Screenplay, part 2

Sort of a continuation from the Prologue (no English translation for the prologue).

English translation provided at the end of the Chinese text. The screenplay format was used as it would allow a decent level of detail to be conveyed without having to resort to fanciful sentence crafting. Anyway, I am unable to produce decent Chinese sentences. Give me time. Lots of time.

Note to Mr. Hon SY: I doubt you’d want to watch this performance on stage- it’s probably too dull. You want sex, drugs and violence, not small talk about today’s weather.


***

第一幕
人物：陈一维，林小姐，老板
场景：某餐厅之bar
语文：普通话

（餐馆以关了，只剩三人打扫与准备给明天中午开门。林小姐在bar里的洗碗盆洗杯和茶壶、一维从厨房的大冰橱拿各种饮品填满bar的冰橱、老板在整理餐厅的桌。）

林小姐：老板，你须不须要请新的工人?
老板：为什么呢？
林小姐：我有一个朋友找着part time工作。
老板：（走到bar前根林小姐谈）哦，这样。他有做过的吗？
林小姐：没有。
老板：没有experience怎么做？
林小姐：可以学的吗。怎么样都一定比那个沙发好啦。你知道吗，刚才她多么过分。这里有一大堆杯，她都没有来帮洗，还在那边（指着餐厅里的走廊）走上走下不知干吗。

（老板没出声。）

一维：(蹲在bar里的冰箱旁排饮品的罐和瓶子)可以啦，没有经验还可学的。
林小姐：对呀。你看一维也做得很好吗。
老板：（对一维）阿陈，你以前在那里工作？
一维：（停止填冰橱，转向老板）什么工作？
老板：做hospitality的工作啊。
一维：我没有做过的。这是第一次。
老板：（吃一经。大马音调强）哈？你以前不是更我讲你有做过？
一维：（笨笨的微笑）哦。。。没有办法啦，要找一个开始。
老板：（大马音调强）哎呀，你骗我啊？要跟你罚款五块钱的啦。。。

（林小姐小声的笑。）

（老板走开打扫餐厅、一维继续填饮品、林小姐洗杯。）

（第一幕终）


***

Act 1
Characters: Tan Yee Wei, Miss Lim, Boss
Scene: the bar of a restaurant
Language: Chinese/Mandarin

(The restaurant has closed for the day, and only three people remain to tidy up and prepare for the next business day’s lunch opening. At the bar’s washing sink, Miss Lim washes used glasses and tea pots. Yee Wei is bringing various bottles and cans of drinks from the large fridge in the kitchen to restock the bar. Boss is tidying the dining area.)

Miss Lim: Boss, do you need new workers?
Boss: Why do you ask?
Miss Lim: I’ve got a friend who is looking for a part time job.
Boss: (walks to the bar to talk to Miss Lim) Ah, I see. Any working experience?
Miss Lim: No.
Boss: How will she work without experience?
Miss Lim: She can learn on the job. It will be better than that Sofa anyway. You know, she was really overdoing it earlier this evening. There was a huge pile of dirty glasses here, and she did not come help do them, and was walking up and down there (points to the aisle in the dining area) doing nothing.

(Boss keeps quiet.)

Yee Wei: (squatting next to the bar’s fridge arranging bottles and cans of drinks.) It’s doable, she can learn even if she hasn’t got experience.
Miss Lim: Yeah. Look, Yee Wei is also doing quite well.
Boss: (to Yee Wei) Tan, where did you work previously?
Yee Wei: (pauses stocking the bar, faces Boss) What work?
Boss: Your previous job in hospitality.
Yee Wei: I haven’t worked before. This is my first time.
Boss: (Surprised. Speaks with thick Malaysia Chinese accent) What? Didn’t you tell me when you came in you’ve got experience?
Yee Wei: (smiles sheepishly) Ah yes…I had no choice. Had to start somewhere…
Boss: (speaks with thick Malaysian Chinese accent) Aiyah, you lied to me? I must give you a fine of $5…

(Miss Lim laughs quietly)

(Boss returns to tidying the dining area, Yee Wei continues stocking the fridge, Miss Lim washes the remaining glasses.)


(End Act 1)


***

Appended 2200 1/5/06:

As the cliché goes, an idle mind is the devil’s workshop. As much as I dislike clichés, Mr Hon is one perfect example of this. The following plot is written by him, slightly edited for consistency with the original settings.

This section was not written by me, and is not based on true events.

（一维和林小姐在bar内工作。）
林小姐：一维，你说老板会请我朋友吗？他可是蛮需要找份工的。。
一维：你可以叫你朋友也骗骗老板嘛，说自己有experience。 你看，老板也不会很生气的。
林小姐：你都骗过一次啦，哪能用一样借口俩次的？（埋怨的眼神）
一维：嗯。。。那是因为你诚实嘛。。你是个。。乖女孩。。
林小姐：（甜蜜的笑容）是吗？可没人说过我乖呢！我看你样子都挺诚实的，真没想到你会骗人。你会不会也在骗我呢？
一维：当然不会！我跟你讲话一定很诚实的。
林小姐：哈哈。。咦？你干嘛脸都红啦？
一维：我，我。。。
（老板走到bar前）
老板：喂，你们做东西做得那慢啊？


(Yee Wei and Miss Lim work on their tasks in the bar.)
Miss Lim: Yee Wei, do you think Boss will hire my friend? She needs a job quite badly…
Yee Wei: You could ask her to lie to the Boss and say she has worked before. Look, he didn’t get too annoyed earlier anyway.
Miss Lim: (complainingly) You’ve already lied once, how can the same line be used again?
Yee Wei: Err, that’s because you are honest. You are a… good girl.
Miss Lim: (smiles sweetly) Really? No one told me that before! You look like a honest and morally integral person, who would’ve thought you’d tell lies. Are you bluffing me now?
Yee Wei: Of course not! I will always tell you the truth.
Miss Lim: Haha… Eh? Why are you blushing?
Yee Wei: I…
(Boss walks towards the bar)
Yee Wei: Hoi, why are you two taking so long to finish up?

Reminder: this section was not written by me, and is not based on true events.


Personal

Wonders of the human eye

Current read:
Pirenne MH, ‘Vision and the Eye’, C. Tinling and Co., 1967, London.


The eye: an optical sensor so utterly magnificent that it is consistently used in arguments in favour of religious doctrine.

Disregarding this irrelevant hoo-ha, let’s talk a little about the human eye itself.


The eye can work with a huge variation of illumination, from direct sunlight to illumination by mere starlight (I have experienced this on a clear moonless night far removed from civilisation- the environment remains slightly visible).

The most obvious mechanism is the iris, which regulates the size of the pupil (the orifice that allows passage of light towards the retina). In dimly lit conditions, the pupil dilates to allow more light to strike the retina (the photo-detector), thus improving sight.

However, there is an obvious limit to how much the pupils can dilate. To further extend the operating range of the eye, the retina is equipped with 2 different photo-detectors: rod cells and cone cells. Cones work well with bright light and also respond to colouration of light; rod cells respond to dim light and do not give colour information.

Thus in bright conditions, the rods may be saturated (that is, their output is at maximum) but the cones will be able to provide information regarding the quantity of light falling on each cell. Conversely, the cones will return a zero signal in dim conditions while the rods give good data.

This effect can be observed when one looks at the stars. Bear in mind that cone cells are more densely clustered in the middle of the retina and rod cells are distributed around the periphery. It is often noted that the star that one is explicitly trying to stare at persistently fades from sight- cone cells are not very good at sensing dim light sources. The way to observe a star is to stare away from it and look at it using your periphery vision where the rod cells dominate (and give good low-light seeing).

Compared to a photographic camera, the situation is analogous to having a mixed sensor of say, ISO 50 and ISO 400.

Apart from the variable aperture found in the pupil and the mixed sensor in the retina, the eye has one more trick up its sleeve that further extends its operating range. The light detecting cells have the ability of changing their sensitivity, although this effect is not instant but requires durations on to the order of minutes.

Returning to the photographic camera analogy, one might find that the sensors automatically change from ISO 50 and 400 to ISO 200 and 1600 respectively.

In experiments that attempt to deduce the minimum light required for detection, the test subject is usually dark-adapted (enclosed in a completely dark room) for up to 45 minutes to allow this sensitivity to increase to its maximum. Initially, the sensitivity increases rapidly and this increase slows down until it reaches its maximum.

Experiments conducted in the middle 20th century showed that the eye can detect incredibly dim light flashes. A suitable dark-adapted test subject can detect light flashes of blue-green in colour (wavelength of 507μm) of merely 50 to 150 quanta, corresponding to a range of 0.02 to 0.06 femto-Joules (10^-15 J).


Efficiency of the light sensing element in rod cells

Rod cells contain a pinkish pigment rhodopsin, also referred to as ‘visual purple’. When exposed to light, this pigment changes from pink to clear- absorption of energy provided by light bleaches the pigment. The reaction stimulates nervous endings in the rod cells, thus giving the resulting information on amount of light falling on each rod cell.

The previous experiment showed that about 50 to 150 photons need to enter the eye for the flash to be detected. However, not all this light is absorbed by the rhodposin. Absorption occurs at every stage the light passes through- the cornea (the outermost layer of the eye), the aqueous humour (a fluid between the lens and the cornea), the lens, the vitreous humour (the gelatinous mass in the eyeball), the finally rhodopsin.

However, the rhodopsin does not absorb all light falling on it, and some is transmitted to other parts of the slightly reflective retina. Light reflected by the retina then reverses in direction and exits the eye in the same manner it entered, again with a proportion being absorbed at each stage it passes through.

As already stated, it is known that 50 to 150 photons need to enter the eye for detection to occur, but how much must be absorbed by the rhodopsin itself?

To find out, very dim light of known intensity is shone into the dark-adapted eye of a test subject. The quantity of light that is reflected back out of the pupil is measured. By comparing the two values, the quantity of light absorbed by the entire eye is easy to deduce.

Next, a bright burst of light is shone into the eye. This serves to bleach the rhodopsin so that it no longer absorbs more light.

Immediately after, before the rhodopsin returns to its pink hue, another dim light of known intensity is shone into the eye, and the reflected intensity measured. Again, the quantity absorbed by the entire eye is easily deduced.

By comparing the absorption of light with and without rhodopsin, the quantity of light absorbed by rhodopsin can be inferred.

It was found that a mere 5 to 15 photons are required for optical stimulation, which is remarkably close to the theoretical limit of 1 photon.


Natural science

The mechanical arm

Yesterday, I got my father a book for his birthday present.

The cashier at the bookshop was a young lady with a prosthetic left forearm and hand. It was quite a sight, the arm being coloured in olive drab (army green, one may say) and with a cable running the length of the arm and several metal supports for the cable. In place of 5 fingers, a wide aluminium clamp is used to grasp items. I reminded myself not to stare rudely at her prosthetic, thus I noticed that she had a neck length, densely curled dark blonde hair, grey irises in her eyes, a generally pretty face and a cheerful smile.

As I watched her go about processing the customer before me, I was quite fascinated with her comfort with her artificial hand.

While she was bagging my book, I ventured a question. "Excuse me, mind if I ask how you actuate that..." I trailed off, looking for a suitably concise phrase that would not be as dumb as 'fingers' (because it's a pair of pincers, not 5 fingers).

"Oh you mean how this works? Sure, I’ll show you in a minute," she replied, putting my father’s book in a brown paper bag.

She handed me the book, now wrapped in its brown paper bag. Flexing her pincers, she pointed out the cable that pulls them open. The cable runs to a metal scaffold protruding from the 'wrist', where it is then shrouded in a plastic tube very much like the coaxial brake cables found in bicycle brakes. The encased cable runs along the length of the forearm, where it is held by another metal structure near the 'elbow'. She pulled the sleeve of her blouse up a bit, revealing the more of the cable. The plastic shroud ends, and the bare cable is attached to a fabric sling of sorts that disappears up to her back.

By flexing certain muscles in her back, she can cause the contraction to pull on the cable, which in turn pulls the pincers open. Relaxing those muscles, the pincers close on their own accord by the action of springs.

"Impressive!" was all I could say. But then, show me the inner workings of a system and I’ll be impressed anyway.

"This hand is a simple one, but I quite like it," she continued, "the mechanical ones are too complicated with motors and the electrodes..."
I was lost. Isn’t this a already mechanical arm? A burst of clarity hit me- she actually meant 'motorised', which should be termed electro-mechanical, or at least electrical.
"The batteries too," I chime in, trying to act like I know the prosthetics trade from front to back. I mean, anterior to posterior.
"Yup. And sometimes they hurt, so I’ll be sticking to this one for a while. I’m happy with this," she said.

I thanked her for her time, and went on my way.

I do have a tinge of regret of not getting her to pose for a few portraits. I was actually worried she might be offended, but in hindsight, probably not. After all, she seemed very at ease with her prosthetic, and made no attempts to hide it. It was not in a long sleeve shirt. It was not skin coloured, but more like a slightly watered down shade of British Racing Green.

Damn it.

Next time, I must remember to ask myself,

What would Jesus ob!ique do?


End note:
Notice it did not even cross my mind to be curious about how and why the forearm had to be amputated?

Personal

untitled

I haven’t done one of those annoying questionnaires in ages, which is a good thing seeing that they are in fact annoying, as already mentioned.

I came upon one such questionnaire on Yvy’s blog, and something in me stirred.

1. Grab the book nearest to you, turn on page 18 and find line 4.
They must have felt as if a treasury had been opened before their eyes. Listen to the words of Bernard of Chartres, a scholar living in 12th century France: “We are…”

2. Stretch your left arm out as far as you can.
And then what?

3. What is the last thing you watched on TV?
It’s been ages since I actually turned on the television to watch something.

4.Without looking, guess what time it is?
9.40pm

5. Now look at the clock, what is the actual time?
9.23pm

6. With the exception of the computer, what can you hear?
A clock ticking. More precisely, the escapement mechanism of a clock ticking.

7. When did you last step outside? What were you doing?
This afternoon. Went to a beach area with David to jalan-jalan.

8. Before you started this survey, what did you look at?
Porn.
Cynical Idealist, Ah Pek and plink’s blogs. And of course, the source of these questions, Yvy. Yes, Ah Pek did it too but I read Yvy earlier this morning.

9. What are you wearing?
No one cares ok.

10. Did you dream last night?
No.

11. When did you last laugh?
Probably sometime this afternoon.

12. What is on the walls of the room you are in?
They’re bare. I still haven’t got the hooks to hang those stuffed animal heads and polished swords.

13. Seen anything weird lately?
Articulating my opinions might cause me to be classified as homophobic by self righteous radicals.

14. What do you think of this quiz?
Yvy said ,"let’s just say I prefer the ones where I can unleash my creative vocabulary."
I would agree.

15. What is the last film you saw?
The Machinist.

16. If you became a multimillionaire overnight, what would you buy?
Pfft... I haven’t actually thought how I would spend money that comes dropping out of the celestial sphere.

17. Tell me something about you that I don’t know.
What if there exists at least one god?
What if one of these gods is all-knowing?
What if one of these all-knowing gods is reading this?
Then what am I to say?

For the sake of this question, I’ll make the assumption that an all-knowing god does not exist.

I’m a sucker for good lighting. Especially diffuse and natural lighting.

18. If you could change one thing about the world, regardless of guilt or politics, what would you do?
Wouldn’t it be easier to change the self?
Anyway, I’d make 6 x 8 = 42.

19. Do you like to dance?
No, I’m too self conscious. Which is really quite a dumbass excuse.

20. George Bush.
Why did Osama kill his wife?
Because when he lifted her skirt he saw Bush.

21. Imagine your first child is a girl, what do you call her?
Eta Carina.

22. Imagine your first child is a boy, what do you call him?
Andromeda.

23. Would you ever consider living abroad?
Stay, yes. Live, no.

24.What do you want god to say to you when you reach the pearly gates?
"Woi! Remember me arr?"

25. Five (5) people who must might want to do this meme in their journal.
I cannot imagine who...

Hotel Infinity; some infinities are larger than others

Note: The story of Hotel Infinity has absolutely nothing to do with the fact that some infinities are larger than others. That is an altogether different story that is treated seperarely below.


I’ll start off by narrating the story of Hotel Infinity before talking about the actual topic of today.

Hotel Infinity is an infinitely large hotel with an infinite number of rooms. The rooms are labelled with the natural numbers 1, 2, 3, 4…

On a particularly busy weekend, every room was occupied. A man came into the lobby, asking for a room. Despite the every room being occupied, the manager told him of course he may have a room.

A message was sent requesting existing guests to move from their current rooms to the adjacent room. The guest in room 1 moved to room 2; the guest in room 2 moved to room 3; the guest in room 3 moved to room 4…
Thus room 1 was made empty, and the man had a place to spend the night.


The next day, an unexpected busload of infinitely many tourists turned up. To accommodate them, the manager cannot ask the guests to advance their room numbers by infinity- that would be senseless.

Instead, guests were requested to move from their current rooms to the room whose number is double of the current room number. The guest in room 1 moved to room 2; the guest in room 2 moved to room 4; the guest in room 3 moved to room 6…

Thus all the odd numbered rooms 1, 3, 5, 7… were made empty and the infinite busload of tourists had rooms to stay.


It so happened that the Infinity Chain owns an infinite number of Hotel Infinities in all parts of the universe. The Infinity Chain was downsizing, and our Hotel Infinity would be the only to remain. Guests in all other hotels would be moved into the remaining Hotel Infinity.

The posed a headache to the manager, until he devised a plan. Each hotel was to be assigned a number, starting with his own hotel, labelled 1. The other hotels would be labelled 2, 3, 4, 5…

To uniquely identify the guests, they needed to quote their hotel numbers and room numbers in the following format, (H, R) such that a guest from the fifth hotel’s 9th room would be labelled (5,9).

These numbers were then arranged in the following order:
(1,1)
(1,2) (2,1)
(1,3) (2,2) (3,1)
(1,4) (2,3) (3,2) (4,1)

The ordering is done such that the sum of H and R in each row is the same. For example, the second row of (1,2) (2,1) results in 1+2 and 2+1, both equalling to 3.

Having ordered the infinite hotels full of infinite guests, they can then be shuffled into the only remaining hotel infinity. The room assignation is such that their new room numbers in hotel infinity would follow their order in the chart:

1
2,3
4,5,6
7,8,9,10
:
:
:

And thus Hotel Infinity has demonstrated it can accommodate an infinite number of infinities.

By the way, this final trick was part of a proof to show that there are equally as many rational numbers as natural numbers by associating one rational number with exactly one natural numbera. Instead of H and R, the terms were Numerator and Denominator, and only relatively prime N and D were allowed into the list to disallow double counting. After all, 1/2, 2/4 and 54/108 are same and only need to be counted once.


***

Some infinities are larger than others

Now, consider a set of three elements, such as
S = {A,B,C}

There are 8 subsets of this set S:
a = {} the empty set that contains none of the 3 elements
b = {A}
c = {B}
d = {C}
e = {A,B}
f = {A,C}
g = {B,C}
h = {A,B,C}

The set S contains 3 elements, but there are 8 subsets of S, each being a unique combination of the elements of S.

If we collectively call the subsets of S as another set, S2 = {a,b,c,d,e,f,g,h}, then there are 256 possible subsets of S2 (since 2^8 = 256).

If the original set S did not contain 3 capital letters A, B and C, but instead contained ALL the natural numbers,
S= {1, 2, 3, 4, 5, 6… }
Clearly, the size of S in infinite.

However, as we have seen with the illustration using 3 capital letters, there are more possible subsets of S than the number of elements of S.

The number of elements in S is infinite, but the number of elements in S2 is infinitely larger than S.

The quantity of natural numbers (the size of S) is then denoted by Aleph-0 while the number of elements in S2 is denoted by Aleph-1.

One can repeat this process from Aleph-0 to Aleph-n, each step being infinitely many times bigger than the previous.


I’ll stop here, purely because I have no rigorous demonstration of why there cannot be one-to-one correspondence between the elements of the set S and the elements of set S2. This is especially so after having been able to stuff an infinite number of infinities into one infinity as demonstrated in the final Hotel Infinity trick. Something is wrong, since I appear to be able to produce a one-to-one correspondence between S and S2. Oh dear me, I hope I’m right and I’ll be able to upstage Cantor’s infinities. In reality, it’s probably a conceptual glitch on my part.

Personal

Crap updates. Absolutely nothing important here.

我姓陈。英文写成Tan。
有的人叫我Tan。这因为我的英文名不很容易记。

在大马，我的姓名是以马来音调念的。在世界很多地方Tan就读成ten，自己听了很不自在。

老板：阿Tan,七号吃完了，你跟我收他们的碟回来。

同事：你是叫Tan呢，或是Ten?
一维：Tan。原子弹的Tan。
同事：哈，这么好玩！

同事：跟你讲个笑话。。。
同事：牛排和羊排在路上见面但是不打招呼。为什么？
一维：不知道。
同事：因为不熟。


***

The above material cannot be translated satisfactorily into English without losing the essential bits, owing to the intrinsic properties of spoken Mandarin.

To keep everyone entertained (assuming many conditions), here’s an MSN chat excerpt for those who do not read Chinese. [Slightly edited for grammar and syntax.]

The Architect: Some of my colleagues are using Pentium 2 computers running Windows 98.
The Architect: So even thumbdrives don’t work... have to burn CDs.
Tan Yee Wei: Oh shit
Tan Yee Wei: doesn’t Photoshop kill those computers already?
lol…
It does…thus they dun run Photoshop
Haha
Most presentations are hand coloured
With colour pencils
Definitely what some would say 'old school'
In fairness… it does look quite good
At least you can be sure their hand eye coordination are good
lol
And yes, nothing out of the lines. The ultimate sin of kindergarten academic work [eye rolling emoticon]
...
Ah wells… See, the thumbdrive transfer method as a way to promote relationships between colleagues.

[omitted]

Think I'm falling sick soon... better sleep more
Good night
Enjoy your ‘all work and no F1’ Sunday tomorrow.
Ah nvm, got pretty girls so it's not so boring
Wow.... u've changed
Girls instead of F1?
No lah
Not SO boring
lol


As the title already disclaimed, nothing important here.

Personal

Stuff of (impermanant) dreams

For several years already, I have been adhering to the ‘no attachments’ school of thought for certain aspects of my life.

If one binds one’s ego to an impermanent characteristic/object, one is bound to be pained when that characteristic/object disappears. Which is bound to happen, seeing that it is impermanent in the first place.

However, it could well be a case of rationalising my failure to achieve much in those aspects of my life. In other words, sour grapes.


***

“Nay, there is no point to owning a car. Look at the price cars are selling for these days! And think of the petrol prices, maintenance costs, parking fees and taxes. Insurance!”

“I’d rather live without a car- one less attachment to fret over.”

Then along comes this bright yellow race-spec Lotus Elise. Wrapped around the circumference of its magnificent BBS rims are Yokohama sports tyres, with barely a few treads just to get around the regulations. A black wing stretches across the car’s rear, and a carbon fibre diffuser is in place of the original aluminium underbody panels. An uprated engine block, racing gearbox and limited slip differential justifies the aerodynamics and suspension upgrades.

The Lotus idles noisily, occasionally burping and popping loudly through its unsilenced exhaust pipes. Abruptly, it accelerates brutally down the main straight, the waste gates hissing angrily at each gear change. It brakes and downshifts into turn one, flames crackling from the exhaust. Through the apex the car sweeps, accelerating out with a menacing wail.

“I think I’d like a car like that…”
That grape might not be so sour after all...

Little did I know that a car like that is a humongous hassle. The gearbox is not synchromeshed, demanding perfect shifts every time. The clutch bites like a crocodile’s jaws, with little room for error. The steering geometry does not allow 3-point turns; it advocates 7-point turns. In rain, the slick tyres grip like ice blocks. There is no seat for a passenger, neither is there room for groceries. There is no air-conditioning except for a pipe that funnels air from the front of the car into the driver’s face. There is no insulation, noise or thermal. The suspension feels like they were machined out of solid granite.


***

And I'm not talking about cars; not this time anyway.


Personal

购买衣记

星期六那天，餐馆的老扳看着我的t-shirt，对我说最好穿长袖的衣。
我也迟早要买件黑衣，因为暂时穿的衣是表哥的。

今天星期一没上工，我就到Melbourne Central走走，找一件便宜的黑衣。购买的条件很简单-颜色只限黑，不可有其他颜色或花纹。而且价钱不可吓死我。

可惜的，要找件黑衣也不容易。在架上见到黑，就走过去看看。可是，大部分都有画上花纹的，不然价钱就有点贵，或者颜色原来是深蓝。走上走下都不见的多黑衣。

我现在可以承认我没有自己卖过衣裤。我本身穿衣随便，不注重时尚。差不多整齐就行了。有的时候，母亲带我去购买衣的时候，她会感得我很不耐烦。所以，很多次衣服都是妈妈一个人买的。而且，过新年的时候，阿姨表姨们有时会送一两件衣给我。造成，买衣裤的必要我一点都没有。

我在Melbourne Central里的Myer男幢部走了两圈都只看到一件不错的衣。算了吧，有一点点贵，还不会离谱。买了它就可回家吃饭。

到今日，我还不了解好看衣裤裙的人。我有是怕跟我的表哥逛街，就因为他很喜欢慢慢看衣裤。没有打算购买也每件每式都摸一摸。会闷死我的呢!

但是反回来看，这都是靠个人兴趣的。我猜，很多人也不明我对数学与物理学的兴趣。


Personal

Is this philosophy of mathematics, or is this bullshit?

Lately, I've been curious as to why the number 2 is so important. The number 2 crops up everywhere, so pervasive that I’ve never noticed it until lately.

Concave, convex.
Positive, negative.
Left, right.
Yes, no.
Sky, earth.

The importance of two turns out to be very fundamental- it is precisely because two is one more than one. Symbolically, 2 = 1 + 1.

Say we have a "dimension". For now, we will restrict the geometric properties of this dimension to being a straight line. We are on an arbitrary point along this one dimension, and we can only travel along this dimension. Think of a railcar running on its tracks.

Strangely enough, there is only one station on this rail line. It is Piccadilly Circus, far away in the distance. The railcar travels in one direction, towards Piccadilly Circus.

So far, we have only worked with one's. There is one dimension, and along this dimension is a preferred direction. And now, to invoke "two".

If the railcar was made to reverse its direction of travel, such that it moved further and further away from Piccadilly Circus, then it would be travelling in the opposite direction. Obviously, this direction is not the same as the direction that leads to Piccadilly Circus.

And thus there are now two directions: to Piccadilly Circus, and away from Piccadilly Circus. Relating back to the earlier equation 2 = 1 + 1, we can see that the two comes from going along the dimension's 'preferred direction', and in the reverse direction.

Thus the "two" is constructed.

Of course, this dimension's geometric restrictions can be lifted, and the dimension can then be made to fit between any two extremes.

North and South.
On and off.
Stupid and clever.
Civilised and barbaric.
Bright and dim.
Light and dark.

As one can see, the dimension can be fitted not only to geometric extremes like North and South, but also to conceptual poles such as civility.


Edit 20 April 2006:

Here is a better derivation of 'two' that does not depend on vectors nor time derivatives of position.

On that railway, there lies one railcar. The presence of this one railcar seperates the railway into two distinct regions. So yeah, one dimension, one obstruction, two regions. Simple.

Personal

Mathematics

Experimental formatting- Chinese screenplay

Edited 4th May 2006: a sloppy English translation has been appended to this post.


序幕
人物：陈一维，Tracey，大厨师，餐厅顾客
场景：某餐厅之bar

（餐厅顾客少。一维在bar内的洗碗盆洗杯子。Tracey在对面与他聊天。）

Tracey：你是从马来西亚来的是吗？
一维：对，靠近首都吉隆坡。那么你呢？
Tracey：我来自中国。
一维：中国哪一部？
Tracey：四川。

（厨房双门打开，大厨师升出上半身。）
大厨师：（对着一维，摆手叫他过去）来，来。有空就教你点东西。

（一维把杯子冲干净，双手抹干，跟大厨师入厨房。Tracey继续洗杯。）

大厨师：现在不忙就可指给你看怎么准备铁板鱿鱼。（拿出个木板， 到火炉，从旁拿一个铁钩，便用钩把炉上烧着的铁盘托到木板上。在铁盘上落些生洋葱，加些食油。从炉上拿起蜗。）如果很忙的话，我就把煮好的料倒在碗里。你要准备铁板然后把料倒上。最后加点酒上去，就好了。

（大厨师把蜗里的鱿鱼倒上铁盘，然后加上米酒。盘里啥了一声。）
（一维从厨房拿出铁板鱿鱼和一盘白饭，摆在客人桌上。）

一维：Your sizzling calamari and a steamed rice.
客人：Looks good. Thank you.
一维：Enjoy your dinner.

（一维回到bar边站。Tracey还洗着杯子。）

Tracey：今天是你第一天在这里工作？
一维：第二天。昨晚我也有来。
Tracey：你以前有在餐馆做过吗？
一维：没有。这是第一次。
Tracey：哦，那么以前做什么种工？
一维：近来都没有做工。
Tracey：（吃一小经，从洗碗盆望上）哇，好幸福呀！
一维：（不知如何回答）Errrr…

（两人静一阵。Tracey洗杯，一维注意着顾客们。）

Tracey：（想想后）读书时不用打工都瞒爽的。。。
一维：那是真的。时间多，压力也少。
Tracey：还可以参入各种学会和活动。
一维：对呀。

（两个客人从前门进入餐馆。）

Tracey：（把头轻轻地向前方点一点）有人到。

（一维拿两本菜板，去欢迎顾客。）

（序幕终）


***


Prologue
Characters: Yee Wei, Tracey, Head Chef, restaurant customers
Scene: A restaurant
Language: Chinese/Mandarin

(There are very few customers in the restaurant. Yee Wei is at the bar’s sink washing some glasses. Tracey stands across the bar.)

Tracey: You are from Malaysia, is that right?
Yee Wei: Yes, close to the capital Kuala Lumpur. Yourself?
Tracey: I’m from China。
Yee Wei: Which part of China?
Tracey: Szechuan.

(The kitchen’s double doors open and the Head Chef leans out.)

Head Chef: (To Yee Wei, waving his hands to invite him over) Come, come. I’ll show you around while we have time.

(Yee Wei finishes cleaning the cup, dries his hands and follows the Head Chef into the kitchen. Tracey takes over washing the remaining cups.)

Head Chef: Now that we’re not busy I’ll show you how to prepare a sizzling calamari dish.

(The Head Chef reaches for a wooden tray, heads towards the gas stoves and grabs an iron hook from a side counter. Using the iron hook, he manipulates the steel dish on the burner and puts it on the wooden tray. He then adds some raw onion pieces, a dash of oil and removes a wok from the main stoves.)

Head Chef: If we’re busy, I will pour the cooked calamari into a bowl here. You’ll have to prepare the hot plate and pour the calamari onto the dish. Finally, add a dash of cooking wine, and off you go.

(The Head Chef pours the calamari into the heated dish, and adds some wine. They make a noisy hiss as each ingredient contacts the hot metal.)
(Yee Wei brings the dish of sizzling calamari and a plate of rice to a customer’s table.)

Yee Wei: Your sizzling calamari and a steamed rice.
Customer: Looks good. Thank you.
Yee Wei: Enjoy your dinner.

(Yee Wei returns to the bar’s side. Tracey is still washing glasses.)

Tracey: Is this your first day here?
Yee Wei: Second day. I worked yesterday night too.
Tracey: I see. Have you worked in any other restaurants in the past?
Yee Wei: No. This is my first.
Tracey: Oh. So what kind of work did you do before?
Yee Wei: I haven’t worked in recent times.
Tracey: (Surprised, and looks up from the glasses) Wow, how fortunate!
Yee Wei: (speechless) Ermm…

(They keep quiet for a while. Tracey continues washing the glasses, Yee Wei keeps an eye on the customers.)

Tracey: (after some contemplation) It must be nice to not have to work while studying…
Yee Wei: That’s true. You have a bit more time and less stress.
Tracey: And you can join the activities of carious clubs and groups too.
Yee Wei: Yup.

(Two new customers enter the restaurant.)

Tracey: (Nodding gently towards the front of the restaurant) Customers.

(Yee Wei grabs two menus and goes forward to greets the new customers.)

(End Prologue)


Personal

Ice cream, yoghurt, banana and peaches

I just had the best bowl of ice cream in ages! Wheehehehe...
Ok, that sounded daft.

Anyway,

Several large scoops of Neapolitan ice cream.
One banana, sliced.
Several tablespoons of yoghurt.
Several tablespoons of peach puree.

Dump them all sufficiently large bowl and give the mess a slipshod stirring to coat the banana pieces and spread the peach puree around.

The puree was made of real peaches blended in a food processor then doped with sugar and lemon juice. The reason I had made this is not relevant to the discussion here.

Of course, there are no photographs. At any rate, the bowl of stuff is ugly- it’s been lightly mixed, remember.

It was delicious though, if the first sentence did not already suggest so.

The mix of textures was remarkable. There was the soft, airy feel to ice cream; the runny, but almost gritty texture typical of yoghurt; that yielding, starchy sensation of banana pieces; and tiny lumps of fibrous fruit in the peach puree.

Not to mention flavours. The ice cream gives 3, to come up with a total of 6.

The fun bit was the C and P of sensations. Combinations and permutations, in case anyone thinks of copy and paste.

A light drizzle of chocolate sauce and a healthy blob of whipped cream would help, but that’s probably asking for trouble on the calorie count side of business. Closer to reality, something to contrast all those smooth textures would be nuts of some sort. Peanuts or cashew might be a good idea. Or a slight sprinkling of crushed biscuits. Roasted almond slices would be very nice though.

I wonder if a dash of Bailey's Irish Cream would go well with the mix. It surely would. Bailey's is never wrong.


Personal

So, how long is this 'eternity'?

Eternity- an ever present concept (at least in the various religions)

Imagine the earth turned into a solid orb of steel- a smooth, shiny sphere, carbon-tinted silver in colour, drifting lazily in the emptiness of the inner solar system, catching the sun’s rays and reflecting them in all directions.

Also imagine a fly, an ordinary house-fly, with deep red compound eyes, its black exoskeleton tinged with an infinitesimal layer of shimmering metallic blue-green colour and on its thorax, delicate translucent wings that on closer inspection appear to be made of crystal grown from the finest crystal shrubs in the gently rolling hills of southern France.

This fly, ordinary in every sense except for its exceptionally long life, travels far and wide within the solar system. Every thousand years, it arrives at the earth- that gleaming orb of carbon steel- and stops for a moment to rest its crystalline wings, then flies off towards the baking heat of Mercury.

Over time, after countless landings, the fly’s legs have worn away part of the earth’s metal by the gradual effect of friction.

In due course, the earth would be completely worn away, and the fly would have to find another resting place along its interplanetary flights.

And yet, despite the unimaginable duration in the meantime, eternity is not yet halfway over. Why, it has not even started!


***

On a completely different note, I read an automotive magazine ‘Motor’ just a few hours ago. Or more accurately, I flipped through the publication half heartedly.

There was an article about the Lamborghini Gallardo. Crammed between the columns of text and graphics, were quotes from the article itself in bold, attention grabbing fonts. One of these quotes went,

The exhaust note barks with a visceral noise [...] like Kylie Minogue being ripped apart by a pack of wild dogs.

I put it back onto the shelf with disgust.

Having thought about the issue at some length, I’m still not sure if that sentence was brilliant or just plain crass. It’s either A (in which case the journalist and editors would deserve a Pulitzer, ignoring the rumour that the Pulitzer is a prize awarded for achievements in American journalism, literature or music) or F (where they would be condemned to licking fly legs for eternity) .


Personal

A discussion with the Flying Spaghetti Monster

I had a strange flash of thought. Insights have been rare these few days, which is not a good thing. No, random number generators and self-propagating essay assignments do not count as insight.

What would my thoughts and outlook be like if I knew I was going to die in approximately n months?

[Truncated. I don’t think anyone would bother to read this anyway.]


***

FSM: How would you want to die?

TYW: Happy, duh. That’s everyone’s answer.

FSM: Define happy.

TYW: Well, I want to be clear minded, not in pain, with my loving family by my side when I die.

FSM: How are you going to achieve that?

TYW: I’m going to die. What do you mean by ‘achieve’?

The family. How will you ensure that you have a loving family? As far as I know you have no serious desire to get married. Not to mention children.

I could adopt by sibling’s family as my own. I know of some single people who stay with their siblings for the rest of their lives.

Indeed I know of such arrangements. But to incorporate it into your long-term strategy is rather unique. What if the siblings do not consent?

I’d have to think of something else...

Have you thought of ‘living for the day’? It’s an Epicurean saying. A tagline, even.

No I haven’t, actually. Without an end, a target, isn’t living for the day simply a random walk?

Actually, no. No doubt it's chaotic, but definitely not random. If you mistake ‘live for the day’ as a war cry to indulge in all manner of pleasures that guarantees suffering in the future, you are wrong. It’s actually like an optimisation of short and long term benefits.

Impressive. Do you have the algorithms to run this optimisation?

Of course not, are you daft? There is such a thing as free will. I’ll not go into the details of the Newton and the mechanistic view of the universe. Nor will I detail how Heisenberg shattered that view with quantum theory.

Pfft. By the way, have you heard of the joke about the mystic who requested to be ‘made one with everything’?

No I have not. Who did he ask?

That’s the interesting part. He asked the hamburger vendor to make him one with everything.

Hahahahaha.


Related links:

Flying Spaghetti Monster
Mechanistic view
Heisenberg
Mystic



Personal

Intake Horns - an excerpt from the draft of 'Automotive Engines'

I have gone back to writing my book. Yes, it sounds grand doesn't it?
Writing on my book.

Just remember that many books get written. A large quantity can never meet the standards required of publication. Some of those published never make it anywhere significant (the rubbish tip is somewhere, but...).

Anyway, here's a first draft of my latest section, "Intake Horns", from the chapter "Induction and Exhaust".

As this is a draft, I would be very happy if errors and omissions of any sort are pointed out. Thank you.


***

Intake Horns
An excerpt from the draft version of 'Automotive Engines' by Tan Yee Wei

Induction manifold: a branching pipe that delivers air and fuel to individual cylinders.

In many engines, intake air is filtered to remove dust and grit that may harm the engine, then piped towards the carburettor or fuel injectors, then diverted towards the engine block. Here, the pipe splits into smaller pipes, each delivering air and fuel to individual cylinders. This is when the induction manifold is relevant.

However, some extremely high performance and short race duration engines can make do without an air filter. It is also likely that this engine will have individual fuel injectors at each cylinder. Thus there is no need for the intake manifold which only serves to distribute air that has been modified by a central facility, namely the air filter and fuel injector.

In these cases, the induction ports of each individual cylinder are equipped with a pipe that widens at the opening in a horn shape to improve airflow. For obvious reasons, these are called intake horns.

These extremely high performance engines not only gain an advantage in not having to draw air through an air filter, they also do not have to draw air through long lengths of piping. The upside is less energy required to take air into the cylinder.

This advantage can also be applied to engines that require an air filter (but still retaining individual fuel injectors at the cylinders). The entire collection of intake horns can be enclosed in an air-tight box, which is connected to the air filter by a sufficiently large pipe. Thus the intake plenum is born, also referred to as the air box. The advantage of this arrangement is that the connection between the plenum and the air filter can be made arbitrarily large to reduce resistance, and the overall resistance in the intake system can be reduced significantly by taking the manifold out of the picture. In some cases, the air box also doubles as the air filter: the walls of the air box are made of air filter material, thus doing away with the extra piping.


The benefits do not stop there: these induction horns can be easily tuned to optimise airflow at certain speeds. This can be done by simply changing a set of horns for a longer or shorted set. Performing a similar operation with an intake manifold would be a terribly convoluted exercise, in all senses of the word.

In a competition engine, one might expect the horns to be tuned to perform best when the engine is producing its peak power, since the engine will be operating near its peak power most of the time. However, things might differ in the case of a passenger vehicle’s engine that is expected to operate at various speeds. The horns may be tuned to give the extra bit of power where the engine is lacking in power, so as to give it decent performance all round its operating speeds.

The major point of consideration in tuning the intake horns is the length of the horn. In general, longer horns give good performance at low engine speeds, and short horns give positive results at high speeds.

A simplified explanation of induction tuning is presented below.

Consider one cylinder of an engine with intake horns installed. At this moment, it is in the midst of the intake stroke- the intake valves are open and the piston is moving downwards, drawing air into the cylinder through the intake valves. Air in the intake horn is moving inwards towards the engine.

When the intake stroke is complete, the intake valves close. At the instant the valves close, air in the intake horn is still moving inwards. We would expect that this bulk of air will be stopped, since it will not get past the closed valve. Thus the air piles up against the closed valve- its velocity slows to zero, while the pressure and density increases.

This pressure build up then starts to push the air backwards out of the intake horn, the backflow only stopping when the excess pressure is dissipated.

This is the point when induction tuning becomes relevant. The length of the induction horn is adjusted such that the duration of the pressure increase corresponds with the time it takes for the engine to complete one cycle (2 revolutions). Thus at the time the pressure is ideal, the intake valves are already open for the next cycle of air intake.

The pressure and density build up thus aids to push air into the combustion chamber. Of course, one may see that if the engine speed is slower than ideal, the air would be already moving backwards by the time the valves open for the next cycle. The result is an engine that gives good performance only in a narrow range.

The next question would obviously be directed in the general direction of giving excellent performance at all engine speeds. In the upper echelons of high-tech, big money motor sports, variable length intake horns are used. Prior to 2006, variable length intake horns were used in Formula 1 engines. This naturally gave spot-on induction and good power at all engine speeds.



Personal

Applied science

Rainy Day

Rainy Day
A true story by Tan Yee Wei


"Wei, wake up!" an urgent voice swirled around me.
"We need to take in the laundry, it’s raining!" the voice continued.

I woke up with a start. David was imploring me to hurry up before the clothes get drenched. I glanced at the window. Indeed, there were several elongated streaks of rainwater on the glass pane while more were being added every moment.

With effort, I temporarily banished all slothful inclinations and got up. The mind was eager to rescue the clothes, but the body was not ready. I lumbered towards the door; David had opened it and was already running towards the stairs, laundry bucket in hand. His brisk footsteps faded into the distance.


The overcast sky’s diffuse light blinded me. I stumbled to a stop, blinked and rubbed my eyes while waiting for my pupils to contract. Gritty bits of dried discharge rubbed off from my eyelashes onto my fingers, which I brushed away.

Some moments passed while my eyes adjusted to the light, and I stepped out of the doorway as quickly as my hesitant steps would allow. The cold, damp wind surprised me in my cotton t-shirt. I made my way to the stairs, my slippers sliding and slapping on the concrete walkway from my still-infirm steps.

Even as I walked, the rain intensified. The falling droplets, which had appeared sparse in the air just seconds ago, were starting to crowd out the sky. The wind was still bitingly cold.

I climbed the steps to the roof, my left hand grasping the railings to help haul my body upwards. Every muscle was not to be wasted; each additional second brings more rain water to our clothes. My injection-moulded plastic slippers pattered annoyingly on the concrete.

Rainwater splattered on the outer edges of the stairs; I kept to the inside of the zigzagging stairs. From a great height, silvery strands of falling rain drops slanted by the wind pierced earthward. I recalled a novel I read yesterday…

"From the garden, I could hear the rain beating on the leaves and into the clay, and I pictured it, falling straight and shiny as wires through the windless dawn."

With a tinge of regret, I noted that my rain fell diagonally.


I arrived at the top of the stairs. David was holding an armful of t-shirts, plastic hangars still in them. He rushed towards a shaded area, shoved the clothes into the bucket, and went back into the rain to collect the rest.

I headed out into the rain, ducking my head to avoid running into the braided steel cables that serve as laundry lines. With the t-shirts removed earlier, all that remained were briefs and socks. Undoing the clothes pegs before taking each garment down, I reflected on how I had fastidiously pegged every piece of clothing the day before. Now I had to unpeg each and every piece, as quickly as possible while being drizzled with cold rainwater and breathed on by the chilly breeze.

We stuffed the remaining articles of clothing into the laundry bucket, and hauled it back downstairs. Hurriedly, we pattered back to the flat, with less urgency as before but still eager to be out of the cold.


The season of tolerable climate is behind us, and this drab, cold weather hangs like a stubborn pall over the landscape. How quickly the seasons snapped around, from the 30 degree heat a fortnight ago to this 15 degree misery today.


Author's notes:

The quote was from John Banville's novel 'Shroud', Pan McMillan, 2002, London.
Click here for my writing.com entry.
David is my cousin.


Narration

I'll be away for a while

Due to some chi-bai circumstances, I am effectively without an internet connection till the end of the month. Or, more accurately, every Mb i download will cost me $0.15.

Yeah, Telstra's Bigpond ISP is a fucker. The new unlimited download package will commence next month. In the meantime, I'll use the internet connection in the university's libraries or the council library.

Updates (7th April 0120):
I've taken to limited browsing and surfing with images turned off. So I only see text, no pictures. The effect is quite dramatic.

I'm alive!
Bah. Wankers.


Personal

Another guided composition

Update 2.40pm April 5th:

The following individuals have done their compositions. It seems the uncommon words have kicked everyone's brains into afterburn- just look at the incredible works out there. Congratulations.

Charmaine - humour. A man with PMS and a mamak who graduated from the World Toilet University.

Yuan Harng - academia with a touch of humour. "Why does papa have to die in that accident of crashing Ox carts?"

Yvy - drama. "O my Lordy!! What are you babbling about, young man?!"

***

Just for the heck of it, I’m going to (attempt to) break into Yvy’s niche of producing essay challenges.

Write a composition using the following 10 words.
The composition is not to be more than 300 words in length.
The words must be used in the order found on the list.
Each word presented in the list must be used only once.

10 random numbers were generated using MS Excel, and their values correlated to the entries in the Oxford English Dictionary.

So here goes...

Actinide
Juvenescence
Ease
Oval Office
Cottager
Accede
Biryani
Crashing
Screenplay
Space shuttle


Okaaay, this is a tad bit more challenging that I had expected…

Now to define the slightly trickier terms:

Actinide - chemistry any of the series of fifteen radioactive metallic elements from actinium (atomic number 89) to lawrencium (atomic number 103) in the periodic table.

Juvenescence - formal youth.

Cottager – a person living in a cottage

Accede - (usually ‘accede to’) formal
1 assent or agree to.
2 assume (an office or position).

Biryani – variant spelling of biriani
An Indian dish made with highly seasoned rice and meat, fish, or vegetables.

Screenplay - the script of a film, including acting instructions and scene directions.

Actinide
Juvenescence
Ease
Oval Office
Cottager
Accede
Biryani
Crashing
Screenplay
Space shuttle


***

“So, what’s this actinide you say your men found in my land?” the weathered man asked, all traces of juvenescence having been erased from his face by years of hard work. He had asked the question with an ease commonly found in people not intimately familiar with the periodic table’s lower rows.

“It’s a class of radioactive metals. Exactly which element we are not sure, but it might well be Berkelium or Fermium,” said the man, a fake grin plastered on his face. He had aspirations for the Oval Office, although his secretary mistress says it’s impossible.

“I see. So is it safe for me to continue working in the fields?” the cottager asked. If the land was too dangerous to work on, he’d have to hire Mexican hands to do the job.

“The problem is that Washington may demand the land from you. It’s impossible not to accede to their wishes. Mind-control bastards…” the senator explained, “must be the things they put in the Biryani rice.”

“The what rice?” The farmer had never liked rice, partly due to the fact that he planted wheat for a living. Mentioning rice to the wheat farmer was like a dramatic crashing of ideologies.

“Nah, I was joking. Just something I picked up from a screenplay,” the senator tried to smooth out the bump. The farmer continued to glare at him suspisciously.

“So, did you see the space shuttle’s catastrophic launch yesterday?” the senator tried to make small talk.

“Nope. No TV,” the farmer replied gruffly, “What about my land?”

257 words

***

I'm not explicitly asking anyone to do this, but it may be of interest to Ah Pek, Charmaine, plink, Yee Hou, Yuan Harng and Yvy. Oh whatever... you're all tagged. Go do it.

Narration

The View from the Top - Melbourne Cityscape at Night

Two of my cousins' apartment is a 25th floor unit in the middle of the city. Needless to say, it has a fantastic view.






The View from the Top - Melbourne Cityscape at Night

Click here for large size image
Which is required if one wishes to see the lights in any detail






Photography

10's complement- an algorithm to fast subtraction

Sometime is my life, I read about a numerical method for use in subtraction. It’s called the 10’s complement, and the mechanism allows the addition algorithm to perform subtraction, with a little modification.

A brief comparison of addition and subtraction algorithms will be compared:
For addition, the procedure is simple. Add the right most digits, and carry excess 10s over to the next digit and continue the addition process digit-by-digit till completion.

For subtraction, the procedure is not a simple right-to-left operation. The borrowing of deficient 10s is performed before the subtraction of the digits, and if there is a series of zeros in the number, the borrowing will have to continue left until a non-zero digit is reached, and all these zeros will have to be changed to nines. Subtraction operations require read and write operations that move in a zigzag fashion.

The 10’s complement addresses this annoying issue of zigzagging areas of attention by introducing a simple subtraction step before performing an addition step.



Illustrating with the following example:

5006002 – 209137

Doing it using the long subtraction way (the normal way):



Subtraction of the right-most digits require a borrowed 10 from the digits on the left, thus changing 3 digits on the left. The subtraction process then returns to the first digit and the progressing on to the next.

Of course, the borrowing of 3 digits is consists of 3 distinct steps. If the next number is not capable of providing a 10, in the case of a zero, then the subsequent number will have to be considered until the first non-zero is reached.

The fourth digits also require a borrowed 10, and another 3 digits on the left have to be modified before returning to the actual subtraction.

As one can see, the areas of consideration while going through the subtraction process moves in a saw tooth fashion with intermittent hops left and right.



The 10s complement takes advantage of the fact that 209137 (the subtrahend- the number that is to be removed from 5006002, the minuend) is 999999 – 790862.

209137 = 999999 – 790862
209137 = 999999 – 790862 + 1 – 1
209137 = 1000000 – 790862 – 1

With this in mind, the subtraction can be rewritten as follows:

5006002 – 209137 = 5006002 – (1000000 – 790862 – 1)
5006002 – 209137 = 5006002 + 790862 + 1 – 1000000

The actual calculation procedure is shown below. Doubtless, there are more steps compared to long subtraction, but the business of borrowing is completely eliminated.



First, the complement of the subtrahend is taken. Sufficiently many digits of 9s must be used as to match the longest string present in the calculation. This is to ensure that the end result can be obtained simply by truncating the most significant digit from the answer.

The minuend is then added to one and the complement of the subtrahend.

Finally, a power of 10 is removed from the sum. If the number of 9’s used in the complementing process is a good choice, this final subtraction is a mere removal of the leading 1, as is the case here.

The explanation and derivation is unwieldy, but when performed with a sheet of paper and a pencil, the 10s complement method is an extremely easy method to reliably calculate subtractions of large numbers.



When working with binary numbers, the complement method is even more effective. This can be justified by the fact that the 2’s complement of binary numbers is trivial to perform.

This is because the complement is done by taking the difference of each digit with the largest number available in the base system, in the case of binary, one.

Due to the fact that 1 – 0 = 1 and 1 – 1 =0, taking the complement of each digit is exactly the same as flipping 1’s to 0’s and vice versa.

Working with binary numbers, here is another example:

110110 – 101

111111 – 000101 = 111010 (bit flipping of the subtrahend, 101)

110110 + 111010 + 1 = 1110001
1110001 – 1000000 = 110001

Therefore, 110110 – 101 = 110001


Mathematics

End of the Age of Oil, part 4

The following narration is a self-indulgent fragment of nothingness set in the era defined by previous essays:

End of the Age of Oil, Chapter 1: The Decadence of the Average 20th Century Dweller of the Developed States
End of the Age of Oil, Chapter 2: Towards 'E'
End of the Age of Oil, Chapter 3: Social changes

End of the Age of Oil
Chapter 4: untitled

Two figures emerged from the Meyrin* control centre. They were taken by the unexpected coldness, and zipped up their jackets to the last few millimetres. The sky was a glittering sea of sparkling stars, glowing nebulae, fuzzy galaxies, speckled clusters and unblinking planets.

"Nice, isn’t it?" Freyja asked the man beside her.
"I personally find it a bit too cold," Gowda replied dryly, seemingly huddled in his jacket.
"I mean the sky! Look at the stars, the constellations, clusters, super clusters, binaries, neutron stars, accretion discs!"
He raised an eyebrow. "You can tell the difference between a neutron star and an accretion disc?"
"Of course not. I don’t even know the difference between them."
"Yes, it is a pretty sight. My grandfather said the sky used to be less visible when he was young. I’m so used to this," he waved his hand at the sky, at first vigorously, but then quickly slowed down because he was cold from the breeze on his hand. "I cannot imagine it being drowned out by light."
"Yeah, just imagine the quantity of light that would need to be produced just so that the light reflected off the atmosphere was brighter than the stars..." she trailed off, engrossed in the NGC 2632 cluster. She suddenly pointed, "a falling star!"
He whipped around, but the meteor had already burned out.

They headed for the bike shed, currently shroud in darkness. When they got closer, LED lamps sequentially illuminated, giving the impression that the lights were slowly coming to life. It looked much friendlier than an abrupt illumination of the lights. The interior of the bike shed took on a dim white glow, with bright strips of lights along the floor directed at the bikes to clearly distinguish one bike from the other.

With the ever increasing cost of electricity, every Watt of power had to be spent carefully. First, incandescent bulbs were replaced with fluorescent tubes, then more efficient tubes, then motion sensors were used to replace the permanent on switches, then LED lamps were used. The latest cost saving measures had introduced very dim ambient lights with a few location-specific lights.


Somewhere in the past before the complete exhaustion of oil, people took to driving smaller and smaller cars as a reaction to the persistently rising price of fuel. After a while, motorcycles became popular. When even the petrol consumption of a motorcycle was becoming too burdensome, people took to cycling and public transport.

As fuel and energy prices soared well beyond the imagination of 21st century dwellers, cycling remained the only viable option for cheap commuting. With cycling suddenly thrust into the role to mass transport, various modifications were made to classical layout. Most human powered vehicles took on the general layout of the recumbent bicycle in an aerodynamically efficient shroud.

"Well, my bike’s here. I’ll see you next week," Freyja bid her farewell to Gowda.

His jaw nearly dropped at the sight of Freyja’s magnificent machine. It was a Prodrive .12R sports bike adapted from their racing machines, just barely street legal. The name .12R was derived from its fantastic drag coefficient of 0.12, and obviously R is for racing, as vehicle marketing had always been. Taking the recumbent position to the extreme, the pilot’s seat was moulded to fit the body in an inclined position. The cockpit was not a compartment; it was tight as a suit. There was no room apart from the single seat, pedals and numerous hand controls beside the seat.

"Wow! Mind if I take a closer look?" Gowda asked. Never in his life had he seen a Prodrive, much less a .14R with all the trimmings.
"Haha, it’s my brother’s. I’ll turn on the lights." Freyja found the switch that controlled the main lights, and the rest of the LED lamps in the shed glowed.

"So, this is a carbon-fibre monocoque?"
"Yeah, even the wheel rims are CF. This thing cost my brother a fortune. I only got to use it after much persuasion."
"I would guess so. What’s the drive train like?"
"Don’t know… some fancy Zeroshift gearbox. It’s got about 8 speeds and a 3 speed reduction gearbox. Weird thing, it shifts in a H-pattern like those cars back in the 20th century. It’s got a shaft drive to the rear though, which is nice since you don’t get the slack normally found with chains."
"Fantastic. The Zeroshift gives you no break in power transmission, is that the one?"
"Yeah. My brother is into drag races. He even changed the pedal crank lengths to fit his legs a bit better."

Gowda continued admiring the bike, peeking into the cockpit to see the pedal crank and the gearshift mechanism, running his fingertips against the various joints in the bodywork to feel the precision of the panel work, peering at the meticulously bonded cockpit canopy.
"So, where’re the wing mirrors? Or do you make do without?"
"Nah, we’d get in trouble with the law. Here, they pop out from within the nose cone." Freyja reached inside the cockpit, and tugged at a lever. A pair of panels opened inwards, and aerodynamic mirrors slid out on both sides. When she pushed on the lever, the mirrors slipped back into their cocoons and the doors sprung shut. "Nifty, isn’t it?"
"Very much so."

"Well, I’ll take my leave now, its too cold to stay out for long. Thank you for showing me your brother’s bike."
"No problem at all. Good bye."
"See you on Monday."


***
* The Meyrin site is the main access point to the CERN. It has conference theatres, computer centres, restaurants, dorms, security centres among other facilities.

Narration

A step-by-step logical guide to improving a basic punch

In karate and taekwando, the forms/patterns/katas are routines with blocks, strikes and different stances. While they may be viewed as boring compared to exciting take-down techniques or sparring sessions, forms can be used as an invaluable teaching tool.

In all probability, the first form will involve the simplest of movements, with the punch and forward stance playing a major role.

For beginners, instructing on the stances is easy; how to execute a strike with forceful commitment is the tricky part. This essay will attempt to introduce a guide based on logical arguments that will arrive at a workable punch.

The forms will be used as the starting point, or axioms. One can even say that the forms will be accepted solely on the faith that years of development have refined it to its most practical incarnation.

The form (an excerpt):

The practitioner executes a block/strike and a forward stance, with the leading hand and leading foot on the same side of the body. The next movement is a step forward into another forward stance, with the other hand (now having become the leading hand due to the step) executing a punch.

A requirement of the form is that the step is finished the same time as the punch.

Argument 1:

The punch is designed to hit hard.
Therefore the fist is needs to move fast during impact.
In the form, the step and the punch is to be completed at the same time.
But the step is slow compared to the maximum speed of the punch.
Hence the practitioner should start stepping first, and start the punch near the end of the step such that the conclusion of these 2 motions coincide.

Argument 2:

The punch is designed to hit hard.
Therefore the fist is needs to move fast during impact.
To supplement the velocity provided by the extension of the shoulder and elbow, the shoulder itself should be propelled forward.
This can be done by rotating the upper body to push the shoulder forward, and also to lean the upper body forward in the direction of the punch.
Fist extension, body rotation and leaning must be performed simultaneous to ensure that the relative velocities add.

Argument 3:

The punch is designed to hit hard.
Therefore the fist needs to move fast during impact.
The extension of the fist relies on the upper arm rotating forward to drive the elbow up and forward, and the forearm rotating downwards to drive the wrist (and fist) forwards but not upwards (despite the elbow travelling with an upward velocity).
If the constraint of the elbow joint was ignored (the elbow can turn through 360 degrees as opposed to the real world where it only straightens to 180), at full extension of the fist, if the upper arm was still rotating, it will still bring the elbow upwards, but backwards. (The motion of the fist in the horizontal direction can be modelled as x = 2A sin (θ) where x is the horizontal distance from the shoulder, A is the lengths of the forearm and upper arm, and θ is the angle the forearm makes with the vertical. Refer to diagram.)
Therefore, maximum extension is achieved when the elbow is straight, but the fist’s velocity during maximum extension is zero.
Therefore, a punch that impacts during maximum extension is not a punch that hits hard.

Argument 4:

The practitioner does not wish to hurt oneself in the course of delivering a punch.
The elbow cannot turn more than 180 degrees (full extension)
At the instance maximum extension, if the upper arm is still being rotated by the muscles, and forearm is rotating downwards to keep the fist along a horizontal path, the elbow is moving upwards but not forwards not backward.
The elbow joint’s architecture forbids the elbow from travelling upwards because of the limitation of being only able to turn 180 degrees.
Any upward momentum of the limbs during full extension is dissipated via an impact within the elbow joint.
The elbow joint is not infinitely stiff.
Hence, there is an upper limit on the momentum that can be dissipated upon each impact to avoid damage.
Unfortunately, this upper limit is easily within reach of most people.
Thus to avoid injury, the practitioner must ensure that if the punch is not delivered to a target, the fist must be stopped before full extension by the action of muscle contraction instead of impact at the constraints of joints.

Argument 5:

The punch is designed to hit hard.
Therefore the fist is needs to move fast during impact.
The form is such that the previous step was a block/punch with the other arm extended, but this hand will be retracted to the side of the hip upon execution of the next punch.
Retraction of the returning arm will imply a net forward force acting on the upper body of the practitioner (a direct example of Newton’s statement that every action has a reaction).
This forward momentum can be directed towards the other hand that will execute the next punch.
Thus in addition to simultaneous extension of the fist, rotation of the upper body and forward leaning (as shown by argument 2), the previously extended hand should also be retracted at the same instance as the punching fist extends.

Proposition 6 (by Yuan Harng):

"Keep the greater parts of the body which do not contribute to the generation of momentum relatively loose. I found this to be of utmost importance in increasing the speed and strength of my movements."

The effect of this suggestion may not be obvious with the stepping foward stance punch, but it is very relavent for technically challenging moves. Do keep this bit of advice in mind when you are told you need to be 'less tense'.

This is not a complete guide but will hopefully help direct those in need of advice in the right direction.


End note:
Please do highlight any counter arguments, logical gaps or deviation from norm.





Mathematics