts I'd conclude that I haven't hit any highs or lows in a while. That's probably true. For the most part I've been stuck at a static state of restless indifference. Almost an oxymoron.

I've just been chewing at some questions, which seem to continue in a circular pattern around my head where there are no conclusions but a tangle of hypotheses and half-formed theories based on postulates that are questionable at best.

Faking until you make it...it's just manipulation of self-efficacy, isn't it?

Playing your own game is sketchy

I feel like I ought to do something. Something more useful than listening to music, solving a rubik's cube over and over, checking on my virtual reality games. There's scrapbooking to be done, college essays to be written, pictures to be taken for my mom. It's not much, but somehow I'm managing to do none of them. I don't dread the day I become productive - it's actually an exhilarating feeling - I just can't seem to stop doing nothing. So I'm blogging, while other people have internships and volunteering hours and work experience. This is the problem, isn't it? In golf, one of the things that all my coaches agreed on was that it was important not to worry about how everyone else was doing. It was important to just focus on one's own game. The competition isn't with everyone else, but with oneself.

Hm. There must be a much more eloquent way to word that.

Just focus inward?

No, I don't think it has to be a narrow, steely eyed concentration. It's not quite complacency either. It's almost a simultaneous awknowledgement of the situation tinged with quite indifference tempered with a clear objective. Being, I guess, "in the zone." Except with memory. Consciousness. And not in sports.

I'd wanted to do one of these

To the owner of the red minivan,

It is bad enough that the cars in front of me have already cleared out, despite the fact that the sign clearly says "Speed Limit 45 mph" and I am already pushing 50. Then you have to have your car lurk so close to mine, as if you are rushing to be at the side of your wife and your firstborn, only you can't, because I am trying to keep the car from veering out of control. I understand that I may be keeping you from a kodak moment, but I just can't stand it when you look at me like that. I am a very fragile person. With a very fragile driving confidence.

Sincerely,

Two-month old teen driver

My Summer Schedule

6:00 to 7:30 --Wake up

7:30 to 10:00 --Snooze/lie in bed

10:00 to 10:30 --Brush teeth and breakfast

10:30 to 12:00 --Computer time [games, pondering college essays, writing a sentence and going back to games]

12:00 to 4:00 --T.V. [comedy central] intermitently laced with computer and eating time

4:00 to 5:30 --Staring blankly at the wall pondering college essays

5:30 to 6:00 --Shower

6:00 to 10:00 [varies] --Dinner[with NCIS]

10:00 to 11:00 --Computer time

11:00 to 11:30 --Brush teeth

11:30 to 12:00 --Read Mental Floss History of the World

12:00 to 6:00 --Sleep

Conclusion: Should read more and rot brain less.

I lost my camera. My dad bought me a new one yesterday.

It bothers me that it's practically a parallel of a kid that crashes his car and gets a new one from his parents.

Is that it? I'm not sure why I want my parents to yell at me, to refuse to buy me another. Maybe I'm just a masochist.

I hate looking at the new camera. It hate that I was careless and I let my old one out of my sight. I hate that now more than ever I seem like this irresponsible, spoiled idiot.

How can this one mistake hurt so much? Why don't I have normal regrets about normal things?

Math is fun. Math is beautiful.

I apologize in advance. I will try not to laugh maniacally or melt into a puddle of smugness. It will be difficult, but I will try. A little.

Guess what I got on my math final?

Guess!

I'll give you a hint - it raised my grade 3 percent. Three percent.

I got 101!

As in the number of Dalmations.

I guess it should be a bit sad that this is really happy news for me. But it isn't. This definetely ranks on one of the list of Best Things That Have Happened to Me This School Year. Maybe number 4, or number 5. I have yet to actually make the list.

Finally. Finally, finally finally. I got 101 on the final. I have an A in math. It doesn't even matter that it won't show up on my high school transcript. Because when I go to college I'll laugh maniacally and shove my college transcript with my A [and B...] in everyone's faces. Then I will be sad because everyone will hate me.

Finally. I actually feel smart now. [It's wierd, how much you identify with what you're good at. Except when it fails. It's hard to continue believing that you're a good student if you can't even get good grades.]

I studied. Actually, that's not what I'm particularly proud of. I did study, in a cursory sort of way. But what the trick is, more than studying, is the ability to think when it really matters. And I'm happy, because finally, I did this. I probably went over both tests [it was a two-day final] five or six times, because the first time around only a few problems made sense. But relax, think, organize your mind, figure out what you know and what you need to find...

My math teacher is right. All of my math teachers from the past three years were right. Math is beautiful. Calculus is beautiful.

And now my excitement has worn off, and I'm slightly embarassed that after a long hiatus I have written another post about math.

Guess what?

I found this out yesterday.

And I still laugh/cry when I think about it.

Just listen to music - I am

Because my work ethic sucks...
Because I have to do my math homework right now. Again.
Because my brains are scrambled...
Because apparently the closer you get to me the more likely that the first impression of being intelligent turns into eccentricity....

I suggest that you go to youtube and listen to "Thunder" by Boys Like Girls. And while you're at it, look up "Forever Young" by Jay Z.

It pretty much sums up whatever it is I have to say without relying too much on my clumsy syntax.

I want to trade my heart for another brain.

Titleless because I'm just a number

This system of starving through the ap test then stuffing self with junk food from Jack in the Box isn't doing wonders for my health. Or sanity. Or sense of balance. I'm glad it's over.

But they were pretty fun, in retrospect. Maybe, just maybe, my essay writing can finally be deemed "good."

It would make me really happy.

A symphony of disagreeing body parts

I've always wondered at my lack of personality. Basically all I do is read, eat, study, sleep, and play bubble spinner.

I understand now. My personality isn't out there, in the real world. Perhaps this conversation that I had before and during ap testing will explain.

Car ride.
Mom: I got you sushi!
Me: No thanks.
Stomach: No. No sushi, please. I can't take it. In fact, I'm pretty sure I'm about to barf.
Mom: Cookies?
Me: No thanks. Maybe later.
Stomach: I want to toss my cookies...
Heart: OMG OMG I REALLY WANT A 5 BUT I WON'T GET ONE.
Brain: Lenses. Burning point. p,q, kq over r square. Zen. You can do this you can do this.
Bladder: Um...guys?

At Testing Center.
Mom: Good luck!
Me:*smiles weakly*
Heart: Doppler effect. dadadadadadadadada
Brain: I wonder if AP Bio has gotten out yet? No? Yes? Hm...there are clumps of people outside the door. I really hope you're not late.
Stomach: I really hope we can find a trash can.
Bladder: :) There's a toilet in there!
Brain: kq over r squared kqover r squared..okay. I know that. Do I know anything else? Nope.
Me: *Wading over to the corner of the room near a bunch of backpacks squished on a plastic table.* Hi.
Brain: Study time! :)
Heart: Doppler effect. DA DA DA
Person: *studying*
Me: *studying*
Brain: *studying*
Heart: *people watching*

During Testing.
Brain: Hey, this isn't too bad...I think I can do this. No I can't. Yes...well...meeeeh....poop.
Stomach: Hm...I think I kinda want food...
Heart: I think I kinda want to stalk prom pictures.
Brain: Think think think think. Hm. I'm thinking about thinking but actually I'm not doing any thinking.
Stomach: Food?
Eyelid: *twitch*
Stomach: I seriously want some food now.
Brain: Be quiet.
Hand: Hey, brain? ...I wanna bubble. Are you going to solve these problems or not?
Brain: You too.
Stomach: FOOOD
Brain: SHUT UP.
Stomach: *grumble*

Breaktime:
Stomach: Food?
Hand: Bank cookie. Here.
Brain: Hm...am I going to be thirsty later?
Stomach: Hungry.
Brain: Fine.

Testing, part two.
Brain: Crap. I don't know how to do the first problem.
Mouth: I taste wierd.
Brain: Kinematics should be the easiest problem.
Throat: I'm thirsty.
Brain: I don't know how to find heat transfer. Or x or theta.
Heart: I DON' WANNA FAIL.
Brain: Gr....
Stomach: *growl*

Good grief. I hope I can't always be persuaded so quickly.

prom makes me want to cry

Prom is supposedly the zenith of every girl's life. That's really depressing. Prom makes me think about how old I'm getting. It makes me think about people pairing up and leaving. It makes me think about the future, which I think about more and more, and less about the past, which I'm mired in.

I want to go to prom but I'm afraid of what it represents. I want to go but it's not something I'll be able to go to easily. I'm fearless, excited, even, about the AP tests that are coming up within the week. They're fun and I like them. But if I go to prom I'll probably die of stress. I don't understand.

I hate it when I look at a guy and I lose track of my thoughts. I hate this bizarre focus on relationships, this tunnel vision that tunes out everyone else except for the significant other. I see couples walking through the school, and they are just a couple and no one else. Where are their friends? DON'T THEY SEE that there's plenty of time for that LATER? Okay, so prom isn't entirely about relationships, but it's mrrrhhhskft and trrpapd and durf.

This post is probably incoherent. There are just no words to describe this. It's like a tumbleweed of negative emotions and hormones and crap. My English teacher was right. Teenagers are too damn hormonal. I probably should see a doctor. Or I could just read a psycology book. Yeah. That's what I'll do. During prom night.