Dunmore Cave

Double Rainbow on 21 Jan 2012

2012-01-22T14:16:00.003+08:00

On that day after ensemble Boyang saw the rainbow first, as did many across the island, and we went out and gawked at it to our hearts' content and played the Rainbow Overture at it. And then we went home.

Sophomore Journal 2.3.11

2011-10-26T11:31:00.007+08:00

Sjöankans Vals in concert

Inorganic Chemistry
A/P Huynh has taken to frequently showing us videos in order to take a break from talking and go and cough a bit, he says. He also joked once that he was chronically depressed, which wasn't very funny and slightly worrying. The class has developed an addiction to (fake) alkaline metal explosions:

Mid-terms featured a quiz on scientists' names, rather unsurprisingly on retrospect.

Organic Chemistry
I have given up printing notes, because I have the textbook, which has almost everything the notes have and much more, and increases my tolerance towards heavy textbooks.

Labwork featured each of us being given a mixture of two unknown substances for to separate, purify and crystallise. The luckier ones among us got yellow crystals, or crystals with some kind of form. For me, fortunately, I got the long needly crystals (salicylic acid) and the big flaky ones (acetanilide).

The professor in charge of our lab sessions was Dr. Ship, who had the naggy, secondary-school teacher vibes.

Thermodynamics
Yesterday I was finally convinced that numbers (as numerical answers) in Thermodynamics are the last things one should worry about, far behind understanding the ideas behind what has been taught.
Admittedly, understanding the workings of thermodynamics has also been challenging. To illustrate, the school printer at S10 has helpfully screwed up all the notes printing at the maths.

In other news, we have finished the most awesome lab of the semester, the Tin-Zinc phase diagram. Be it due to oxidation or impurities, melting the mixtures of the two metals produced an amazing and unpredictable array of colours:

Structure of Materials
It was too easy to get a full mark this mid-terms, so the marker had the pleasure of penalising us on the most unimportant slights.

Picked up a textbook in Science Library the other day about the Structure of Materials. None of the content was at all familiar. For example, the first topic to be featured was the rotational symmetry of crystals. When I did crystal structures in the software CrystalKitX, it just so happened that one has to know them in order to make even a SC or FCC, etc.

Anyway,
!!!!!!!!!!!!!!!!!

In Other News
I've signed up for a UROP project. The title is
Modelling and Simulation of structures and TEM images of crystals
which is why I'm doing stuff on CrystalKitX all these days.

SEP application closes today. My 5 choices:
1. École Polytechnique Fédérale de Lausanne (EPFL)
2. Eidgenössische Technische Hochschule Zürich (ETH Zürich)
3. Uppsala Universitet
4. Institut Polytechnique de Grenoble
5. University of British Columbia
Fingers are crossed for Francoprovençal small-talk and cross-border grocery shopping

Karantez Vro

2011-10-26T09:22:00.005+08:00

Karantez Vro
Anjela Duval (lyr.) / Nolwenn Leroy

E korn va c’halon zo ur gleizenn
’Baoe va yaouankiz he dougan
Rak siwazh, an hini a garen
Na gare ket ’r pezh a garan
Eñ na gare nemet ar c’hêrioù
Ar morioù bras, ar Broioù pell
Ha me ne garan ’met ar maezioù
Maezioù ken kaer va Breizh-Izel !

Ret ’voe dibab ’tre div garantez
Karantez-vro, karantez den
D’am bro am eus gouestlet va buhez
Ha lez’t da vont ’n hini ’garen
Biskoazh abaoe n’am eus en gwelet
Biskoazh klevet keloù outañ
Ur gleizhenn em c’halon zo chomet
Pa ’gare ket ’r pezh a garan.

Pep den a dle heuilh e Donkadur
Honnezh eo lezenn ar Bed-mañ
Gwasket ’voe va c’halon a-dra-sur
Pa ’gare ket ’r pezh a garan
Dezhañ pinvidigezh, enorioù
Din-me paourentez ha dispriz
Met ’drokfen ket evit teñzorioù
Va Bro, va Yezh ha va Frankiz !

En mon coeur est ma blessure,
Depuis ma jeunesse y reste gravée
Car, hélas, celui que j'aimais
Ce que j'aime n'aimait pas.
Lui n'aimait que la ville,
La grande mer et les lointains ;
Je n'aimais que la campagne,
Beauté des campagnes de Bretagne.

Entre deux amours il me fallut choisir
Amour-patrie, amour de l'homme ;
A mon pays j'ai offert ma vie,
Et s'en est allé celui que j'aimais.
Depuis, jamais je ne l'ai revu,
Jamais connu de ses nouvelles.
En mon coeur saigne la blessure
Car ce que j'aime, il n'aimait pas.

Chacun sa Destinée doit vivre,
Ainsi en ce monde en est-il.
Meurtri, certes, fut mon coeur,
Mais ce que j'aime, il n'aimait pas.
A lui, honneurs et richesse
A moi, mépris et humble vie.
Mais je n'échangerais contre nul trésor
Mon pays, ma langue et ma liberté.

Le Cher Dirigeant

2011-10-17T21:53:00.003+08:00

Nous sommes enseignés souvent sur un personnage très mystérieux. C'est celui que nous appelons le Cher Dirigeant. On ne le voit que sur la télé ou sur des affiches. Il paraît assez laid et ne sourit jamais, bien qu’on le loue par tas des chansons et danses.

Sa vie, je la trouve mystérieuse. Quelques disent qu'il demeure dans les cieux, et ne descend que pour rejoindre les gens de la Corée pendant la Fête d'Arirang. Les autres ne sont pas d'accord. Ils croient qu’il est un amiral valeureux, toujours en patrouillant autour la Mer de l'Est, qui empêche que les capitalistes ne nous envahissent. Chacun a une histoire incroyable à raconter, malgré qu'aucun ne connaisse le Cher Dirigeant.

Mon professeur me disait souvent : le Cher Dirigeant est né au sommet du Mont Paektu, sept mois après un colibri magique est arrivé dans notre pays à prédire sa naissance. Quand il est né, toute la nature l’a célèbré. « C’est une naissance merveilleuse, plein de promesses ! » crié mon professeur un jour « Et pourquoi nous sommes encore tant pauvres ? Il semble qu’il ne soit qu’un mensonge ! » Bientôt après, mon professeur a disparu mystérieusement.

(198 mots)

This Week Is E-Learning Week in Faculty of Science

2011-10-03T23:17:00.002+08:00

I'm going to be sitting in front of this soul-sucking machine for hours listening to disembodied voices. I'm going to write here more than is necessary. I'm going to be alone in this room, with no friends to talk to, and no practice problems to hurl at each other with. I'm going to miss A/P Huynh and his vaguely German accent and his laid-back attitude and his dubious logic. I'm going to miss Mdm Saradha's patient and crystal-clear presentations. I'm going to pine for Mr Ong's condescending drill-sergeant air. I'll be missing sitting in the classrooms with the tutors within arm's reach. And I'm beginning to feel that all this e-Learning week may just serve to remind us how beautiful real human contact is.

Exercise au conditionnel

2011-09-08T10:30:00.002+08:00

Si j'étais riche, je serais très heureux. Je rirais beaucoup. Et puis je donnerais tout mon argent à une autre personne afin qu'il rie beaucoup aussi.

Sophomore Journal 2.3.2

2011-08-16T14:17:00.003+08:00

Overview
Taking 5 modules and a respite from a half-year of fun and murderous excitement. Holidays were good; In fact, it is Mighty Fine. Will not deign to elaborate more here *smirk.

With any luck, these modules here listed below will develop themselves out of control and make the school life as hard as it was before. But first,

CM1111 Inorganic Chemistry 1 - DR HUYNH Van Vinh
CM1501 Organic Chemistry for Engineers - DR ZENG Huaqiang
Dr Vinh is the lecturer for this ere 4 hour per week module. He has a weakness for Youtube and pronounces all the French and German words properly, much to my delight and to the surprise of those around me.

Chemistry lectures at this point are quite similar in content, although Inorganic seems to be progressing more slowly, with more gossiping about dead people in wigs.

MLE2101 Structure of Materials - DR CHIU Cheng-Hsin
MLE2102 Thermodynamics and Phase Diagrams - DR WANG Qing
As anticipated, Thermodynamics would be the most challenging and the most somber module which the Materials Science students will take this side of Christmas. The lecturer, who people say look like me, opened the lecture with the question of why everything in this world must eventually die. It seems that one is unable to think about Thermodynamics on any other level of emotion.

Structure of Materials starts out rather dodderingly with lecture notes which look almost the same at every page. However, its lab activities for this week prominently features this:

The experiment is entitled "Preparation, Structure and Properties of a High-Temperature Superconductor", although it would be preferable to refer to it as the Flying Bits of Metal Experiment.

LAF3201 French 3 - MRS Francesca MANGANELLI-LENG
The first lesson was on Monday, carried out to the setting sun. And it would gradually come to light that French would be used in class almost all of the time, but what else can one expect after scraping into this class through the placement test?

On the other hand, the penciled notes on Tina's textbook have been great help!

Valedictorian Speech

2011-08-02T10:43:00.003+08:00

It just so happens that recently, in a university near you, a speech by a valedictorian filled the air with outrage and disapproval from those who fancied themselves respectable.

I feel that I must join them, but only because I have watched her speech and found the exit to be poorly executed. Sneaking in the f-word timidly like she did does no justice to the feelings of joy and accomplishment which typifies the occasion. It is more befitting for her either to stick to a no-swearing regime or to vault to mid-stage after the speech and do a lewd dance until her friends, posing as security officers, rush onstage to subdue her with tasers (or anything else to that effect). Future valedictorians, I leave you to consider your choices.

Grand Bal de Kermanria-an-Isquit

2011-07-21T18:39:00.003+08:00

Une chanson jolie et macabre, d'une église qui se trouve en Bretagne.

Titre: Grand Bal de Kermanria-an-Isquit
Comme chantée par: Tri Yann (France) 1981
Index: T09.fr

Nobles rois, venez couronnés
De forces et prouesses renommées
Ne pensez plus en dignité
Pauvres à la danse viendrez
Pauvres en cendres serez

Connétables, d'honneurs parés
Ni vert, ni gris plus n'avez tirés
Rendez compte pour être acquittés
Tant riches en vie vous étiez
Pauvres en cendres serez

Gens d'église par Dieu nantis
En grant détresse laissez ici
Chapeaux rouges, chapes de gris
En tristesse tout finit

Nobles dames d'or empesées
De grâce et jeunesse délaissées
Fûtes jadis environnées
De grands lignages et comblées
Pauvres en cendres serez

Gens de peuple et roturiers
À cette danse vous mènerez
Riches qui vous ont méprisé
Tant pauvres en vie vous étiez
Riches en cendres serez

Fulinghalling

2011-07-12T23:41:00.002+08:00

A rambling dance number for the härjedalspipa, accompanied by a jew's harp and a plucked string in low E.

Title: Fulinghalling
As performed by: Hedningarna (Sweden) 1989
Code: T08.se

Tutskov's Polska

2011-07-10T19:14:00.003+08:00

A childlike song for guitar ensemble (APBCGr + Soprano + Prime Cembalo).

Title: Tutskovin Polska / Tutskov's Polska
As performed by: Värttinä (Finland) 1987
Code: T07.fi

Juho's Contradance

2011-07-08T20:55:00.002+08:00

A hyperactive song for guitar ensemble.

Title: Juhon Kontra / Juho's Contradance
As performed by: Värttinä (Finland) 1987
Code: T06.fi

The Sea Duck's Waltz

2011-07-08T08:56:00.005+08:00

A very cute song for 3 guitars (Soprano, Prime and Bass).

Title: Sjöankans Vals / The Sea Duck's Waltz
Composer: Olov JOHANSSON
As performed by: Olov Johansson (Sweden) 1998
Code: T05.se

Björnlaten

2011-07-06T12:06:00.006+08:00

A very sad song for Viola, Violoncello, and 2 Guitars

Title: Björnlaten / The Bear Tune
Comp: Traditional Swedish
As performed by: Hedningarna (Sweden) 1989
Code: T04.se

La première nouvelle en Anglais

2011-06-24T22:34:00.009+08:00

An evening at the airport.

Yesterday afternoon, I am arrived at th'airport at Changi. Then I had very hunger, because that I had taken an airline too cheap. I have therefore decided to-dine at somewhere nice and not too expensive in the terminal. When I was-being in the-process of eating, I have seen my big-friend Benjamin. When he me has seen, he him is seated next to me, and he to-me has said:
- I am passing-by. I go to-meet my girlfriends later ! One will-go to the discothèque this night.

He there has towards 2 hours for doing of-the trash-talking. And sudden, we have heard a noise loud. The girlfriends of Benjamin are arrivedes to the café ! Them-girls have said:
- We are really sorries ! We come of to-have a jam of traffic. Let'sgo-there Benjamin; We go to-be lates !
- One must meet well-soon, you can me to-call if you want ! Said Benjamin.

And next, them-guys have left, and I have been alone again.
Now I am in the-process of to-read a newspaper. I see a-lot of those tenses literaries... This'is such pity to see that this or that thing happened, rather than that they have happened, in writing only. I think that to-read des stuffs seriuses in French is always more easy than to-do of-the trash-talking. And so I take a sip of my coffee and read eagerly as regimes fell, people died, wars broke-out and great discoveries scientifiques them appeared.

Une petit histoire sur l'armée de Napoléon en Russie

2011-06-09T13:25:00.020+08:00

Again, in-class scribblings with Benjamin, edited to include the pluperfect and imperfect tenses.

Napoléon et son armée sont allés à la Russie. Il y avait beaucoup de la neige. Dans les temps froid, ils n'avaient pas de mangers et pas d'eau. Deux semaines après, les français ont vu leurs ennemis les russes. Les généraux de Napoléon se sont écriés :
- Nous allons tout mourir ! Les maudits russes vont couper nos gorges !

Les russes étaient des bons gens pourtant ; ils étaient assez ivres aussi. Ils avaient apporté des aliments et des vodkas. Sur le champ de bataille, ils ont pendu la crémaillère avec les soldats français. Tout l'hiver, ils ont mangé bien et ils ont bu le vodka jusqu'au petit matin chaque nuit. Tout le monde était heureux. Elle était la meilleur guerre jamais !

Also to revise my German a little, realising with horror how comparatively little I have learnt with this language:

Napoleon und seine Armee gingen nach Russland. Da gab es viel Schnee. Im kältes Wetter hatten sie kein Lebensmittel und kein Wasser. Zwei Wochen hinterher sahen die Franzosen ihre Feinde, die Russen. Die Generäle von Napoleon riefen aus: „Wir werden alle sterben! Die Russen werden schneiden unsere Kehlen!"

Die Russen waren doch nette Leute. Sie waren auch ziemlich besoffen. Sie brachten viel Essen und viele Wodka. Dann fingen die Russe ein Fest mit die Franzosen über dem Schlachtfeld an. Da waren sie immer satt, und sie tranken den Wodka bis Morgens den ganzen Winter. Alle waren sehr glücklich. Das war der besten des Krieges!

Une petit histoire sur l'homme dans la peinture «L'Art de Vivre»

2011-06-08T23:18:00.009+08:00

Classroom scribblings based on a found picture, with edits.

C'est une peinture de René Magritte, un artiste belge. Il y a un homme très bizare. Cet homme a la plus ronde et grande tête du monde, mais son visage est un peu petit et il n'a pas des oreilles et des cheveux. Il vient d'arriver au balcon. Maintenant il est en train de rester sur le balcon et devant des montagnes. Il fait très beau aujourd'hui, mais l'homme s'ennuie. Ensuite, il va aller au restaurant pour prendre le déjeuner avec ses amis. Cependant, sa tête se bloquera à la porte quand il essaye de entrer. Alors, il s'écriera :

- A Monsieur Magritte ! Pourquoi vous m'avez donné cette trop grande tête ?! Je ne marche plus bien parce que je suis toujours maladroit, et maintenant j'ai cette maudite porte - Donnez-moi ma normale tête bientôt, s'il vous plaît !

I Ha'e Discovered Malinky

2011-05-30T22:26:00.002+08:00

Malinky
Steve Byrne, Fiona Hunter, David Wood, Daniel Thorpe

St. Mary of the Angels

2011-05-22T21:23:00.009+08:00

A disorganised account:
At the Church of St. Mary of the Angels, the spiritual center of the area comprising the town of Bukit Batok and the surrounding communes. Duration: 0815 to 1210. Purpose: Fundraising, publicity for CSS Orientation camp (Also exploration)

0815 was when Mandarin mass was on-going. No-one from CSS was there yet.
The pedestrian entrance leads up a small slope from Bukit Batok Avenue 6. There is no sign at the pedestrian entrance. I passed by the church 10^n times without realising it was there.
The road entrance is on the other side of the church. It is always jammed in between masses, although I have not had a really good look.

The chapel is visible from the pedestrian entrance. It is a smallish box-shaped building graced only with a huge metal cross. Inside, the monstruand is in the middle of the square room, with cushioned seats at the four sides. There is a stack of books beside the door.

La place devant l'église, c'est un endroit joli. Si on passe l'entrée, on voit un jardin à gauche, l'église à droit, et beaucoup des fontaines partout. The space outside the prayer hall was paved with cobblestones. Cute, but not ideal for driving.

Isaac: Not that we're allowed to, of course.

Si on traverse la place et descend les escaliers, Il y a un columbarium... Cet endroit est très silencieux. It was either Cheryl or Brian or both who asked me afterwards if I had seen that place. I had, but not too far in. It was always fascinating to see such places in churches; since Holy Cross doesn't have one, it always occurred to me as a novelty.

The ground floor had the canteen and a thrift store.

Dwayne: Have you tried from the canteen? The food there is quite famous.

Never mind that, the food fair upstairs was enough to keep the gob busy.
The thrift store is another novelty of a place. It held an abundance of old clothes and books. It was no rag store; the items were donated and then sold for charity. Among the items:

Textbooks, comics, pulp fiction, books on the Catholic faith
Clothes
Last-century toys and board games.
Old shoes, relatively-unworn boots from recently-uncaged NSFs
Glassware
Crucifixes, decorative icons

The place was sadly not well tended-to, and housed a stubborn musty stench. Piles of a mixture of assorted stuff were left around the place when I was there, but I hope that was only temporary.

The mass attended: 9am (with children's mass)
The kids flocked off after entrance antiphon to a place downstairs, which if I remember the place correctly was a hall opposite the columbarium.
The prayer hall was revamped 5 years back, by Brian's account, by an architect among the parishioners.

Seats are carved out of the pews individually, as are the hassocks. When the time comes for them to be deployed, it was a different kind of cacophony from the other churches.
Missals are absent. In their place are copies of the hymnal Breaking Bread.
The choir sits facing the door.
The cry rooms are away from the edges of the hall. Seats for latecomers are provided at the space between them and the walls. It was where "children are always running".
When I mentioned "beaucoup des fontaines", there were two, one of which was the baptismal font in the middle of the hall.

The capacity did not seem large. On special times of the year where more people came, they arranged seats outside in the space in front of the hall, and latecomers watched a telecast of what went on inside, and were left to the mercy of the elements.

The giant crucifix above the altar is the exact inverse of a protestant cross. Namely, it has a Jesus but there is no cross. The crucifix appears to have been knocked together crudely because it had a lot of holes on every limb. It is supported from the ceiling with three cables. On the ceiling of the prayer hall are lights arranged to form the shape of a cross, as if to compensate for the absence.

Brian: Our crucifix had a cross last time, but that was dropped because it was too heavy.

Cette église a un chat. Il s'appelle Angelo, et il est le plus rond de chats du monde. Nous pensons qu'il est comme Garfield exactement. He also rolls over when you try to scratch him.

The activity took place intermittently between masses, and fared not as productively as hoped.

This is a question that should never be asked

2011-05-16T22:15:00.001+08:00

This is a question that should never be asked
If asked, then it should never be answered
Since no answer that is worth hearing about
can be expressed in our terms.

If you affirm it, you are wrong
If you deny it, you are also wrong
A blank stare may not make you right,
but it is the best reply.

Dans l'Alliance Française

2011-05-08T21:51:00.006+08:00

1. Summary of week 1 of French crash course, taken mainly by students who are in a hurry or have time to burn every weekday morning from 9 to 12:

Tuesday: The Alphabet, numbers 1-69.
Also:
Pronounciation and liaisons
Question word [comment]
Reflexive verbs [s'écrit], [se prononce]

Wednesday: conjugation of [être], grammatical gender
Also:
Greeting and taking leave
Time of the day

Thursday: conjugation of [avoir] and verbs of type [-er], negation
Also:
[beaucoup] ≠ [un peu]
"Tu as quel âge?"
How to distinguish [ils sont] from [ils ont] and [dessus] from [dessous]
[tout le monde] (this one 囧)

Friday: articles, possessive pronouns
Also:
[avant] ≠ [après]
Days of the week

2. A brief foray into Esperanto, soon-to-be secret/joke language spoken twixt me and my sister Marie.

We take courses from this place:
http://en.lernu.net/
It is the easiest language I have touched since Indonesian, and here are some reasons for it:
1. It has only one gender
2. It has only one plural form
3. It has only two cases
4. It has shitloads of cognates with languages I already know (a bit of)
5. All nouns end with o, all adjectives with a, all infinitives with i, and all adverbs in e.

In Esperanto, "how are you?" is rendered "kiel vi fartas?". We like to think of it as asking someone how they're farting whenever we meet. As soon as we get over this immature fixation on [fartas], we shall proceed and learn the rest of the language.

Tale of the Fishwife and its Sad Fate

2011-05-07T09:18:00.009+08:00

Note: [See original post] noun genders are indicated by colour

It is a bleak Day. Hear the Rain, how he pours, and the Hail, how he rattles; and see the Snow, how he drifts along, and of the Mud, how deep he is! Ah the poor Fishwife, it is stuck fast in the Mire; it has dropped its Basket of Fishes; and its Hands have been cut by the Scales as it seized some of the falling Creatures; and one Scale has even got into its Eye, and it cannot get her out. It opens its Mouth to cry for Help; but if any Sound comes out of him, alas he is drowned by the raging of the Storm.

And now a Tomcat has got one of the Fishes and she will surely escape with him. No, she bites off a Fin, she holds her in her Mouth -- will she swallow her? No, the Fishwife's brave Mother-dog deserts his Puppies and rescues the Fin -- which he eats, himself, as his Reward. O, horror, the Lightning has struck the Fish-basket; he sets him on Fire; see the Flame, how she licks the doomed Utensil with her red and angry Tongue; now she attacks the helpless Fishwife's Foot -- she burns him up, all but the big Toe, and even she is partly consumed; and still she spreads, still she waves her fiery Tongues; she attacks the Fishwife's Leg and destroys it; she attacks its Hand and destroys her also; she attacks the Fishwife's Leg(?) and destroys her also; she attacks its Body and consumes him; she wreathes herself about its Heart and it is consumed; next about its Breast, and in a Moment she is a Cinder; now she reaches its Neck -- he goes; now its Chin -- it goes; now its Nose -- she goes. In another Moment, except Help come, the Fishwife will be no more. Time presses -- is there none to succor and save?

Yes! Joy, joy, with flying Feet the she-Englishwoman comes! But alas, the generous she-Female is too late: where now is the fated Fishwife? It has ceased from its Sufferings, it has gone to a better Land; all that is left of it for its loved Ones to lament over, is this poor smoldering Ash-heap. Ah, woeful, woeful Ash-heap! Let us take him up tenderly, reverently, upon the lowly Shovel, and bear him to his long Rest, with the Prayer that when he rises again it will be a Realm where he will have one good square responsible Sex, and have it all to himself, instead of having a mangy lot of assorted Sexes scattered all over him in Spots.

-- Mark Twain, in The Awful German Tongue (1880)

Abstract and Postmodern Art

2011-04-28T10:03:00.012+08:00

This came up on the front page of ST a while back:

This is bad. It seems that the word "abstract" has been stripped of its original meaning and used as an sweeping term for modern art. Maybe I haven't been to any art conventions lately, but I have hardly seen any piece in the Singapore Biennales which I can call "abstract" with a clear conscience and a straight face.

Most of the works, however, can be labeled as "postmodern". Now this is a word which can be abused much any way you like, because not even artists can agree on what it is really about. Allow me to make clear this distinction between "abstract" and "postmodern":

Abstract Art
1. MONDRIAN Piet: Still Life with Gingerpot I - Cubist
2. Ibid.: Still Life with Gingerpot II - Simplified (both 1912)

These pieces are very easy to understand. Basically, they are still-life drawings of kitchenware drawn in a very interestingly sloppy manner. This shift of styles towards ingenious sloppiness or simpler form is what we call Abstraction.

Postmodern Art
3. ČERNÝ David: Mimi Kampa (2000)

Postmodern art happens when the artist hates you.

It is still a gross oversimplification, but it sounds smarter on the newspapers.

Real Analysis

2011-04-26T20:40:00.016+08:00

So the exam was over on Monday. I am still not sure if I will need to do an S/U on the module, but if I ever get so much as a B+ I would be content and hell I'll drag Surya out to one of those green spaces left around school and dance around with him in joy. (FYI: Surya is the other guy from Engineering who took this module for fun.)

Artist's Impression

Bidding for this module was foolhardiness from the start. Learning the methods of Real Analysis has been an uphill task, but explaining its contents to interested passers-by was also difficult, so I'll do just that.

The Meaning of Real Analysis

Calculus, the crown jewels of MA1505, was invented independently by different folks in the 14th to 17th centuries. Apparently where caluclus started, it was mathematically sloppy, but got away with it for being so useful. Nonetheless it was met with attacks from other scholars, among them my old friend Bishop Berkeley. In time, the properties of the calculus-universe would be gradually built up and moulded by those willing to clean up Newton's and Leibniz's mess, and the cleaning process became the field we call Real Analysis.

Formalities: Definition, Theorems and Proofs

Because it looks base-wards from calculus, rather than to the frontiers of math, most of the concepts we tackle are simple and intuitive. This sadly does not make them any easier. It does, however, mean that we have to scrutinise our every preconception to all that we think we know to be true. This is achieved by definitions made precise with numerical gauges and basic rules of algebra. A case in point:

Continuity of a function is
MA1505: "that you can draw its graph in one go without having to lift your pencil from the paper."
MA2108: "if ∀ε>0 ∃δ>0 such that ∣x-a∣<δ ⇒ ∣f(x)-f(a)∣<ε, then f is continuous on a."

So instead of drawing a continuous line without lifting the pencil from the paper to prove a point, you broke everything up into numbers and shifted them around and prayed hard that they agreed with you.

This may seem frivolous at first, but as the lectures go on we saw the definition spew out quite some interesting conclusions. For example, a function can be continuous at only one point. Trying to show it with pencil and paper is quite pointless, but you will be able to show, with definition, that something like

f(x) = {x² if x is rational, 0 if x is irrational}

does just that at x=0.
Also I mentioned Thomae's Popcorn function some entries back. You guys totally should look at it again. The idiot is continuous on all irrational x and discontinuous on all rational x. It is so crazy I still find it hard to swallow, even if I am able to prove it back to front.

The start of the module was the hardest because we were having our hands tied up behind out backs and mulling over things like a+b = b+a like we were newborns. Things got better later on when we found out certain theorems have been proven so that we can use them with impunity. But then there were other things to worry about.

Aesthetics: Niceness

This is to recall the things I picked up last semester about mathematicians being artists inside. William Byers wrote about mathematical beauty. David Hilbert complained about finding not enough imagination in his students. Leung Man Chun played the Concierto de Aranjuez before every lecture.

Artists would be familiar to the fact that mathematics can be, and are often used to make art. In particular, I have come across a section of the shelf on Medical/Science library (5th floor) with material on Splines, NURBs and other cool inscrutable stuff we find mentioned and used all the time in 3D modeling software. Apparently meshSmooth, spline curves, and modeling by contour uses Real Analysis. This is so interesting

I would like to take this opportunity to show off my "modeling by contour"

In Real Analysis, niceness is a real thing, and is mathematically defined. A continuous function is a nice mapping of ℝ on ℝ, and a uniformly continuous function is a nice continuous function. And a properly divergent sequence diverges quite neatly also. And together they bask your notes in a warm glow.

How to prepare for this module

Being a Math student helps. Having taken MA1100 Fundamentals of Mathematics also helps, because your teachers will assume you picked up from there. If you're one of my ilk, it helps to understand that this is no maths that you have seen before. It is useless to think of anything as "plug in formulas to get a number" (even though I have guiltily indulged in "plug in theorems to get a proof" from time to time). It is helpful to remind yourself that nothing is static, everything is uncertain, and that skepticism is the rule before where the fatal QED lies. Having a lively mind helps, so taking up some sport would be a good idea.

Postscript
Exam Qn 3 b) iii)
Ohmigod, look at this guy, just look at him.

Freshman Journal 1.2.13

2011-04-17T11:48:00.009+08:00

A: Real Analysis
Cue from Bartle and Sherbert (2000) Chapters 2, 3, 4 and 5 (corresponding to school notes 1, 2, 4, 5). Chapter 3 (Infinite Series) is sadly not represented in textbook.
Summary:
Chapter 1: ℝ
Chapter 2: Sequences
Chapter 3: Series
Chapter 4: Limits of functions
Chapter 5: Continuous functions
Modus Operandi: Mop up unanswered questions in tutorials (without reference to answers), finish textbook exercises.

B: Engineering Maths II
Cue from Farlow et al. (2007) Chapters 1-6 and 8.
The textbook syllabus is matched to the school notes as follows:
(School notes : Textbook sections)
Part 1. ODE and applications
Chapter 1 ODEs: 1.3, 2.2, 4.2-5
Chapter 2 Oscillations: 4.1, 4.6, 4.7
Chapter 3 Modelling: 1.1, 2.3-5
Chapter 4 Laplace Transform: 8.1-3
Part 2. Linear Algebra and applications
Chapter 5 Matrices: 3.1, 3.3
Chapter 6 Linear Transformations: 5.1-4
Chapter 7 ODE Systems: 6.2, 6.4
Part 3. PDE
Chapter 8 PDEs: refer to Advanced Engineering Math textbook by Kreyzig
Modus Operandi: Finish remaining textbook exercises, start past-year papers, create help-sheet based on compiled summary.

C: Engineering Physics II
Broad subtopics covered in First-year Engineering Physics, NUS:
1) Classical Mechanics (PC1431)
2) Thermodynamics (PC1431)
3) Electromagnetism
4) Optics
5) Quantum Mechanics
6) Atomic Physics
Modus Operandi: One-page summary per field + detailed overview of derivations (although to derive all that stuff in 4) or 5) is a bit trying)

D: Electrical Engineering
It turns out the content is really quite sparse and can be taken down to one page per chapter. Modus Operandi: copy everything down to a pocket-size (A6) notebook, then read on the bus.

E: German Language
A scheme of organising new vocabulary in the process of being perfected:
1. Nouns (organise into feminine / masculine / neuter)
1.i. by categories: ideas / things/ quantities and events / people / places
1.ii. by verb endings -ung / -eit / -ion / -ie / -ik (all with plural -en; female only)
1.iii. By gender-specific subcategory: e.g. [quantities], [days], [languages]
1.iv. By etymology: I use only [International] for nouns
1.v. By plural forms: e.g. ["-e], [e], [n]
1.vi. By composite roots: e.g. [-tasche(n)], [-pl(ä)tz(e)]

2. Verbs
2.i. Category 1: Modal (e.g. wollen, können, müssen)
2.ii. Category 2: Simple native (e.g. essen, schlafen)
2.iii. Category 3: Compound native (e.g. be.zahlen, ver.kaufen)
2.iv. Category 4: Cognate - native with English correspondent (e.g. trinken)
2.v. Category 5: International - Romance etymologies (e.g. notieren)
2.vi. Category 6: Separable (e.g. vorbei/gehen, wieder/sehen)
"." and "/" are used for clarity.

3. Prepositions
3.i. Accusative prepositions (e.g. bis, durch, entlang)
3.ii. Dative prepositions (e.g. aus, bei, mit)
3.iii. Variable-case prepositions (e.g. an, in, auf)
* note some prepositions can/must come after instead of before its subject

4. Others (these are not subdivided further)
4.i. Conjunctions
4.ii. Adjectives
4.iii. Adverbs

A person to look up to

2011-04-17T00:12:00.007+08:00

He may not be a genius, or know everything
He does not need to be great, to be a model of success
He does not need you to feel small around him.

The person you look up to, he lights a fire in you.
He is a person who wakes the sleeping giants
He exists not to be adulated, but to be surpassed.

Für der dritten Vokabeltest

2011-04-07T21:12:00.005+08:00

On nouns eg. Leute, Ferien for which only a plural form exists:

If a noun exists only in the plural form, does it have a gender?
If a tree falls in the forest and no one is around to hear it, does it still make a sound?

On nouns for which the plural form does not conform to any of the 8 regular forms

This ist ziemlich interessant. Notieren Sie that such words tend to be of foreign origin, in particular from Greek or Lateinisch. Let's have a look.

die Praxis - Praxen: Ancient Greek πρᾶξις
das Stadion - Stadien: Ancient Greek στάδιον
das Zentrum - Zentren: Latin centrum - Ancient Greek κέντρον
die Basis - Basen: Ancient Greek βάσις auch via Latin
das Taxi - Taxen: borrowed word short for taxicab, portmanteau of taximeter and cabriolet - taximeter is from French taximètre, which is from German (!) Taxameter - Taxameter is coined from medieval Latin taxa, meaning tax - taxa comes from proto-Indo-European, let's not go there.
die Cafeteria - Cafeterien or Cafeterias: borrowing from the American Spanish, which in turn is a borrowing from French, which borrowed from Turkish, and then Arabic etc.

Let's just forget the last two

Some more things that need clarifying

2011-04-07T14:23:00.003+08:00

Concerning (apparently) obscure fields of study

1. Astronomy

Clarification: If you ask an astronomer to read your star signs, you are asking for a beating with a blunt instrument which you may not even know the name to.

2. Linguistics

Clarification: Linguistics is not equal to foreign languages.
To add: My Arts GEM shall be a linguistics module, and so will my SS if there ever is one

3. Mathematics

"Why would anyone want to take a minor in Mathematics?"
Clarification: Mathematics is actually awesome

Songs from 3 April 2011

2011-04-04T16:52:00.004+08:00

El Silencio
Federico García Lorca
As heard in El Jardin de la Vida y la Muerte

Oye, hijo mío, el silencio.
Es un silencio ondulado,
un silencio,
donde resbalan valles y ecos
y que inclina las frentes
hacia el suelo.

Listen, my son: the silence / It is a rolling silence, / a silence / where valleys and echoes slip / and it bends foreheads / down to the ground. // Life and death? / La Vida y la Muerte? / Eros and Thanatos

Raghupati Raghava Raja Ram
Vishnu Digambar Paluskar
As heard in Satyagraha

रघुपति राघव राजाराम, पतित पावन सीताराम
सीताराम सीताराम, भज प्यारे तू सीताराम
ईश्वर अल्लाह तेरो नाम, सब को सन्मति दे भगवान

Raghupati raaghav raajaaraam, patit paavan sitaram
Siitaaraam, sitaram, bhaj pyaare tu sitaram
Iishvar Allah tero naam, sab ko sanmati de bhagavaan

Chief of the house of Raghu, Lord Rama, uplifters of those who have fallen, Sita and Rama,
Sita and Rama, Sita and Rama, O beloved, praise Sita and Rama,
God and Allah are your names, Bless everyone with this wisdom, Lord.

Freshman Journal 1.2.11

2011-03-30T17:32:00.007+08:00

Strings of Time Concert is this Sunday, 7:30pm.

Analysis
Things have stopped being what they seem to be when it came to continuity of functions: After a very convincing proof that Thomae's popcorn function is indeed continuous on all irrational points and discontinuous on all rational points, I am still not convinced to the guts that it is really so. Seriously, look at this guy

Differential Equations and Linear Algebra
Was the first in my 6 courses to wrap up. I'd be glad to pick up MA3220 as a more rigorous continuation of this theme in the indefinite future when I would feel like a risky challenge again.

Engineering Physics II
We're at quantum physics. Not too tough a nut to crack. Weird as it is, the subject is after all something we grew up with.

Tipps für Sprachtraining

2011-03-06T00:18:00.008+08:00

A couple of coursemates asked me this earlier, and so I compile a list of all the desperate measures I have taken in learning German. No, I have never learned German before, and I have never even touched the language save one or two swearwords. So maybe this list would help aspiring upstarts in this new language to find a foothold. Also,

1. Label everything about the house with colour-coded cards (I use blue for Maskulinum, pink for Femininum and purple for Neutrum). Walk around when slacking and note each label passively every time you pass by them. It is best if they are put in as conspicuous a place as possible. This makes your life easier and gives you something to show off to guests.

2. Because not everything can be labeled, rewrite new vocabulary into a notebook and classify by nouns / verbs / adverbs / prepositions. Take special care to divide nouns by the three genders, and better still to subdivide them again: for this task, I use this scheme of classification:
i. Abstract concepts
ii. Mensural quantities
iii. Places and collectives
iv. Objects

3. Speak in a bastard pidgin of German and whatever languages you know already. This is arguably easier for Singaporeans who have been doing language syncretism all their lives. The idea is to feel a sense of ownership towards German.

4. Do your tutorials in German for subjects other than German. The ideal subjects to do this in would be Mathematics and Physics (more logic than number of scientific terms) so you can learn a minimum of German specialist terms and proceed confidently from there. Again, this is more for growing into the language than anything else.

5. Specialist terms: You might have come across a few German words as you read through class notes, novels, textbooks, etc. In that case, remember them and do not let them go! Many such terms have since been borrowed into English. Some examples:
Gedankenexperiment - thought experiment (usually used in Physics)
Schadenfreude - happiness derived from someone else's misfortune
Gestalt - The "thingness" of a group of things (usually used to sound smart)
Gesamtkunstwerk - total work of art (Art)
Sprachbund - group of superficially similar languages (Linguistics)
Urheimat - original homeland of speakers of a particular language family (Linguistics)
Weltschmerz - a feeling of despair about the world (Literary Criticism)
Urtext - musical scores as written by the composer (Music)

6. Learn from cognates: Using a little bit of imagination, link German words to their English correspondent. e.g.
die Rechnung - the "reckoning" (= calculation) - the (restaurant) bill
jetzt - "yet" - now

If you are feeling adventurous, rope more languages into the game:
das Fenster - fenestra (Latin) - window
warum - värfor (Swedish) - wherefore (early modern English) - why
kennen - ken (Scots) - to know

These may or may not be true cognates, but anything goes if it works as a memory aid!

----------------------------------------------

Additional possible tip for verb conjugation: You might have noticed a pattern in the verb conjugation tables: some irregular verbs may not be so irregular after all! As it seems, some verbs actually fall into another category i.e. those with a change of pronunciation when applied to (du) and (er/sie/es). This pronunciation shift is called an ablaut (German linguistics term again!) and so we term these verbs "ablaut-regular"

eg 1: (wir/sie) nehmen - (du) nimmst - (er/sie/es) nimmt - (ihr) nehmt
ablaut: e to i
eg 2: (wir/sie) schlafen - (du) schläfst - (er/sie/es) schläft - (ihr) schlaft
ablaut: a to ä

note that the ablaut tends to be from a "broader" vowel to a "narrower" one
note also that there is no ablaut when (ihr) is concerned.

Freshman Journal 1.2.7

2011-03-05T23:24:00.004+08:00

I. Recess Week
Wonderful seven days of mug marathon with Zhang Hao, Lin Xi, Bartle & Sherbet, Young & Freedman, and Farlow et al. all around school. Also featured were good food from Blooie's at Science Park and spectacular artistry from Dance Synergy (Tuesday) and Bubble Tea (Friday).

The NUS Science/Medical Library is a truly underrated destination in the school. Serious muggers should study there. In fact all engineers should shun Central Library and just come to study there instead, although on second thoughts that might not work out so well.

Another underrated place is the Music Library, for its cleanliness, quietness, and shelves after shelves of bundled-up Awesome.

II. Test Summary
Analysis
Time spent on Analysis in Recess Week: ~2 out of 7 days
Test was on Monday. Proceedings were beautiful and clean-cut; you know how well you've done as soon as you hand the paper in, although I'm not sure if 70% is a good grade in this module.

Differential Equations
Time spent on DEs in Recess Week: ~5 out of 7 days
Returned score: 6/10
Outcome: Anguish, heartbreak, wailing and gnashing of teeth.

Electrical Engineering
Time spent on EE in Recess Week: ~0 out of 7 days
No problem on this one... Again, I see the disconcerting inverse relationship between effort and results.

Physics
Time spent on E&M in Recess Week: ~1 out of 7 days, but progress is largely made on panicking last-minute revisions during term time.
Outcome: probably better than maths.

~~Programming~~ Don't even mention this psychopathic mid-term.

Think about what C can be like!

Horehronie

2011-02-27T13:33:00.002+08:00

Horehronie
Kamil Peteraj (lyr.) / Martin Kavulič (comp.) / Kristína Peláková

Keď sa slnko skloní na Horehroní chce sa mi spievať, zomrieť aj žiť
Keď sa slnko skloní na Horehroní túžim sa k nebu priblížiť
Na tráve ležím a snívam o čom sama neviem
V tom vánku, čo ma kolíše keď je slnko najnižšie

Najkrajšie stromy sú na Horehroní to tiché bratstvo vraví mi poď
Sem sa vždy vrátim keď ma niečo zroní, vravia to stromy: z pliec to zhoď
Na tráve ležím a snívam o čom sama neviem
V tom vánku, čo ma kolíše keď je slnko najnižšie

Keď sa slnko skloní na Horehroní tam niekde v ďiaľke náš zvon zvoní
Keď má ma to bolieť tak nech ma bolí raz sa to stratí do čiernej hory
Na tráve ležím a snívam oči tíško plačú
V tom vánku, čo ma kolíše keď je slnko najnižšie

Na tráve ležím a snívam oči tíško plačú
V tom vánku, čo ma kolíše keď je slnko najnižšie

Najkrajšie stromy sú na Horehroní

When the sun goes down in Horehronie, I want to sing, die and live
When the sun goes down in Horehronie, I wish I could get closer to the sky
I’m lying on the grass and dreaming, of what, I don’t even know myself
In the breeze that gently sways me, when the sun is at its lowest point

The most beautiful trees are in Horehronie, a silent brotherhood is telling me: come
I come back here when I feel sad, the trees are saying: shake it off
I’m lying on the grass and dreaming, of what, I don’t even know myself
In the breeze that gently sways me, when the sun is at its lowest point

When the sun goes down in Horehronie, out there somewhere far away our bell is ringing
When it hurts, let it hurt, one day it will vanish in the black mountain
I’m lying on the grass and dreaming, my eyes are crying softly
In the breeze that gently sways me, when the sun is at its lowest point

I’m lying on the grass and dreaming, my eyes are crying softly
In the breeze that gently sways me, when the sun is at its lowest point

The most beautiful trees are in Horehronie

Street Brawl Mathematics

2011-02-23T21:34:00.022+08:00

A summary of MA1506 class notes, Chapter 1
Imagine that you are taking a stroll home after a long day spent doing Real Analysis and pitting proving skills against tea buddies. It is very late into the night and your wife is getting impatient, so you decide to take a shortcut home through the deep, meandering alleyways through the city's underbelly.

It is your first time here; you do not know yet that by entering the slums, you have thrown Real Analysis to the four winds and yourself into that desperate quagmire which is Differential Equations.

Before you know it, you have angered the denizens of the alley. You meet your first adversary.

This is a passing drunkard who just needed someone to blab at. Fortunately, you know that these drunkards can easily be subdued using Leibniz's notation of the derivative, dy/dx.

The poor fellow has scarcely put up a fight. He does not even try to get up again, so you roll him to his side, lest he choke on his own vomit.

As you advance, several more drunkards appear (have you been walking close to a club?). They do not look as soft as the first one, but you pwn them anyway by using simple substitutions and then invoking the power of Leibniz.

Photo by John Hutchinson
As you retreat further away from the hypothetical nightclub, your assailants become less and less benign. News seems to have leaked that a novice mathematics student has wandered into D.E. territory, and the first bandits move in to the plunder: the First Order Linear gang with the Bernoulli and Ricatti clans.

However, they have sorely underestimated your prowess; obsessed as you are with logical clarity and intuition, you are not above borrowing the ideas of the masters without questioning. The raiding party learns this the hard way.

The defeat of the Linear First Order sends shock-waves through the bandit community. Clearly, this guy knows a thing or two, even if all he knows is engineering math! Not admitting defeat, the bandits send out a second detachment.

Unfazed, you tackle the leader of the pack first: the homogeneous equation. You subdue him with a risky but deadly substitution

and reduced the pack leader to a shapeless heap of general solutions.

The rest of the pack are scared shiteless, because by the Superposition principle, they are already halfway into utter defeat. Working down the hierarchy with the Method of Undetermined Coefficients, you make sure that the gangsters with the polynomial, exponential and trigonometric forcing functions wish they had never been born. In that very order.

Source: Farlow et al. (2007)
This is an ancient and arcane martial art, the underlying wisdom to which you have very little idea of. But never mind, right now it is enough to know all the moves. Besides, you have to confront your next opponent, the real boss of this line-up, the all-encompassing Nonhomogeneous Second Order Monstrosity with Nonconstant Coefficients.

You are forced now to use a tactic which is so tedious, your trainers expect you to refer to the manual every time the need arises.

Source: Mid-Terms field manual.
Heaving a sigh of regret, you recall that you have accidentally left your prize weapon at home, or was it at the tea party? Where is your Laplace Transform when you most needed it?

In any case, you eventually bring down the boss with the Variation of Parameters, a method even more inscrutable than the last. In fact, it is so arcane that it is not even clear why it is called "Variation of Parameters".

The coast is clear, at least for now. You look wistfully at the Farlow et al. (2007) 2nd ed. which has guided you through this tough journey. Unfortunately, you are still very far away from home. Feeling absolutely worn out after many fights, you drift to sleep to wake up in the real world that you call your own.

Appendix: A little background:
Real Analysis here refers to the module MA2108 Mathematical Analysis I, taken by all 2nd year mathematics and statistics majors (and foolhardy idiots like yours truly).

Differential Equations here refers to the first half of the module MA1506 Mathematics II, taken by all 1st year engineering and physics majors in NUS.

Note that these two fields are related. That is, that the logical foundations of MA1506 are established in MA2108. Together, Analysis, Calculus and Differential Equations form a continguous chain. That is,

Notice how below "MA1506" I have put "MA3220". This module is THE D.E. module as offered to math majors, so you get and idea how deep we engineering year 1 students are in the ground right now. But still, life goes on.

Strings of Time

2011-02-21T04:56:00.004+08:00

Before everything else,

STRINGS OF TIME: 30 YEARS OF GENUS
This concert is going to be so awesome. To understand why, please refer to the concert repertoire.

1. CASTEELS Robert: El Jardín de la Vida y la Muerte
_______ with the flamenco dancers from Los Tarantos
2. CASTEELS Robert after RAVEL Maurice: Bô Vélo
3. ISHIZUKA M.: Nagashino
4. ABISHEGANADEN Alex: Huanyin Vanakam
5. GOPAL Balraj: Satyagraha (To the Great Soul)
6. Gabrielee and Alvin: The Phunk Experiment
_______ with NUS Electronic Music Lab

Date: 3 April 2011, Sunday
Venue: Yong Siew Toh Conservatory Concert Hall (close by UCC)
Tickets are priced sixteen and nineteen dollars.
The calluses on my left hand! May you never fail me

Für der zuerst Vokabeltest

2011-02-15T00:07:00.008+08:00

Start is male - Ending is female

Word is neuter - Syllable is female - Stressed syllable is male

Language is female - German is neuter

Banknotes are male - Coins are female

Water is neuter - Other drinks are male - Drinks are neuter

Dialogues are male - Conversations are neuter

Sound is male - Music is female

Bounded pages are neuter - Pages are female

Cafés are neuter - Cafeterias are female

Girls are neuter

Schrank is cupboard
Schränke is cupboards
Schranke is barrier
Schranken is barriers
Cupboards are male - Barriers are female

Absent Parade

2011-02-12T10:29:00.003+08:00

Stuff from my 2008 diaries, a short dialog involving two soldiers on midnight prowling duty and the existence of ghosts.

a. It's cold tonight; let's get back.
b. Aren't we going through the parade square this time?
a. This time? No. We'll just fill the checkpoints in and be off.
b. Why?
a. Look across the parade square.
b. I see.
a. A little dark?
b. Ah, well?
a. Do you see people?
b. Yes... vaguely. They're not supposed to be there, are they?
a. They don't belong there at all. Maybe not some point in the past, but not now. They would be marching in formation near the guard house every twentieth night of the month, and have been doing so for as long as I am here, at least.
b. Do you mean they're ghosts? Now that is hard to grasp, because you aren't really spooked and I don't believe they exist.
a. You're right there, they don't. You just have to shine a light at them to know that they... aren't really there. They never do us real harm and we get used to them.
b. What would you see with the lights on?
a. You'd see an empty parade square.
b. Why don't we try it now, then?
a. I wouldn't do it so much; wouldn't want to annoy their CO.
b. Their CO?
a. Wouldn't like to get into trouble with an officer, even one who isn't really there. Ah well... I don't believe in ghosts either.
b. But you talk about them all the time!
a. Do you believe in women, since you talk about them all the time also?
b. But they exist, don't they? Hey, that's a different matter!
a. Still, it doesn't matter if it is there or not; I've gotten used to it.
b. So you have. Let's get back, we've been staring at nothing for ages.

Let him boast

2011-01-30T22:04:00.005+08:00

Take yourselves for instance, brothers, at the time when you were called:
how many of you were wise in the ordinary sense of the word,
----- how many were influential people, or came from noble families?

No, it was to shame the wise that God chose what is foolish by human reckoning,
and to shame what is strong that he chose what is weak by human reckoning;

Those whom the world thinks common and contemptible
-----are the ones that God has chosen
----- -- those who are nothing at all to show up those who are everything.
The human race has nothing to boast about to God,
but you, God has made members of Christ Jesus
and by God's doing he has become our wisdom,
----- and our virtue, and our holiness, and our freedom.
As scripture says:
----- if anyone wants to boast, let him boast about the Lord.

1 Corinthians 1:26-31

Freshman Journal 1.2.3

2011-01-27T17:52:00.007+08:00

Analysis
I've started to refer to this subject colloquially as "Gay Maths" for obvious enough reasons.
Some things (other than class topics) they taught this week:
1. Good mathematicians always cover their tracks. This is why proofs are so inscrutable.
2. Direct proofs are preferred over contradiction proofs.

Started on practices in the textbook because I've been lagging behind. It turns out that I had been too complacent for the first two weeks. Never mind, I will catch up. Watch out, PRCs!

Yesterday, I proudly produced my first contrapositive proof. My first! And to think that now we are at limits!

Differential Equations
Zhuo Min said: Your lecturer probably taught differential equations as little more than a bag of tricks to solve specific equations (variable separable, those amenable to funny substitutions, etc.), many of which do not arise in practice. Such pedagogy will never convey the beauty of the subject.

THAT WAS EXACTLY WHAT WAS HAPPENING
although later on, we would be entertained to death with cute Java applets.

Physics / Electrical Engineering
These subjects are still the least of my worries, but please, don't go the way of MA2108 such that I have to panic later!

O Mastering Physics, Wherefore Art Thou Always Lagging?

Programming
Lab assignment was conducted through Vim, a compiler interface developed in 1990, which contrasted strongly with the futuristic setting where tutors can open windows on your desktop and mess with your screens remotely and with capricious glee.

German
I am in need of a German sänger to accompany me through this ongoing Deutschkurs.
The German folk music scene seems sadly stunted... Apparently, it has never been through a revival stage, like what they had in Ireland or Sweden.
Also, the only German classical composer I really listen to is Hildergard of Bingen, the 12th century polymath genius who wrote her songs in freakin' Latin.

It should be time to warm up to my old flames, 1. Philosophy and 2. the avant-garde Art world (with a capital A)
How are you, documenta!

Freshman Journal 1.2.2

2011-01-22T20:19:00.004+08:00

Analysis
Real Numbers was rounded up pretty peacefully this week. Analysis is straightforward FOR NOW.

Differential Equations
"On the other hand, if y₀ is a solution of (2) and y₁ is a solution of (1), then clearly y₁ + y₀ is again a solution of (1)."

I have no better way to express my feelings than

Physics / Electrical Engineering / German / Programming
How can these subjects turn out to be so simple!

Guitar Ensemble
2 new songs have been added to the concert repertoire since the last entry. They are:
CASTEELS Robert: The Garden of Life and Death
Gabrielee and Alvin: The Phunk Experiment

You might have seen it coming, but the original composition by our musical director also prominently features this:

Elsewhere
I always love it when La Niña comes to Singapore and wishes it would stay a bit longer, but not absolutely.

Freshman Journal 1.2.1

2011-01-14T10:35:00.003+08:00

Elsewhere:
My 2006 painting has found its third resting place, this time in one of the new principal's offices. For some strange reason, Temple Hill has had much better publicity than my more recent and better delivered works. Now I have to wait for him to get tired of the painting before I can take it back, fix it and put my signature on it.

This is how it looks like at the moment:

MA2108 Mathematical Analysis I
The semester was kick-started by this introduction on how to make Calculus rigorous mathematics i.e. more kickass.
Only 3 topics are covered in the module: real numbers, sequences and series, and limits and continuity of functions.
The plan for my math minor modules are dominated by Analysis rather than maths of any other sort. I'm not too sure if it is a good plan to do this in terms of variety and wtfness of subject matter.
In summary,
Minor modules (projected)
MA1505 Mathematics I
MA1506 Mathematics II (Engineering Math modules)
MA2101 Linear Algebra II
MA2108 Mathematical Analysis I
MA3110 Mathematical Analysis II
MA3209 Mathematical Analysis III

MA1506 Mathematics II
The semester's second lecture was on Differential Equations, something rather more inscrutable, technical, and reliant on rote learning than Calculus. I shall see what I can do about it!
In summary,
MA1505: Calculus
MA1506: Differential Equations and Linear Algebra (Also prerequisite to MA2101)

EG1108 Electrical Engineering
A brief foray into the subject my dad teaches.

PC1432 Physics IIE (Engineering Physics part II)
The first lecture is basically the same thing as that of EG1108

CS1010E Programming Methodology
Sitting in the first rows didn't prevent me from falling asleep. Sorry Lecturer

LAG1201 German I
First serious attempt to learn a foreign language after halfhearted attempts at Hungarian, Russian and French.
Herr Döpel took over from our lecturer, who was absent that morning, and there we recited the German alphabet to the rising sun.

Barroca and Waltz

2011-01-02T19:27:00.004+08:00

Title: Barroca - Mil e uma Noites (Arabian Nights)
Music: (composer unknown)
As performed by: Uakti (Brazil) / 1982
Code: T02.br

Title: La Valse des Belugas (Waltz of the Belugas)
Music: André Marchand
As performed by: La Bottine Souriante (Canada) / 1988
Code: T03.ca

Lo, how a Rose e'er bloomin'

2010-12-24T23:16:00.003+08:00

1. Es ist ein Ros' entsprungen (adap. Praetorius 1609)
2. Nu är det jul (Trad.)

Ale Möller (Mandola and flute)
Lisa Rydberg and Esbjörn Hazelius (Violins)
Roger Tallroth (Bouzouki)
Olle Linder (Double Bass)

A Blessed Christmas to all in this sainted year 2010!

Sjömansvisan

2010-12-19T12:34:00.007+08:00

My first complete transcription on Sibelius 5, a slow-ish sailor's ballad:

Title: Sjömansvisan (The Sailor's Song)
Lyrics: Traditional Swedish
Music: Ulrika Bodén
As performed by: Ranarim (Sweden)
Code: T01.se / [see complete PDF]

Lyrics:

Skeppet seglar och vinden blåser
nu hissar vi våra ankar
vi ska segla till vännen kära
den vi har i våra tankar
Räck mig nu den snövita handen
om du vill bliva min kära
och vi ska tacka både fader och mor
om vi varandra skall äga

Dagen lider och solen skrider
och stjärnorna tändas upp igen
inte kan jag till vännen komma
varken åka, rida eller gå
Räck mig nu den snövita handen
om du vill bliva min kära
men jag får vänta till sol och sommardag
då jag seglar över böljan blå

Translation:

The vessel sails and the wind blows
Now we raise our anchors
We’ll sail to our beloved,
who is in our thoughts
Reach out your snow-white hand
If you will be my love
We shall thank both Mother and Father
if we shall have each other

The day passes and the sun moves across the sky
The stars are again lit
I cannot reach my beloved,
neither ride nor wander
Reach out your snow-white hand
If you will be my love
But I must wait for sun and summer days
to sail the bounding main

Inscription 640

2010-12-19T12:30:00.002+08:00

A summary of the previous weeks:

2 to 5 December
As the dust begins to settle over No Man's Land, the soldiers prepare themselves for the Christmas Truce party.

6 to 12 December
GENUS Music Camp.
Unbelievable wacky fun-filled camp with daily sectional and ensemble practice sessions. Location: Prince George Park

14, 16, 18 December
Some more practice sessions to top it.

13, 15 December
Practice and execution (respectively) of Carolling tour with NUS Catholic Student's Society. Locations: Church of St. Ignatius, Assisi Hospice, Orange Valley Nursing Home, some kindergarten.

17 December
Jedi's birthday party

18 December
On duty in church for 2 weddings in the morning, playing the role of a DJ of sorts. (Most on demand: The Wagner and Mendelssohn wedding marches)

Upcoming:

21 December
Release of Examination Results
GENUS Prime outing

28 December
RCIA Baptism and Christmas celebration

Allegro Gentile

2010-12-02T11:29:00.006+08:00

Concierto de Aranjuez
3rd movement: Allegro Gentile
Joaquín Rodrigo (Comp.) / Narciso Yepes (12-stringer)
Before each Wednesday or Friday evening lecture, Prof Leung liked to play Concierto de Aranjuez from Youtube as a kind of mood setting. Usually only movements 1 or 2 were played, but the third movement is my favourite, so here you go.

List of Solutions in GEK1517
Disclaimer: These are my own solutions, not the ones derived in class; so if I couldn't get a solution or the lecturer's solution is the same as mine, I would not post it. It should follow that the demonstrations are imperfect and not final.
Tutorial 1: Black Fridays
Tutorial 3: Cracking Tiles
Tutorial 6: Fibonacci's Rabbits
Tutorial 6: Turtle Crawl
Tutorial 8: Szymborska's Utopia
Examination: Proving the Obvious

Miscellany:
Application to MA1505: The Nabla Vector (use of metaphors)
Application to MA1505: Theorems of Vector Calculus (graphical demonstration)
Quote: Bishop George Berkeley (how not to learn science)
Quotes: Polanyi, Annan and Byers (somewhat random)
Concierto de Aranjuez, second movement

About the Course
A course in the ideas behind breakthroughs in mathematics. In the course, complicated ideas are broken down into simple ones and presented as the mathematicians would have imagined it. This idea is mirrored in the test/exam/tutorials, where one arrives at proofs using guided instructions. This course reveals the joy of mathematics. Despite this, it probably put off some people from maths forever.

Because some things cannot be unlearnt, the ideas of GEK1517 has stuck on me and follows me wherever I go, surfacing occasionally and unexpectedly in my other modules (Calculus, physics, chemistry and even writing!).

Proving the Obvious

2010-12-02T08:15:00.009+08:00

GEK1517 Examination / Question 1:

(i) Preface: Peano's Axioms
UT: The set of all natural numbers ℕ = {1, 2, 3, ...}
UT: 1
UT: Successor (here denoted by ')
(A1): 1 is a natural number
(A2): If a number a is a natural number, its successor is also a natural number
(A3): 1 is not the successor to any natural number
(A4): If two numbers have the same successor, they are the same number.
(A5): If 1 is a member of set K, and if for every natural number a, a is a member of K implies that a' is a member of K, then K is the set of all natural numbers. (Mathematical Induction).
The proofs in the following also feature reflexive equality (Ar) strongly. This is the first axiom in Peano's original list of axioms but was omitted from class notes. Essentially, it means x = x.

(ii) In the Peano axiomatic system for natural numbers, addition '+' is given inductively by the following two properties.
(+₁): a + 1 = a' for a ∈ ℕ
(+₂): a + b' = (a + b)' for a, b ∈ ℕ
Using (+₁), (+₂), and mathematical induction, show that
1 + a = a + 1 for all a ∈ ℕ

Solution:
Let P(a) denote (1 + a = a + 1 for all a ∈ ℕ)
P(1): 1 + 1 = 1 + 1 (true because (Ar))
P(k): 1 + k = k + 1 (force true)
P(k'): 1 + k' = k' + 1
(+₁): 1 + k' = (k + 1) + 1
(+₁): 1 + k' = (k + 1)'
(+₂): (1 + k)' = (k + 1)'
(A4): 1 + k = k + 1 (true because P(k))
(A5): Statement proven for for all a ∈ ℕ

Lemma 1 (L1): Commutativity of +
To prove: a + b = b + a for all a, b ∈ ℕ
Let P(a) denote (a + b = b + a) , b ∈ ℕ
P(1): 1 + b = b + 1 (true because (ii))
P(k): k + b = b + k (force true)
P(k'): k' + b = b + k'
(+₁): k + 1 + b = b + k'
(ii): k + b + 1 = b + k'
(+₁): k + b' = b + k'
(+₂): (k + b)' = (b + k)'
(A4): k + b = b + k (true because P(k))
(A5): Statement (L1) proven for for all a, b ∈ ℕ

(iii) In the Peano axiomatic system for natural numbers, multiplication '×' is given inductively by the following two properties.
(×₁): a × 1 = a for a ∈ ℕ
(×₂): a × b' = (a × b) + a for a, b ∈ ℕ
Using (×₁), (×₂), and mathematical induction, show that
a × 2 = a + a, and
a' × b = a × b + b for a, b ∈ ℕ

Solution part 1:
Let P(a) denote (a x 2 = a + a)
P(1): 1 × 2 = 1 + 1
What is 2? Take 2 = 1' (oh no...)
P(1): 1 × 1' = 1 + 1
(×₂): (1 x 1) + 1 = 1 + 1
(×₁): 1 + 1 = 1 + 1 (P(1) true because (Ar))
P(k): k × 2 = k + k (force true)
P(k'): k' × 2 = k' + k'
(2 = 1'): k' × 1' = k' + k'
(×₂): (k' × 1) + k' = k' + k'
(×₁): k' + k' = k' + k' (true because (Ar))
(A5): Statement proven for for all a ∈ ℕ

Solution part 2: Commutativity of ×
Let P(b) denote (a' × b = (a × b) + b), a ∈ ℕ
P(1): a' × 1 = (a × 1) + 1
(×₁): a' = a + 1
(+₁): a' = a' (true because (Ar))
P(k): a' × k = (a × k) + k (force true)
P(k'): a' × k' = (a × k') + k'
(×₂): (a' × k) + a' = (a × k) + a + k'
using P(k): (a × k) + k + a' = (a × k) + a + k'
(+₂): (a × k) + (k + a)' = (a × k) + (a + k)'
(L1): a + k = k + a
so (a × k) + (a + k)' = (a × k) + (a + k)' (true because (Ar))
(A5): Statement proven for for all a, b ∈ ℕ

Colophon:
The idea: you must forget all your arithmetic before you tackle this question. There is no arguing that "everyone knows" a+b = b+a; the only way is to prove it from the given axioms and properties. This is the intellectual equivalent of bailing out from a plane into the rainforest and building civilisation from the bottom up, right down to foraging for food, starting a fire, etc.

This is the first and only real proof in the series... I hope this is rigorous enough, and I hope the formatting makes it clear to follow (Facebook users please allow yourselves to be redirected to the "original post")

Regrettably, I did this only today, when the dust has settled over the exam period and freedom, merriment and general goofing off is in order. Never mind, enjoy the holidays folks.

Freshman Journal 1.1.R2

2010-11-17T22:54:00.002+08:00

USP Chatterbox
The hell was I thinking when I said no? USP is like some heaven on earth!

Revision Round-up
Maths
Made understandable: L'Hopital's Rule, Fourier coefficients, Green/Stokes/Gauss Theorems
What still needs to be looked into: Taylor coefficients, Hessian determinant, Vector dot/cross products

Physics
Done: Flowcharts for Newtonian Mechanics + Thermodynamics
Made understandable: Adiabatic free expansion (!!!!!)
I don't need to take out notes anymore AHAHAHA

Chemistry
Memorise stuff.

Mathematical Thinking
Philosophise.
Panic.

Szymborska's Utopia

2010-11-15T23:15:00.004+08:00

GEK1517 Tutorial 8 / Question 1: Discuss the metaphors and associations used in the following poem 'Utopia' by Ms. Wisława Szymborska (Nobel Laureate in Literature, 199[6]).

Ms. Wisława Symborska
I am sorry to find out, after a brief background search on Ms. Symborska, that her life displayed all the dweeb-patterns as seen in Jaromil, the Milan Kundera character I love to deride so much. This is not a very good poem; it makes an awkward reading, but the mathematical ideas expressed makes it relevant to the module and especially interesting.

This is reason enough for me to offer a free-rambling intepretation, so if you'll indulge me for one post--

Island where all becomes clear.
1. The island is Mathematics. Welcome to the world of Maths!

Solid ground beneath your feet.
2. "Solid ground" undefined terms, axioms of mathematics(?)
3. "Solid ground" everything else is groundless (?)

The only roads are those that offer access.
4. The only questions asked are constructive
aside: There are roads that "don't offer access"?!

Bushes bend beneath the weight of proofs.
5: Proofs open up new paths through ignorance (foliage)

The Tree of Valid Supposition grows here
with branches disentangled since time immemorial.
6: This vaguely refers to speculation, or intelligent guesses (?)

The Tree of Understanding, dazzlingly straight and simple,
sprouts by the spring called Now I Get It.
7: This vaguely refers to the "eureka" moment as cherished by all bona fide nerds.

The thicker the woods, the vaster the vista:
the Valley of Obviously.
8: At first I thought this was stating the obvious, but then
9: Imagine looking across the valley, specifically at the trees on the other side. You can see all the features there very clearly, but you have not found a way to get to the other side! For that, you will need some "[bush bending] beneath the weight of proofs."

If any doubts arise, the wind dispels them instantly.
10: Possibility 1. The atmosphere discourages you from thinking critically.
11: Possibility 2. In this Utopia, nothing stays unknown or unresolved for long.

Echoes stir unsummoned
and eagerly explain all the secrets of the worlds.
12: Because you get all these dead mathematicians whispering stuff into your ears.

On the right a cave where Meaning lies.

On the left the Lake of Deep Conviction.
Truth breaks from the bottom and bobs to the surface.
13: Conclusions comes only sporadically. Once it is freed from the lake bottom, it bobs quite readily to the surface. Maybe this means that the first step is always the hardest.

Unshakable Confidence towers over the valley.
Its peak offers an excellent view on the Essence of Things.
14: Possibly uncharacteristic praise of dogmatism.
Corollary to 14: Possibly, after all this doubting and questioning and decosntruction of knowledge, being a good mathematician still takes a definite serving of balls and tough braincases.

For all its charms, the island is uninhabited,
and the faint footprints scattered on its beaches
turn without exception to the sea.
15: No one makes mathematics his/her whole reality.

As if all you can do here is to leave
and plunge, never to return, into the depths.
16: Corollary to (15).

Into unfathomable life.
17: Classical dweeb sign-off!
18: Real life is always where we end up in and what we are more used to, even though it is more complicated and much harder to understand than mathematics.

--END OF EQUIVOCATION--

Please comment if you have some better way of deciphering the above poem!

Turtle Crawl

2010-11-13T22:54:00.007+08:00

GEK1517 Tutorial 6 / Question 2.
Consider the turtle's movement:
F means advancing 1 unit in the firection of the turtle's head:
+ / - means, respectively, turning the turtle's head to the right / left by d degrees - the position of the turtle remains unchanged.
Take d = 90˚and start with F + F + F + F (0[th] iteration). In the subsequent steps, let the rewriting rule be
F ↦ F - F + F
(a) Sketch the first two iterations.
(b) It is observed that in the first few iterations, the turtle always returns to the same position where it starts. Does this hold for all iterations? Present the key ideas critically and carefully to support your answers.

Key Ideas:
1: As given, Iteration 0 produces a closed loop.

2: (1) applies because in Iteration 0, F is reproduced 4 times, then joined together so that each F is rotated 90 degrees to the right w.r.t. the previous F. This forms a closed square loop.

3: In every subsequent iteration, the instances of F produce identical segments.
F + F + F + F
↦ F' + F' + F' + F'
↦ F" + F" + F" + F" ...

4. In every subsequent iteration, we find 4 identical segments joined end on end, each one rotated 90 degrees right w.r.t the previous segment. This also forms a closed loop.
Fⁿ + Fⁿ + Fⁿ + Fⁿ

4. If (4) is shown to be true, proposition holds for all iterations
Summary: (1) is given, (1) requires (2), (2)⇒(4) proven, ⇒ proposition holds

-- END OF DEMONSTRATION --

Iterations 3 and 4 for your enjoyment

Fibonacci's Rabbits

2010-11-13T22:27:00.004+08:00

GEK1517 Tutorial 6 / Question 1.
Starting with the letter b, consider the rewriting rules
b → a; a → ab.
For example, the first few 'words' formed by the above rewriting rules are
b, a, ab, aba, abaab, abaababa, ...
Let C(n) be the number of letters in the n-th word (n is a positive integer). For instances [sic],
C(1) = 1, C(2) = 1, C(3) = 2, C(4) = 3, C(5) = 5, C(6) = 8, ...
Prove that
C(n+1) = C(n) + C(n-1)
for all integers n ≥ 2. (Caution: Math. induction may not work well here.)

Spoiler: Lecturer's solution is more elegant, so please bear with me here.

Let number of 'b's in n-th word: B_n.
Let number of 'a's in n-th word: A_n.

Because of the rewriting rules b → a; a → ab.
'b's in a word is generated only from 'a's in the previous word
∴ B_n = A_n-1
'a's in a word is generated from both 'a's and 'b's in the previous word.
∴ A_n = A_n-1 + B_n-1

Now total number of letters in n-th word is C(n)
Total number of letters in n-th word is sum of 'a's and 'b's.
∴ C(n) = A_n + B_n
now
C(n-1) = A_n-1 + B_n-1 = A_n
C(n+1) = A_n+1 + B_n+1

To show that C(n+1) = C(n) + C(n-1), express all terms in A_n and B_n.
C(n+1) = C(n) + C(n-1)
⇒ A_n+1 + B_n+1 (LHS)
= A_n + B_n + A_n = 2A_n + B_n (RHS)
∵ B_n = A_n-1,
B_n+1 = A_n.
∵ A_n = A_n-1 + B_n-1,
A_n+1 = A_n + B_n.
Sub back into LHS:
LHS = A_n + A_n + B_n
= 2A_n + B_n = RHS.

-- END OF DEMONSTRATION --

Chimness

2010-11-12T11:54:00.002+08:00

Self-respecting intellectuals listen up:
If someone says your ideas are "chim", do not take it as a compliment.
It is an INSULT.
Go back home and sleep on a nettle bed.
Hang a snake gall from the ceiling or something to remind yourself of the shame you had to bear.
Later on, make a comeback by presenting your ideas more clearly and intuitively.

Somewhat Random Quotables

2010-11-12T11:25:00.003+08:00

It is only in the popular mind that knowledge equates with facts.
That is of course flattering, since facts are incontrovertible.
But it is also demeaning, since facts are meaningless;
they contain no narrative.

-- POLANYI John Charles

The idea that there is one people in possession to the truth,
one answer to the world's ills,
or one solution to humanity's needs,
has done untold harm throughout history, especially in the last century.

-- ANNAN Kofi (2001)

The certainty of mathematics is different from the certainty one finds in other fields; it is somehow purer and therefore more powerful. To be certain is to know. What an extraordinary feeling it is to know and to know that you know! What strength there is in that position! What confidence one has when one sees into the truth of some mathematical theorem! The angles of a triangle add up to two right angles. It is not a matter of "probably," "almost always," "in our experience," or "as far as we know." None of these usual caveats apply -- there is no quibbling. If you are not completely certain, if you have the slightest doubt, then you just don't get it. Mathematical truth has this certainty, this quality of inexorability. This is its essence.

-- BYERS William (2007), How Mathematicians Think
I just love it when mathematicians get emotional.

Theorems of Vector Calculus

2010-11-05T20:40:00.024+08:00

Notes on the physical meanings of the theorems of Green, Stokes and Gauss covered in MA1505 Chapter 10

Introduction
Those who are familiar with the Mathematics module (the one specially designed to traumatise engineering freshmen) would readily identify the following formulas to be the point where it all starts to fall apart (ignoring Fourier series).

At first glance, these formulae all seem to be coincidence, as what can there be to relate integration over a line with integration over a surface, or to relate integration over a surface with that over a volume? The notes give no helpful explanation either... but the underlying idea is quite simple to understand!

Disclaimer
This following is a demonstration, not a proof. The goal is understanding, not certainty. If one is interested, there are pretty good proofs for Green's theorem as well as the theorems of Stokes and Gauss (TAYLOR Peter D., 1992).

Idea
Special case assumption: When you sum up small loops, they become one big loop.
As seen in this tile of four loops, the interior arrows cancel out and leave the outer boundary of the loop (which has nothing to cancel out with).

We apply this principle everywhere else rather thoughtlessly. Does anyone remember Carnot engines from Physics PC1431? How do you reduce a reversible process to a sum of Carnot cycles?
Yes.
General assumption: The interior boundaries cancel out.
The important thing is that the R.H.S of the three theorems deal with summing up quantities for which the internal boundaries cancel out each other. This is why summations (integral) over a plane/volume can equate to summations over the plane/volume's outer boundary.
This general assumption is necessary to bring Gauss' Theorem into the discussion.

Stokes:A Loopy Proposition
Aside: In practise, it is easier to use Green's theorem to prove Stokes' Theorem rather than the other way round, for an idea how this is done, please refer to Thomas' Calculus (12th ed.), Chapter 16. However, for this section, only Stokes' theorem will be demonstrated (Green's theorem follows as its 2-D speical case, a fact which you may have learnt in class).

The basic idea of Stoke's theorem is to add up the curl (small loops) of the vector field to a closed-path integral (the big loop).
(1)It can be seen that in a 3-D space, many different surfaces can share the same boundary.

(2)As follows from the assumption, any closed loop can be split up into smaller loops, and then split up into even smaller loops, and so on ad infinitium. The sum of these loops, as expected, equals the big loop i.e. the boundary of the surface. This ensures that even for different surfaces, the integral can be the same if the surfaces share the same boundary!

(3)If the big loop can be thought of as the sum of infinitesimal loops, we can approximate each infinitesimal loop to the curl at a point (normal to the surface).

What is the meaning of curl?
Curl is what textbooks describe as "circulation density". Basically, it is how much vectors swirl in the immediate neighbourhood of a given point. The curl vector points upwards if the net circulation is counter-clockwise from above, and vice versa.

The big last step: Approximating infinitesimal loop to curl
After obtaining your infinitesimal surface dS, it is time to match the 2 quantities
(1) Line integral over the infinitesimal loop
(2) Curl over the point

Admittedly, I have not found a way to settle this step yet, but here are 2 important observations:

(1) The quantities a)line integral over infinitesimal closed loop and b)curl derive their values from the same 4 vectors in the neighbourhood of small surface area dS.

(2) Only the components of a) and b) aligned with the surface of dS are taken:

Gauss: Analogy using Jigsaw Pieces

The cutest formula in the bunch also looks the most devastating, not least for its prominent feature of a triple integral. However, the fact that features a divergence operator rather than a curl operator makes it infinity times friendlier to the brain.

Basically, what is says is:
The volume flow rate over a closed surface
is equal to
The net divergence in the volume enclosed by the surface.

What is the meaning of divergence?
Divergence at a point is a measure of the net tendency of nearby vectors to point inwards into the point or outwards away from the point.
Basically,

The cube is a small volume dV in the space enclosed in the surface.
In the jigsaw analogy, we simplify each small volume dV into a jigsaw piece.
The tendency for outflow at one edge, contributing to positive divergence, is represented by a protruding knob.
The tendency of inflow at one edge, contributing to negative divergence, is represented by a hole.

The big step: Cancelling out the interior boundaries
The boundaries must cancel out in between volumes. This is because any vector which contributes to positive divergence in one small volume dV also contributes to the same amount of negative divergence in an adjacent dV, and vice versa.

This is the same as saying in the jigsaw analogy that 2 adjacent jigsaw pieces fit each other smugly.

The "divergence" is found by adding up the knobs (1 per knob) and holes (-1 per hole) along the edge. The "divergence" in the result sum can be thought of as the sum of the "divergences" in the individual jigsaw pieces. It can also be thought as the sum of knobs and holes along the edge of the result (i.e. by giving it a count).

A final observation: The key to understand why Gauss' Theorem works is the same key to understand why a completed puzzle always has straight edges (a particular case of zero divergence) even though all the pieces in it are jaggedy!

-- END OF DEMONSTRATION --

Freshman Journal 1.1.12

2010-11-05T13:02:00.005+08:00

Maths
Maths tutorial this week has disappeared. I don't know if the venue had shifted without warning, but when I arrived there 15 minutes late, there wasn't a class in E1-06-03.
Lecturer went into an exam-question-crunch frenzy, which for all his virutosity is totally useless for revising concepts.
I am into Stokes' Theorem at the moment, partly to distract myself from the existential horror of never being able to get a girlfriend, and partly because it is awesome.
What secrets doest thou hide? O impenetrable formula!

Physics
Completed the Mastering Physics questions. Considering to finish the non-compulsory questions on the site along with those in the tutorials, but I hate doing stuff on the computer.
I realise that our Physics tutor (Ms. Qiu Leiju) is one of the best tutors I've had for the semester.
Syllabus sped in and out of Thermodynamics for the past weeks. The flame of physics was rekindled in me at the point when it went to the Second Law. Holding that disorderliness is ever-increasing and that all energy is eventually useless, this law is a sobering reminder of the mortality of humankind. Who knew that such a profound result could arise from the obscure fumblings of some 19th-century nerds?

Writing
The last lessons were concluded with 2 sessions of final presentations, a group photograph, and some wicked delicious cookies baked for us by our tutor, Mr Griner.

Chemistry
The whole syllabus of CM1417 is so random and counterintuitive that I find it quite unsettling that I will have to face the same sort of courses for all my subsequent semesters.

Cracking Tiles

2010-11-01T20:28:00.021+08:00

GEK1517 Tutorial Three / Question Two: Suppose that there are m×n unit square tiles arranged into a rectangle (a square if m=n; here m and n are positive integers). A crack appears as a diagonal line of the rectangle (see the figure for m=3 and n=5. Speculate on the number of tiles that are ruined and need to be replaced. (Your answers should be in terms of m and n). Provide arguments to support your answers.

Step I: Panic

Step II: After calming down, try the shit out of as many lower values of m and n you could be bothered with.

Assume that the number of tiles follow a rule; nail the rule down to a symbol.
Number of tiles damaged = D(m,n)

Make the following observations which may or may not come useful later on.

m and n are interchangeable.

Extreme case I: Thin rectangle

Extreme case II: Square

After a bit of trying, arrive at the formula
D(m,n) = m + n - 1
which works for the largest number of the cases (including Extreme I cases)
Group cases according to how well they conform to D = m + n - 1 (mirror images are ruled out as trivial)

It should be very clear now what differentiates the two groups.
The left group ("conformist" rectangles) have cracked tiles of continguous shape. The cracks do not pass through a point in between tiles.
The right group ("nonconformist" rectangles) have cracks that pass through a point (or points).
Somehow, passing through a point affects the crack count!

For curiosity's sake, have a closer look at the nonconformist group.

The nonconforming rectangles do not follow a single rule! Evidently, something has to be found out about this group that dictates the D(m,n).

Step III: Observe that every crack starts and ends on a point.

Observe that, if the crack passes through a point in a middle of a rectangle, you can break a smaller rectangle from it with that middle point as a new (top-right or bottom-left) corner. We take bottom-left:

Observe that, if the new rectangle also has the crack passing through a point between tiles, the process can be repeated until there is no point.

A rectangle where the crack does not pass through a point is a conformist rectangle.
We have demonstrated that a nonconformist rectangle can be reduced to a conformist rectangle.

How do you get back the nonconformist rectangle?
Every conformist rectangle, a series of nonconformist rectangles can be constructed by replicating the conformist x times along the crack's diagonal:

What is the D for a rectangle of length xm and height xn?
It is quite clear that this quantity D for a nonconformist rectangle can be taken apart into the sum of cracks for x conformist rectangles.

We arrive at
D(xm,xn) = xD(m,n)
for nonconformists, where D(m,n) is of a conformist rectangle
Which, owing to D(m,n) = m + n - 1, becomes
D(xm,xn) = xD(m,n) = x(m + n - 1) = xm + xn - x

Step IV:
Observe that in nonconformist rectangles (D(xm,xn) = xm + xn - x) width and height have a common factor x
Observe that in conformist rectangles (D(m,n) = m + n - 1) the width and height have no common factors other than 1.
Observe that D(m,n) = m + n - 1 is equivalent to D(1m,1n) = 1m + 1n - 1, which is just a special case for the nonconformists' rule (x = 1).
Observe that x is the highest common factor (h.c.f) between the width xm and height xn; since m and n have no common factors, the common factors include x and possibly a number smaller than x which is also a factor of x (x is still the highest).

Obtain the unified rule for all rectangles of width m and height n:
D(m,n) = m + n - (h.c.f of m and n)
Verify that rule applies to all cases presented above.

--END OF DEMONSTRATION--

Addendum: Ruohan's description of a proof
Set A {(a, an/m), where 0 ≤ a < m}.
Set B {(bm/n, b), where 0 ≤ b < n}.
Each point in A and B correspond to a cracked tile to the right of the point itself. The answer would then be A ∪ B = A + B - (A ∩ B).
Solving A ∩ B would then be solving the integer pairs for an = bm.

Lacuna: I asserted that a nonconformist rectangle be formed by duplicating the same conformist along the crack. I did not explain why a different conformist can not be used. To do so, I may slip into a circular argument.

Spoiler: Lecturer touched on how to count the cracked tiles, and did not arrive at the expression m + n - 1 by accident like I did.

Bishop George Berkeley

2010-10-29T21:20:00.003+08:00

"Men learn the elements of science from others;
and every learner hath a deference more or less to authority,
especially the younger learners,
few of that kind caring to dwell long upon principles,
but including rather to take them on trust:
And things early admitted by repetition become familiar:
And this familiarity at length passeth for evidence."

-- A Defence of Freethinking in Mathematics (1735)

The Chemistry of Plant Communications

2010-10-28T22:53:00.003+08:00

Somehow, plants show up very frequently in my first semester. First lallang for WP2201I, now plant pheromones for CM1417. I can't put a finger on what is really going on despite having chosen the topics myself.

Picture taken from:
Takabayashi, J., & Dicke, M. (1996). Plant-carnivore mutualism through herbivore-induced carnivore attractants. Trends in Plant Science, 1(4), 109-113.

Sakhalin Rock

2010-10-28T22:52:00.003+08:00

Sakhalin Rock
Oki Dub Ainu Band (music) / Morita Takahiro (director)

Ainu music + stop-motion + collage + maps + black and white photographs + Cyrillic script = AWESOME GEEKTASTICNESS

Black Fridays

2010-10-28T20:42:00.014+08:00

GEK1517 Tutorial One: Consider the problem: Is there at least one Black Friday (Firday the thirteenth) in every year? How would you approach such a problem?

a. Of course, being a kid spoilt with the power of computers, the first thing I thought of was of course to devise a computer algorithm which will sift through the calendars of past, present and future years until it arrives at a Black-Friday-less year.

If there is one year where Black Friday does not exist, of course this will be fine. But if there isn't one, this method can never prove that every year must feature a Black Friday. "So you have tested a lot of cases! But have you tested all cases? No! What if the next year has no Black Friday? and so on ad infinitium.)

b. A better way would be to simplify the problem into patterns.
So I temporary f-ked the maths and went into empirical observation. From my handphone calendar, I observed that the 13th days in the months of January, February, etc. fell in this pattern:

{Wed Sat Sat Tue Thu Sun Tue Fri Mon Wed Sat Mon}

How to make sense of this pattern?
Recall that in non-leap years, the number of days in every month are the same.
So, as an example, January is always 31 days long.
It follows that 1 Feb is always 31 days after 1 Jan.
After which we can see that 13 Feb is always 31 days after 13 Jan.

However, you want to express this rule in days of the week (d.o.w.). So 31 days after Wednesday will be a Saturday, because

31 days = 4 times (7 days) + 3 days

Apply this to the pattern above and you can see that only the last term (+3 days) is needed: 13 Jan 2010 lies on a Wednesday, 28 days is exactly four weeks, so 28 days after 13 Jan is still on a Monday. We are only concerned with how the day of the week change, so the former term can boot it. And we write:

January -> February: 3 days
(to obtain the d.o.w for 13 Feb from 13 Jan, we skip forward 3 days in the week)

By this line of thought, Sunday + 1 is Monday.
So it makes sense to visualise the cycle of the week using a number line which looks like this:

Meanwhile, we obtain from the year 2010:
February -> March: 0 days
March -> April: 3 days
etc.
and we arrive at this twelve skip-forward values, from Jan->Feb to Dec->Jan

{3, 0, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2}

Be reminded that since number of days every January/February/etc. for different non-leap years are the same, these skip-forward values apply to all non-leap years.
How to make a conclusion from this array?
We take out the number line again, and put the month on the d.o.w its 13th day lands on, using the twelve skip-forward values for each month after January.
Anyway,

All the days of the week are covered!
You'd be glad (or infuriated) that this says the same thing as the array

{Wed Sat Sat Tue Thu Sun Tue Fri Mon Wed Sat Mon}

But now it is clear that that it makes it obvious that no matter what day 13 Jan lies on in some other year, there will be a black friday somewhere down the year:

To solve for leap years, just take note that a leap-year February has one more day than a non-leap-year February. So the skip-forward value for February->March in a leap year is 1. The other values stay the same.

We see that even in a leap year, the 13th days of the month cover all days of the week. (What I did to introduce the gap of 1 between February and March was just to shift February and January one step earlier)

Yep, the leap year also covers all the days of the week.

[Spoiler: lecturer presented a one-size-fit-all-years solution which ignores February.]

To arrive at the lecturer's strong case, the only step we need to make is to shave of the superfluous months that crowd uselessly at a d.o.w.

The consecutive months of December to April are discounted, and since February is left out of consideration, the same diagram can demonstrate both leap and non-leap years.

-END OF DEMONSTRATION-

I want to whine about whiners

2010-10-25T20:42:00.007+08:00

I want to whine about whiners who whine about other inconsiderate, insensitive and irritating people. You cannot expect all the people in the world to conform to your oh-so-high standards. If you do not accept that people can be inconsiderate then just stay at home. Wake up sheeple, all this is no big deal, GET OVER IT ALREADY. If you want to voice your complaint at least do it with good spelling and corract grammer.

Freshman Journal 1.1.10 / The Nabla Vector

2010-10-23T09:33:00.009+08:00

Poor maths tutor. By the way he's going, it seems that he would fall asleep before the rest of the class does.
The syllabus is actually quite ok. One just has to get around all that stuff about the del operator (∇) which only looks intimidating. The rest is zooming in and out of the infinitesimal, as usual.

Analogy.

I hate it when the notes gives such dry-as-dust statements like "the curl/divergence of a vector field F is defined by [formula]". O, how we will revel in the rote memory! Here I'll try a more helpful description on the concepts of gradient, divergence and curl.

The Mysterious Nabla vector ∇ (and applications thereof)
∇ is basically (∂/∂x)i~ + (∂/∂y)j~ + (∂/∂z)k~. It is not a vector in totally good faith, but it behaves like one and we treat it like one anyway (to hell with details).

Gradient: product of ∇ and a scalar field
Metaphor: Liken the scalar field f to altitude in a hilly area (say in Temburong).
Imagine that are a 2LT navigating your way to Lakiun Camp with your mates. At some point of time (and some point of f(x,y)) you decide to torture them by leading them directly upslope. The gradient of the terrain is a vector that points to the direction of "directly upslope".

Note: A force field which is a gradient of a scalar is called a conservative force because it "conserves mechanical energy". But why does it have to be that (F~ = ∇f) ⇔ (F~ is conservative)? This needs some looking into.

Divergence: dot product of ∇ and a vector field
Metaphor: Liken the vector field to a crowd of people moving with various velocities.
Imagine a crowded city square in Xi'an. At this instant, someone unearths a timed explosive at A, and someone else unearths an ancient national treasure at B. The crowd near point A will scramble away from A out of fear, while those near point B will scramble towards B out of curiosity. We say that the divergence at A is positive while the divergence at B is negative.

Curl: cross product of ∇ and a vector field
Metaphor: Liken the vector field to the surface of a rough sea.
Imagine going to fish in your new yacht when suddenly a freak storm arrives and your boat is send tossing and turning. The curl of the surface of the sea at (x,y) is the force that sends your boat turning (rather than tossing).

Note that curl of a conservative field (∇f) is zero. This is because
curl(∇f) is ∇×∇f.
∇ and ∇ are "parallel"
so ∇×∇ is 0
curl(∇f) is ∇×∇f, which is zero times f, which is zero.
Weird! And questionable.

Existential Crisis

2010-10-23T09:30:00.004+08:00

The more I know, the more I am painfully aware of my ignorance.

A small note for GEK1517

2010-10-21T22:01:00.003+08:00

Concierto de Aranjuez
2nd movement: Adagio
Joaquín Rodrigo (Comp.) / Narciso Yepes (12-stringer)
Dear visitors, I have noticed that many of you wind up on this site by searching for GEK1517 Mathematical Thinking tutorials. You might have been dismayed because so far I have been documenting only all the silly trivial stuff.

Yes, a GEK1517 tutorial solution set is in the plans.
No, it will not be the lecturer's solutions. Lifting and presenting them will totally spoil your pleasure (and that of all future generations) of going for tutorials. They shall be my own independent attempts.

Meanwhile, You'd be glad to know that a compilation of (own) tutorial answers can be found at Aldrian Obaja's website. I personally don't find his presentation very helpful, but it is a good source of encouragement for those who despair on the impregnability of the questions.

Ultimately, the best way around the tutorials is to try the questions yourselves, and then post it online afterwards, like the braggart I am going to be.

The Alternative Invasive Species

2010-10-19T10:22:00.007+08:00

Imagine if I ditched the insidious but boring Imperata cylindrica (L.) Beauv. for an invasive species with an aspect that would better capture the public imagination:

Didymosphenia geminata (Lyngbye) M. Schmidt!
[Source]

Also considered: 2 species of ant, 2 species of snail, 1 snail-eating flatworm, 1 comb jellyfish, common mynah, sparrow, rock pigeon, rabbit, brown rat and brown trout.

Now back to work.

Freshman Journal 1.1.8

2010-10-10T22:17:00.008+08:00

Year 1, Semester 1, Week 8
This week was not a very good week. Had problems like not being able to fall asleep at night, lack of motivation to work and the like nonsense.

Sisters got Confirmed in Church today, in an event graced by the Archbishop. Marie got herself a new middle name, after a saint famous for cracking a stupid joke while he was being martyred.

I. Modules

Ia. WP2201I Messing With Nature: Unintended Consequences
I was sifting through the mound of information found concerning lallang/cogongrass online. Some of the useful info that needs the unearthing:

Cogongrass, properties
Cogongrass in SE United States, status, methods of eradication
Cogongrass in Asia and Africa, status, methods of eradication
Cogongrass in South America, yada yada
Wickedly ingenious extermination methods

I don't like it when they ask me to purchase the article!

Ib. MA1505 Mathematics I
I am in the habit of drawing graphs in order to make sense of the equations, determinants or whatever nonsense they teach in class. Even though the derivations may not work out, the exercise tends to ram the equations deep into my memory.

Ic. GEK1517 Mathematical Thinking
W. Byers, author of How Mathematicians Think, gives an unpleasant revelation that Calculus is not really rigorous mathematics.

Id. PC1431 Physics IE
I am so saddened by the mid-term results that I have not touched this subject for one week. Ok, I know that this is not the best way to approach the problem.

II. CCA

IIa. MIR
10km run last Tuesday. Did not fare well. Alas, all the knolls of Upper Kent Ridge Road now bear testament to my drop in fitness. I need to train more as my schedule would allow. Eating more could also help. AHAHAHAHA.

IIb. GENUS
The last 2 weeks saw insane Saturday practises. Despite this, I decided that practising in Prime II was not insane enough and asked for a switch to Alto I, a proposition I regretted making almost immediately. Thankfully, it did not get through.

A couple of defectors from Alto I joined our section on Saturday, bringing up the strength to 20.

Stapletonian Statements

2010-10-05T08:10:00.007+08:00

Quote 1:
"[S]anctimonious bigots should be added into the blender with half boiled eggs. mix well for eternity."

--[Name withheld] status update.

Quote 2:
"They [Singaporeans] are the rudest f***ing people I have ever seen; they need some basic training in civic awareness. They don’t feel that anyone else exists outside this tiny island."

--Paul Stapleton, quoted by Sydney Morning Herald, May 31 2010

Freshman Journal 1.1.7

2010-10-02T23:04:00.015+08:00

Year 1, Semester 1, Week 7.
Apologies for extreme randomness

I. This Picture is Actually From Week 5

8 September 2010: Guitarras Viva (The Noob Section)
II. MIR Publicity Campaign Now Public

III. Mid Term Tests
I aimed for full marks in Maths/Physics/Chemistry but it is not likely that I will get a perfect score for any of those in this fateful week.
Please do not feel alarmed. Ideally, everyone should strive for a perfect score. Realistically, normal people will miss the mark. Everyone will nevertheless enjoy for themselves, in return, the infinite joys of mugging.

IV. Mugging
Don't overdo the neurotism. Listen to relaxing instrumental music while studying, and by "instrumental" I mean of course to rule out anything involving synthesisers.

V. WP2201I Expository Essay

[source]
I forgot to elaborate; the topic of WP2201I is Invasive Species. For our third paper, we will be writing a 1000-word essay on an invasive species of our choice. My choice is the Lallang, a.k.a. cogongrass, or kunai, or 茅萱, cỏ tranh, etc.

Reasons for choosing this species fella:
1. Wide geographical spread:
All around the world, below the subtropical latitudes; O Lallang, the sun shall never set upon thy domain.
2. High profile:
Overtook Kudzu as the number 1 dick weed in the southern US, occupying 1.5 million acres of land as compared to Kudzu's 1.0 million acres.
3. Paranormal allusions:
Tendency to Spontaneous Combustion.
4. It's a plant
Plants are very underrated things, if only for them being boring and not inviting dramatic intepretation as readily as other, more metazoan invasive types, like rabbits.

You realise that Watership Down is largely about bunnies, and not at all about the noxious indestructable invasive weed pictured in the foreground.

Also,
[Episode 1. Disclaimer: for time-wasting purposes only]
VI. An Appropriate Freshman Attitude
Let your hair down because now you have your hair. Leave your past behind. Forget the grand achievements you have had, the stories you have accumulated, the knowledge you have gathered under your belt. Forget about looking cool and looking smart: Be childlike so that you can fill your heart with a sense of wonder, and a thirst for knowledge. Be humble so that you may find your place, and to open up to new possibilities. You have come to school again and you have come into this world as a nobody, as fresh as a newborn child. And being a newborn child, this is no time to act all stuck-up.

VII. A Response to the Recently-Announced Exoplanet Survey on Gliese 581g

What, it doesn't rotate?!

The Secret of Kells

2010-09-21T19:11:00.004+08:00

The Secret of Kells
2009 Tomm MOORE and Nora TWOMEY (Dir.)
Bruno COULAIS (Music)
1 hour 15 minutes

It's not a normal classical animated feature when every frame looks like a flippen illuminated manuscript.

I have discovered Kíla

2010-09-20T15:39:00.004+08:00

Kíla
Rossa, Rónán and Colm Ó Snodaigh, Dee Armstrong, Eoin Dillon, Seanan Brennan, Brian and Lance Hogan

Settling Scores

2010-09-20T00:54:00.007+08:00

1. Scores should be settled as and when they arise, in order to preserve goodwill and minimise misunderstanding.

2. A score not settled is injustice allowed to happen. A score not settled is an insult to one's own willpower and to the other's moral standing.

3. A score is often foregone because one is afraid that the other will take offense. He forgoes the score to the expense of his own interests.

This is irresponsible behaviour; one has a limited capacity to which he is willing and able to shoulder the consequences of someone else's actions. He who makes it a habit will eventually give way himself, to the detriment of all around him.

The World is Rather Complicated

2010-09-12T21:05:00.004+08:00

The world is populated with good people; people that have your best interests at heart, people who feel love, people who value friendship, people who find joy in helping others. When I believe this, I let my guard slip... and make bad decisions.

The world is populated with bad people; people who are irrational, people who have hidden selfish motives, people who are hateful, people who are lazy, people who have no sense of priority. When I believe this, I find it hard to tell what people are up to, and what they say often do not make sense. I admit too many possibilities, and fill up my mind with too much information... Eventually, something slips, and I make a bad decision.

Freshman Journal 1.1.4

2010-09-05T22:47:00.008+08:00

Note: "Journal 1.1.4" denotes an entry from (Year)1.(Semester)1.(Week)4

I. Modules

Ia. MA1505 Mathematics I
Now because I take this GEK1517 module, MA1505 seems lame and pedantic.
However, this feeling is deceptive! When I do the tutorials, I keep needing the help of my 1-semester old answers (because in addition to crashing MA1505 lectures from February to April 2010, I also did the tutorial questions).
This can not continue. I must revise the concepts we learnt in class and make it intuitive in the most hardcore way imaginable.

Ib. GEK1517 Mathematical Thinking
I am wholly satisfied with this module and am enjoying all of its lectures and tutorials despite the possibility of me failing it at the end.
The lecturer Assoc. Prof. Leung is a difficult guy to talk to, although his lectures are entertaining.

Ic. PC1431 Physics IE
The lecturer talks with an accent I find unbearable. I cannot reproduce the accent for more than a few seconds without choking on my own tongue.
I MUST WORK HARDER ON THIS

Id. CM1417 Fundamentals of Chemistry
I want to quickly pwn this module because I get kind of embarrassed whenever I have to admit that I did not take H2 Chemistry for 'A' Levels.
To reiterate, the reason for not taking H2 Chemistry was pure stupidity.
Crashed a year 2 Chemistry lecture earlier this week with Brian, who told me that all the wonderful stuff on screen were covered by H2 Chem. Man, what have I missed all these years?

Ie. WP2201I Messing With Nature: Unintended Consequences
First graded assignment in on Thursday.
2 readings due tomorrow (guiltily as I write)

II. CCA

IIa. Mountaineering Club / MIR
I am now in MIR10 EXCO, understudy Publicity i/c.
I chose it not just because it sounds very slack, but also because I have experience in design ('A' Level credentials)!
The batch is small but new members keep coming in. Trainings consist of an endurance run on Tuesday evenings, speed training on Thursday evenings, and something fun and random on Saturday morning till noon.

IIb. Guitar Ensemble / GENUS
After 5 years in and out of guitar noobdom, I am performing in concert!
It's a late notice, but here are the details...

Wednesday 8 September
8pm
University Cultural Centre
Free Admission, Limited Seats!

My group's items are
Francis LAI arr. Koji KUBO: 13 Days in France
Sir Edward ELGAR arr. Masako OHASHI: Salut d'Amour

IIc. Catholic Students' Society / CSS
Infuriatingly, I have to skip lessons in order to attend the activities of CSS every week.
Attended a mass in LT17, School in Business on Friday, presided by Fr. Alex from Saint Joseph (Bukit Timah). It was the first time in my experience that the pews were higher in elevation than the sanctuary.

IId. Astronomy Club / NUSAS
Static.
With apologies to Kenneth!

I now recommend that although one tries their very best to be hardcore, their timetable will invariably disappoint them by clashing. One high-key and one low-key CCA is a good balance, and that is enough.

III. My weight
These weeks have seen increase. Evidently, my active lifestyle is not active enough. Will switch to a more masochistic regimen in short notice.

Needs some clarifying

2010-09-04T17:13:00.002+08:00

Q. Are you Christian?
A. Yes.
Q. Which church do you go to?
A. Holy Cross.
Q. Where is it at?
A. Clementi.
Q. But isn't that a Catholic church?
A. Yes.
Q. So you're... Catholic-Christian?
A. Yes?

NO.

2010-08-26T22:58:00.004+08:00

If you ask me to give up my effort in schoolwork for something less important, I will not do it.
If you ask me to give up my resting time for merrymaking, I will not do it.
If you ask me to forego my ties with Family, I will not do it.
If you ask me to forego my ties with God;
If you ask me to give up my Sunday Mass for something less urgent, I will not do it.
If you ask me to cloud my own judgement of the truth, I will not do it.

The Six-Year Inscription

2010-08-26T16:43:00.002+08:00

18 August 2010 tottered by in the shadows when I was not looking, and Dunmore Cave entered its seventh year. This blog is older than some children, just imagine...

The Real Studying Mood

2010-08-23T20:54:00.005+08:00

School Has Started

2010-08-11T23:01:00.002+08:00

Enough of this denial. As I did not join Orientation last week, this week is quite dreary. I know the people and I do run into them, but they are few and far between.
Anyway,

GEK1517 Mathematical Thinking
Lectures this semester are twice weekly, 1800 to 2000 hours. The lecturer and tutor is the idealistically-inclined Assoc. Prof. Leung. The beautiful poetry he weaves into Mathematics is only offset by his epic accent. The simple childlikeness of his lectures is only offset by the tutorial and past-year questions. I know now why they said this was a tough one, but it is so far very enjoyable.

Prof. Leung also conjectured that, in the film Inception, Dom Cobb fell from limbo into the next level, which is actually the real world itself. Dream layers and reality thus form a closed loop. A loopy proposition!

MA1505 Mathematics I
PC1431 Physics IE
Pre-allocated modules.
Maths I started very quickly, and covered functions as soon as briefing and the IVLE stuff are done with. Lecturer: Prof. Tan Ban Pin.

Physics IE had a bad start. Lecturer went on and on teaching what Physics is and why Physics is so important. Stuff like test timings, teaching cirriculum were pushed to the last few seconds. Lecturer: he didn't introduce himself.

CM1417 Fundamentals of Chemistry
I am taking this module as a punishment for being so stupid in J1 that I decided not to take H2 Chemistry.
I now have a different PC1431 lecture timing than the rest of my course, and also a different MA1505 tutorial slot because of this module. (Though how different it will turn out, I have yet to see.)

WP2201I Messing with Nature: Unintended Consequences
I am taking this module in lieu of EG1413 Critical Thinking and Writing, because it seems more interesting.

Actually I wanted WP2201G very much more. WP2201G concerns Language and Migration. Issues of language use and migration are to me what SNSD group member names are to many guys. So if I take it, life would be a breeze. Too bad it clashes with Maths, Physics and Chemistry all at once.

Lessons start tomorrow.

Close Shaves

2010-08-04T01:11:00.009+08:00

Three unreasonably truncated travelogues in one entry, with a running theme.

December 2009: New Zealand - Fox Glacier
A path leads up to the glacier, ending in an observation post, a chain across our access and a sign saying No Tourists Without A Guide Beyond This Point. Half of my group, including Dad and Jamie, crossed this point without a guide in order to reach the glacier's head, which cannot be seen from the post. They disappeared behind the edge of a rock.

A few minutes later we heard a deep groan and crash as a piece of ice broke off from the glacier's head and crashed to the ground. I freaked out and ran towards the rock where they were last seen, expecting the worst, but found them all slightly surprised but unharmed.

If the stream flowing out from the glacier's head was any weaker, or more conveniently positioned, nothing would have stopped them from actually walking over and touching the ice, which would have put them in the way of the falling block. For an unappetising instant, I contemplated going home without two of the people in the family.

June 2010: China - Fuzhou
In the morning, we found my sisters' room in the hotel deserted... Their belongings were intact, but the door was wide open. I was especially paranoid about my sisters' safety for this trip; I took it to myself never to let them stray from my watch, all through the waking hours, but now I had to lose track of them at daybreak. For an unappetising instant, I contemplated going home without two of the people in the family.

We found them in the restaurant, having breakfast. It turned out to be a simple misunderstanding. Nevertheless I made sure they were sorry for what they had done. And what kind of bonehead leaves their bag in the room and the door open? Sheesh.

July 2010: Russia - Listvyanka
The day we landed in Irkutsk, Dad and I came to our hotel in Listvyanka on the shore, and had dinner in the cafe. There were boisterous Russians at the next table: a doctor and his wife from Irkutsk, and a lady from Angarsk (or was the lady from Irkutsk, and the couple from Angarsk?) who struck up a rapport with us. Soon a family from Moscow (a government worker, his wife, and their toddler daughter) came to join us and together they hauled us both onto the boat for a free one-hour cruise to nowhere, on fabled Lake Baikal.

We had never warmed up to strangers this quickly before. Less than thirty minutes into all the socialising (which featured a significant language barrier) we were rounded up and now we were partying together, far away from shore on that immense lake. Not having snapped out of China Mode entirely, I was shiteless inside. For an unappetising instant, I pictured Dad and myself, both knocked-out drunk, being thrown overboard into the freezing waters; Yea, the Doctor was very insistent in his spamming of tequila.

My fears were unfounded, evidently. My misty eyes drifted from one smiling face to the other. Not a chance would we splosh into the Baikal under their watch. They had families and came as families (except for the lady from Angarsk, who was alone then, but also had a family somewhere). And they were very nice. And we took a few more swigs of the drink, licks of salt, slices of lemon, and pledges of eternal friendship, and so on.

An hour later (or was it two?) we were ashore, many thanks be to God. There at the wharf we kissed the Russians goodbye. When we stumbled back to our room, we stumbled into the correct one, which proves that we were not too drunk, but we also fell asleep very quickly.

A Baudolino Spoof

2010-08-03T16:24:00.005+08:00

A sad-looking man came looking for Baudolino.
"I don't know what my sickness is."
"I know," Baudolino said. "You are slothful."
"How can I be cured?"
"Sloth appears the first time when you notice how slowly notifications appear to you on Facebook"
"And then --?"
"Never log on to Facebook."
"Nothing can be hidden from him," the people of Selymbria were saying.

什么是闷

2010-08-01T22:51:00.002+08:00

悲而不能泣、
悦而不能笑、
望鹿而不逐、
见义而不为者，
曰闷也。

Iasyr Shivaza

2010-07-30T16:27:00.005+08:00

This poem from Soviet Kyrgyzstan is written in the oddly out-of-place language of Dungan, a dialect of Mandarin spoken across Central Asia and written in the Cyrillic alphabet.
The poet in question is Iasyr Shivaza, a.k.a. Ясыр Шывазы a.k.a. 雅斯尔·十娃子, a celebrated Dungan poet.
For those who can read Cyrillic, enjoy!

Source: Rimsky-Korsakoff (1991) (via Wikipedia)

Бый хўтер

Тэйон җошон, бый хўтер, Ни тэ гощин.
Ни лян җин гуон фадини, Чиди чун фын.
Йисыр ни до тяншонли, Зущён бый юн.
Йисыр зу до хуайүанли. Ба щян хуар вын.
Җяр хуардини, вә канди, Ниди щин го.
Дусы ниди да хуайүан, Ни ющир луә.
Ни лян хун хуар фадини, Тэёнйибан.
Дын нидини мо җүхуар. Щүәбый модан...
Нисы чунтян, гуон зоди; Хуар кэди вон.
Зун луәбудо, хўтер-а, Җин фуершон.

白蝴蝶儿

太阳照上，白蝴蝶儿，你太高兴。
你连金光耍的呢，骑的春风。
一时你到天上了，走向白云。
一时走到花园里，把鲜花儿闻。
拣花儿的你，我看的，你的心高。
都是你的大花园，你有心儿落。
你连红花儿耍的呢，太阳一般。
等你的呢毛菊花儿，雪白牡丹。。。
你是春天，光找的，花儿开的旺。
总落不到，蝴蝶儿啊，金树叶儿上。

Claims that need to be verified concerning University Life

2010-07-28T19:54:00.003+08:00

1. UNIVERSITY LIFE, definition
2. That if you do not join orientation, you will spend four years living in a cave, grow a full beard, talk to birds and do maths all day.
3. That life as an engineering student being trying and dreary, is in fact a misconception.
4. Socialising, definition
5. That friends in life are made through silly and slightly inappropriate games.
6. Having fun, definition
7. Make friends, definition

He Must Always Believe In Himself

2010-07-19T23:31:00.007+08:00

He was born on the shores of Baikal,
At the dawn of his race.
Before his birth a rainbow-clad pheasant announced his coming;
She came with a silk banner floating alongside her in the air
She came to perch on the highest mountain of the Kamar Daban
And there she proclaimed with a human tongue,
Lo, I give you today this child
The bearer of truth, the liberator of your nation,
The idol of every man and woman and child,
Bastion against the weaknesses of Common Man.

It departed with a blinding flash,
But Jaromil's name was left behind on the banner draped over the rock.
Ten months later he was born
In deep January Baikal was unfrozen in an instant
And the river Angara burst its banks
Three suns graced the heavens above
Adorned by seven rainbows.
All the animals in the wilderness were awakened
They sang in unison with the heavenly bodies
"All praise be to Jaromil,
Nothing can exist without you.
Nothing can have meaning if not for you.
You are the most perfect being that has come among us;
Let us never stop loving him!"

In a blinding flash fifteen years had gone by.
In the morning of the deepest January the sun does rarely rise
Jaromil rises from his matress from a good rest.
The decaying hovel does not faze him;
The dismal winter does not deter him.
He believes that he is special.
He believes that one day all things will be below him.
He believes that the day will come when nothing can stop him.
He looks with disdain at the row of houses across the street;
The sad abodes of losers.
He must show them what he is made of.
He must prove to them that he is the most worthy.
He must conquer them with his air of superiority.

In the deepest January, alas, the sun has not risen to accompany him,
Nor has the rainbows made themselves seen.
But the time is not yet here, there are much more important things to do.
Jaromil pulls the blanket over his head again.
He needs more morale to keep himself going:
He must see once again the heralding pheasant;
He must draw more strength from the chorus of beasts;
He must always believe in himself;
He must never stop dreaming.

Blogging from Listvyanka

2010-07-14T10:52:00.002+08:00

Sleet today by the lake, whereas the first few days here had been quite sunny. It turns out that Listvyanka experiences not summer, but waning spring in the month of July, many thanks to this Lake Baikal that only completes its thawing in June.

The flea markets just outside the hotel sells interesting (if useless) stuff. The Jew's Harps they sell here caught my eye particularly, but they cost 1800 rubles (~S$ 72) apiece. Maybe the other stalls sell it more cheaply, but I'm not setting my hopes too high.

Wall of Water

2010-07-05T21:41:00.002+08:00

The night after OAC 2010 ended I had this weird dream. I watched a simulation of a tsunami spreading across the Indian Ocean from the Arabian peninsula, and definitely inundated Singapore. I was too lazy to run, though, and a few days later I was lazing on some front porch when I saw that huge wall of water approaching the house. For a few moments I was totally resigned to my fate, and was wondering what dying in a tsunami would feel like. Then I woke up.

Russia

2010-07-03T22:09:00.002+08:00

Will be in Irkutsk Oblast, Russia for 10 to 18 July.
In case some of you might be wondering why I will not be hopping over to Moscow or Saint Petersburg for a peep during this time, this is the reason:

It is also not likely that I will bring a jacket to fight the high winds of Siberia, nor is it likely that I will buy a rifle to fight the polar bears, because then it would be summertime.

Inscription 595

2010-06-27T10:20:00.003+08:00

I am back from China. The trip was harrowing to put it succintly. Maybe a lot has changed in China for the 3 1/2 years I didn't go back; maybe as a homecoming kid I was plain being unobservant. In any case, in the two weeks the myriad incomprehensibilities and contraditions of the country have laid themselves bare.
More on this later.

Anti-Semitism

2010-06-09T02:04:00.005+08:00

Disclaimer:
1. I feel nothing for or against the Jewish nation, only a remote fascination.
2. I think Jewish men have great dress sense.
3. I also think Israel is psychopathic.
4. But I do not deny that the holocaust happened, or is a bad thing.

After reading this passage (written by Terry), I found many things in his response to be puzzling.

The focal point of the tirade was a Twitter post by a Malaysian web user, who posted a quote form Hitler as a reference to the raid on MV Rachel Corrie by the Israeli commandos. As I requote: “I could kill all the Jews in the world, but I kept some alive, so you can see why I was killing them.” The offensive part was that, and that most of the replies followed the same antisemitic streak.

1. The writer was "saddened, repulsed, disgusted and shocked". The writer seems to have a very delicate nerve. I have seen ignoramuses online say worse things about my own race and my church, but never had to come up with 4 synonyms for "offended". Since the writer isn't a Jew himself, and (I guess*) probably doesn't have much to do with them, I find the emotional baggage unnecessary.
*I guess, and with apologies. This is an assumption I have made, though it be an assumption of the usual case.

2. "Instead of putting the blame on the country’s military and/or politicians, people decided to vent their anger directly on Israel as a nation, or the entire Jewish population as a whole." Yes, people on the internet are not known for being discerning. It might be wise now to just forgive them this oversight... and get away from the computer.

3. "The tweet above is the epitome of imbecility" The tweet above has gone the way of a punchbag.

4. "While I do condemn the actions of Israeli naval commandos for storming the ship and causing grievous harm to human rights activists onboard, I do acknowledge that there might be security concerns on Israel’s behalf about what the fleet of ships are actually carrying."
It is a troubling reading of news at face value.

From what little I have read today, I would hesitate to give credibility to whatever the IDF or the Israeli government has to say about the incident.
Be it the recent boat hijackings, the sinking of USS Liberty off the Sinai peninsula in 1967, or the deaths of activists Rachel Corrie and Tom Miller in 2003, these offences were almost immediatedly framed as accidents; none of the official Israeli accounts, however, agreed with those of the eyewitnesses.

This does not enable me to say if MV Rachel Corrie really carried dangerous goods or not, but the proposition seems to me another self-serving move by the Israeli government. In a heavily politicised incident such as this, what resources do the layman have to say for sure which side is correct?

Now, about antisemitism itself:

1. Racism has many faces: racism against blacks, racism against Japanese, racism against Indians etc. Racism against Jews seems to be only one ennobled with its own label, to take its own place, next to racism, in the pantheon of modern sins. Why?

2. Why anti-Semitism? Arabs, Palestinians, Syrians, Lebanese... are they not Semites? Why this dubious label?

3. What special worth does the Jewish nation hold, to warrant not just the sympathy, but also the empathy, of people whose lives they have scarcely touched?

A Crush On Someone Totally Incompatible

2010-06-08T00:07:00.010+08:00

1. Your idea of Love means having an uncontrollable urge to give her noogies. However, her idea is at the polar opposite of yours.

2. She is from a wealthy family. You are a hard-nosed proletariat, and has little patience for bourgeois trivialities and obsessions. But then, she is just so cute

3. You suspect that maybe you are just too chicken to approach her, and is using incompatibility as an excuse to hide your lack of courage. But then, your prudence tells you that she may really be incompatible with you. The two schools of thought are in conflict. And then you ask God. God has not returned with the answer yet.

4. You and her have infrequent and tenuous encounters outside, comparable to the encounter of two ships passing each other on a miles-wide berth. However expansive the distance between you and her, every blare of the foghorn makes the weather a little better to sail in.

5. Encounters aside, her life actually does not touch yours in any way. So when you find out on facebook that she has a stalker, or anything attestible potentially threatening her personal safety in any way... you feel sharp, sanguine pangs of paranoia. Even though you've been stalking her yourself, and it is actually none of your business.

6. Declaring it, even inwardly, as falling in love will leave you no room for turning back.

A Virtue of Clear Thought

2010-06-04T22:03:00.005+08:00

1. Keep to one stream of thought per thread.
{
Know the banks that define the stream;
Know where it doth start and end;
Know the thoughts that flow into it,
____ and the thoughts that flow out;
See that the stream do not burst its banks;
See that stagnant ponds form not where it meanders;
Fret not when the stream seems lacking in grandiosity,
____ but be proud that it stays clear throughout its course.
}

Politeness to Strangers

2010-06-03T19:25:00.002+08:00

About showing politeness to random strangers on the street, I have so far attested 2 schools of thought in practice.

1. Politeness to strangers is a simple acknowledgement of the stranger's existence i.e. greeting and small talk if possible.

2. Politeness to strangers is to not look at them in the face.

One of my life's mission now is to find a happy medium between these two.

Perl

2010-06-02T17:20:00.005+08:00

We'll write more about Perl after we decipher the following code:
perl -wlne'END{print$n}eof&&$n++;/<title>([^<]+)/i&&$n--' *

Intepretation
The code in question (from the collection "The road to Perligata") is a lament over the coming apocalypse, an expression of the author's Weltschmerz and the futility of all human endeavors. Let us take it step by step:

-wlne'
-The world is near its end.

END{print$n}
-At the end the sum of all our sins and virtues will be reckoned and the judgement revealed.

eof&&$n++;
-As the evil of mankind ends, perhaps the end itself is a positive thing.

/<title>([^<]+)/
-We are preoccupied with fame and titles

i
-And insensitive to the suffering of others.

&&$n--
-All this is for nought, and only hastens our demise.

' *
-For in the end, we are but stardust.

[source]

He who is caught in public

2010-05-31T23:10:00.005+08:00

He who is caught in public carrying a guitar, they call him a douche.
He who is caught in public carrying a violin, they call him a snob.
He who is caught in public carrying a harmonica, they give him alms.
He who is caught in public carrying a piano, they give him a wide berth.
He who is caught in public carrying a recorder, they think he is nerdy.

Niceness

2010-05-31T22:05:00.002+08:00

In niceness one treats all men and women the same way; There is a professional distance to be kept in his role as a fellow human being. In niceness there is no allowance, no consideration to the various possible kinds of response that you could get from the other party. Thus, a person who speaks out of niceness speaks not to one person, but to an undifferentiated crowd of platonic Mankind. This is why we are not always nice to our closest friends.

Eyjafjallajökull

2010-05-28T00:28:00.000+08:00

Eyjafjallajökull / signed 28 May 2010
Original picture by unknown

The Emotions of Morosity

2010-05-27T23:13:00.004+08:00

I may be as bland as bread and as morose as a full-day spell of sleet, and not given to emotions of too strong a nature, but that does not stop me from writing about them today. Do morose folk have feelings? Of course we have.

1. Guilt, fear, shame.
The false prophets preach arrogance, greed to push life to greater heights. The negative emotions of guilt, fear and shame are the ones that summarily guide me and protect me day to day. They are very important.

2. Withdrawal to self
I have this to blame for a low level of social aptitude.
Self control is good, but when we abuse it to avoid looking stupid at all times, we end up looking stupid at all times.
It is quite hard to grasp admittedly, esp. for me. I am often withdrawn before strangers, and it is quite the effort to open up (chances are that I'm not the one doing all the work)
But nevermind, because meanwhile there is

3. Ecstasy
I experience this ecstacy in the heats of work, be it military training, or maths homework, or art projects, etc.
I love work. If work was a woman, imma marrying her on the spot. All you slackers out there will never understand this passion.
Which brings us to

4. Arrogance
The 职业病 for commandos is arrogance.
Admittedly it's hard not to feel snobbish from time to time while my term lasted... though generally I liked to be humble. Because arrogance gets in the way of doing work.
Sometimes I do act humble, then try to feel good afterwards. That's doing it wrong. Yea, it be hard to grasp and all.

5. Morosity
I am morose these days for good reason.
You may know as well as I do that the 9 months after ORD are pretty much the most rotten in a life. In these times one turns away from the jungle's beckoning, they cut themselves off the elements with a huge heave of relief, and then they realise that they have also been cut away from their own friends.

-All your friends from school, where are they now?
-Who will you turn to now if you needed to talk?
-Who from your past will remember you?
-Who from your present will accept you?

You are dumbfounded when confronted with such questions, because now you are officially a hobo.
No one likes hobos.
Except for family. Now I know of folks who don't like their family and try to run away. These are either petulant teens or plain fools.

6. Love
Yes, morose people can feel love.
Since my social-butterfly days have been dead and buried for two years and then some, I grab whatever people that's left, and then LOVE THEM TO BITS.
Yea, I be talking about you. Be careful though, I may not be this stable all the time.
I treasure my friends. That is true.

7. Having stupid crushes
Yes, morose people can have stupid crushes.
Sometimes having crushes can get in the way of work. But there are times when I am so inspired by this wonderful blossoming thingimmabob within that I create whole paintings and writings based on their person and dedicate these works to them without them ever knowing or finding out because I am so discreet.
I may have dedicated something to you now. If you ask me I can tell you, but you might not want to know so badly.

8. Disliking politics
Before this post descends further and further into the trivial, here's the last one to disliking politics.
I started this passage becase I read an acquaintance's blog... he was tortured by class politics from the earliest days in JC, even though he was one of the most goodwilled and talented people I have ever had the good fortune to know.
I was starkly reminded of the politics in my own class, I did not notice it at the time, but looking back it was all very blatant.

-Where there is Water, there will be Chinese
-Where there are Men, there will be Politics

I do remember a class outing when they invited everyone but me and three of the guys who were closer to me. I had to find out about it myself and call the remainder along. I will never forget.

Now how did I ever survive two years of this? I don't know, maybe it's because I was somewhere else most of the time, thanks be to God.

In a rat race of this nature, people of my streak rarely play to win, or bother with anything at all that gets in the way of our work. That is why leadership rarely comes in our way, and also why we disrespect authority deep down.

Khanty Reindeer Sled

2010-05-22T23:59:00.007+08:00

Khanty Reindeer Sled / signed 14 May 2010
Original picture by Scott S. Warren - [link to article]

How To Tame Your Canvas

2010-05-22T23:25:00.000+08:00

First you choose your canvas size. This is called sizing up the catch.

Secondly you either make the purchase in an art store or make a special order (if the kill is particularly formidable). If you go to Creative Hands, you can purchase three pieces together at a cheaper price. This is called tackling the herd.

Thirdly you bring the canvas home.
Keep in mind that before you tame the canvas, it is a wild animal. It will fight the fight of the cornered beast. However, you, the artist, must have the courage to do what is right and not back down.

After that, you may proceed to hunt in one of three ways:
1. paint on unprimed surface. You are relying on a combination of luck and machismo for interesting and unpredictable results. This is called tracking by heavenly signs. You are fearless and I respect you.
2. paint on primed surface. You are rigging the canvas to maximise your hunting advantage. Canvases are basically stretchable cloth and priming the canvas makes it vulnerable to the advances of your brush. This can also be called trap-rigging.
3. paint on washed background. The safest option, in my view. In order to maximise psychological advantage over the canvas, you cover the entire primed surface with one colour (usually the dominant colour / undertone that you are working with). This is called setting up enclosure, in Chinese 关门打狗.

After this it is pretty much up to your hunterly skills and styles. For example, painters may tackle a small part of the painting at a time, which takes a longer time. This is also called hunting by attrition, or stalking the rabbit hole.

On my part, I tend to be less nice with such animals. My painting approach mirrors Mental Ray's mode of rendering images and Genghis Khan's mode of conquering Eurasia. The policy is to paint in multiple passes, gradually improving in the treatment of detail as more passes are performed. This is why it is similar to Mental Ray, and why it is also called whittling escape routes on the chase.

The end product is already established and is recognisable in the first pass. Almost on the word go, the canvas' defiance will give way to raw terror and helplessness. This is why the method is also called scorched-earth.

Attrition or no, now that you have the canvas under your power (I assume- no, of course you never gave up). It would be befitting of you, the new owner of this piece of livestock, to place your mark of ownership upon the canvas. This is usually referred to as signing.

You can also bestow upon the painting (yes, it's a painting now) its own name. I know people outside Scandinavia generally feel funny about individually naming their animals. In the code of painters however, this is very much the norm. But if your painting has been unruly, feel free to incur upon it the name Untitled, just to show the accursed beast who's boss.

The New Recorder Hitlist

2010-05-22T23:22:00.005+08:00

Altan - Sláinte Theilinn (A Health to Teelin)
Altan - An Cailín Deas Óg (The Pretty Young Girl)
Altan - Mo Choill
Altan - Adieu My Lovely Nancy
Altan - Island Angel
The Chieftains - An Gaoth Aneas (The South Wind)
The Cheiftains - The County Tyrone
The Chieftains - El Besu (The Kiss)
Dobhran - Nil Sen Lai (It's Not the Time)
Dobhran - Off to California
The Duhks - Annabel
St. Venantius FORTUNATUS (530-609) - Salve Festa Dies
Garmarna (comp. Trad) - Herr Mannelig
Great Big Sea - Tabhair dom do Lámh (bridge part in Captain Wedderburn)
Hermann of Reichenau (1013-1054) - Salve Regina
Evan and James JAMES - Hen Wlad Fy Nhadau (Land of My Fathers)
Joanie MADDEN - Homesteaders
Carlos NÚÑEZ - Carmiño de Santiago
Carlos NÚÑEZ and Eimear QUINN - Yann Derrien
Mari Boine PERSEN - Sáráhka Viina (Sáráhka's Wine)
Mari Boine PERSEN - Duottar Rassi (Tundra Flower)
Eduardo PONDAL and Pasqual VEIGA - Os Piños (Galician national anthem)
Skeeal - Manannan
Alan STIVELL - Hirvoudoù
Tri Yann - Princes Quen Mains Tenez
Tri Yann - Si Mort à Mors
Värttinä - Kyla Vuotti Uutta Kuuta (The Village Awaits the New Moon)
Värttinä - Karjalainen Kehtolaulu (Karelian Lullaby)
Väsen - The Tiliander Menuetts
Väsen - Linnaeus Längdans / Kör i Lunken
Vishtèn - Pour Lui Plaire

I just couldn't help it, recorder is so easy to learn.