David Berlinski's A Tour of the Calculus

I have in my care a brilliant book by a certain David Berlinski, “A Tour of the Calculus”. The San Francisco Chronicle enthusiastically described the author as follows:

“He is both a poet and genius. And he’s funny [...]. The writing is clean and powerful […]. Go Berlinski, go.”

The New York Times’ comment was slightly less cheerful and bubbly, but nonetheless full of praise.

“Playful, witty, highly literate […] a wonderful and enlightening book”



Here are a few of interesting quotes from the book:

But where before there was nothing more than an emptiness answering to the square root of 2, a new number now appears, a Dark Prince, an object utterly unlike any rational number, one flushed from the shadows and full of brooding mystery.

Although his talent was evident from an early age, Dedekind passed his professional life as an instructor at a technical high school in Brunswick, the place of his birth. Nineteenth-century German Hochschule were rather more demanding institutions than contemporary American high schools […]. Still, high schools are all the same, superficial variants of some central high school which is located in Hell.

Now sever the rational numbers into two classes A and B, such that every number in A, when squared, is less than 2 and every number in B, when squared, greater. On one side are the numbers in A, like firecrackers popping off when squared; no matter how they pop these numbers never pop past 2. On the other side are the numbers in B, like firecrackers popping off when squared; no matter how they pop these numbers always pop past 2.

Mathematics

Asparagus, Lemon and Tomato

Asparagus, Lemon and Tomato

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Click here for Deviant Art entry






Photography

The contents of my wallet at this moment

The first notes section:
One A$50 note

The second notes section:
Three RM10 notes
One RM5 note
One RM1 note
A piece of paper with frequently called numbers listed on it

I only started using a mobile phone when my cousin upgraded her phone and had a spare one lying about that I could use. That was in early 2003. Prior to that, I recorded the most frequently called numbers on a slip of paper I kept in my wallet. The secret to its longevity is that it is only half the size of a currency note, thus it is never folded. It is still in my wallet, a not very useful fragment from the past.

The coins pocket:
Four A$1 coins
Two A$0.10 coins
One A$0.20 coin
One A$0.05 coin





The various card slots:
Malaysian Driving Licence, valid till 31 March 2008.
National Registration Identity Card, needs to be updated to the electronic one ASAP.
A prepaid debit card for photocopying.
A membership card for the mandatory international student health insurance.

I haven’t used this one in ages. The problem with health insurance is that if you are healthy and well, you feel cheated of the $350+ annual fee.

Emergency Contact Card

"If the international student carrying this card requires emergency or crisis assistance, please contact:
The International Centre,
The University of Melbourne[…]"

The powers of this card have never been invoked. I wonder what it does.

The University of Melbourne student card
Two ATM cards for my bank accounts
A magnetic card for access into my apartment block
City Library membership card

Another compartment:

A little 符, folded neatly and wrapped in a tight plastic wrapper.It’s not so much if it works (or not), but it’s the fact that my grandmother took the trouble to get one for me.

Personal

This is disturbing.

link
link
link

Finding the value of e

Euler’s number, e, is special in many ways. The exponential function of e is particularly fascinating in that the slope of the function at any point is equal to the function value at the point.




Since this is an exponential function, it should be reasonably easy to see that
f (0) = 1
f (1) = e

But what is the value of e?


Assuming the truth of the Taylor Series expansion of a function:



If we were to substitute the exponential function into the Taylor series, and let x = 0 and Δ = 1, then:



And there it is! The value of e is the sum of all the inverses of factorials. Expanding the summation:






Mathematics

Lost in Space-Time

Lost in Space-Time

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Click here for Deviant Art entry




Photography

The end is near

It is a little surreal. Not because the world has been a bit surreal lately, but mostly because I don’t feel it’s very surreal.

This is the last week of lectures for the semester. Baring any accidents, disasters and catastrophes, this will be the final week of lectures that I will ever undertake in the university.

I was made aware of this 2 Thursdays ago when a lecturer wrapped up his lessons with something along the lines of “it was nice lecturing you guys over the past 2.5 years. Do say hi to me if you see me along the street.” Being so wrapped up in my daily routine, I barely noticed the passing of time until it was bluntly brought to my attention.

“Wh… what?” I babble like a man whose mistress had just told him, “I’m pregnant.”
“I said I’m pregnant.”
“But… how…when…how… how… birth control pills…” I continued to blabber senselessly, at the same time not making any sense of the world around me.
“I forgot them after the time we met in the Buckingham Palace,” she smiled lovingly at the memory. “Do you remember when the guards in their silly red uniforms chased us after…”
“Shut up. This is not funny!”
“Oh, I’ve always wanted a baby. We can raise him in a happy family- you and me with the child, in a little house in the outskirts of town…”
“Wh… What?! Aren’t you getting an abortion? And what about my wife and children?”


Returning back to reality, I’ve got only two more days of lessons. Yes, Friday is my day off ever since we finished the major project and the Computational Mechanics lecturer completed the course with his “say hi if you see me along the street.”

But it’s not ending that soon. I’ve still got my examinations to go through, scheduled on the 15, 16 and 25 of November. Then I’ll be hanging around till I graduate on the 17th December. Then I’ll be flying home with my family on the 25th December, on the 12.45am flight out of Melbourne to Kuala Lumpur.



The future is ahead. I can see it. But I cannot see inside of it.






Personal

New layout

25th October:
The original contents of this post is now void. I've reverted back to the standard decaying-strawberry hue of pink.


To be honest, it's not really new seeing that its a standard Blogger template but with a few modifications. I'm not very satisfied with it. In particular, the boundary between the main column and the sidebar is not present. As such, the jagged right edge of the text block forms the boundary, making for a rather messy appearence.

I also fiddled with the image borders. I think it's for the worse. Bleah.

In all honesty, the usual pink layout will probably return with no changes. I basically did this because my fingers were itchy.




Personal

Oral ulcers are no fun

Imagine a crater-like hole on within your oral cavity. There is no mucus membrane there, and the crater surface is a sickening yellow colour, a bit like the colour of decaying pus, only darker.

Unlike the smooth unbroken surface of good mucus membrane, the inside of an ulcer appears porous and soft, probably more vulnerable than the underbelly of a rhino beetle.

Ulcers are no fun.


I am currently suffering from oral ulcers on my lip. There are two of them in close proximity of each other. One is a big bastard of 7mm diameter; the other is a smaller but by most standards still a biggish bastard of 4mm diameter. They look like a binary star system.

7mm!


Personal

I made it into the Master List of Stupid Things (again) !

Somewhere out there beyond our sensory apparatuses exists a Master List of Stupid Things. It would be pretentious to say “there lies a Master List” since we do not even know if this list is of a longish shape that can be oriented horizontally. Or for that matter, define horizontal.

Somewhere out there, beyond the scope of our ears, noses, orbiting telescopes, very large radio telescope arrays, spiritual mediums, astrologers, crystal-orb gazers, intuition, and gut feeling, exists this Master List.

Rumour mongers and chain letters, but surprisingly not including chain email, claim that Section 1 of this Master List deals with “accidental death by negligence”. An entire subsection 1c is dedicated to “ ‘Don’t worry, it’s not loaded’ and similar misjudgements”. The origins of these claims are entirely unknown, since this Master List is beyond human perception and thus nothing about it can ever be known. Theorists and speculators are of the opinion that these claims are the product of the rumour mongers’ deranged imagination. Conspiracy theorists, on the other hand, categorically state that the opinions of these theorists and speculators are part of a government cover up story concerning the mind reading probes that can also detect and read the Master List. Which government, though, is subject to argument as some say the United States, the ex-Soviet Union, or even Omicron Persei VIII*.

Nonetheless, the Master List of Stupid Things exists. That much is certain.


***
Today, I have caused yet another instance of my name to be added to this Master List. This is my story.

I was walking home in the rain. As usual, without an umbrella.

As I walked past an ice-cream parlour, I realised two things:

I haven’t had a gelato in ages (about 2 months, to be approximately precise)
I was hungry

And so I got my three scoops of wonderful gelato (rum & raisin, almond, choc & orange) on a cone.

Like racing tyres, ice-cream behaves differently in wet weather. Rain drops hitting the ice cream form a layer of water on the surface of the ice cream, dissolving a little of the ice cream, and causing little rivulets of liquid that while not exactly a waterfall, are extremely difficult to control by tongue.

I ended up having ice-cream solution plastered over my fingers in a sticky mess.

Ice-cream should be enjoyable. Definitely not frustrating, annoying and exasperating.


***
Thus in summary,

Do not eat ice cream in the rain, even if it looks like it’s “only a drizzle”.
Yet another entry in the Master List of Stupid Things is in my honour.

* Persei pronounced per-see-I:

per as in “RM45++ per person”;
see as in “Can't you see that I am busy?’
I as in “I am Lrrr, ruler of Omicron Persei VIII.”

Personal

From the disturbing diaries of Yee Wei

From the disturbing diaries of Yee Wei

Where am I?
How did I end up in a room without a door or window on all four walls?

Four walls?

I looked again, and found that I was in a triangular room. But there was something amiss about this room. It certainly did look like a rectangular room. It still does look like a rectangular room. But it has only three walls.

I made my way towards the middle of the room, circumnavigating a few beat-up articles of furniture along the way. I turned around a few times, meticulously counting the number of walls and observing the corners. Indeed there were only flat three walls, and each of the three corners where the walls met were all perpendicular, yet the room was closed in a square shape!

Too disturbed by this apparent failure of geometry, I sat at one of the chairs and rested my head on the table.

The table!
The tabletop was a triangle, but all three corners were right angle corners. And the sides remain perfectly straight.

What sort of perverted, non-Euclidean universe have I gotten myself into? More importantly, how did I get into such a situation anyway? I bet the inhabitants of this twisted universe are all devil worshippers and communists.

I found a pen in my breast pocket. It was the beautiful Parker ballpoint that Grand Uncle gave me for my birthday. For lack of anything better to do, since continuing to puzzle about the 3-sided rectangles was not really getting me anywhere, I doodled on the table.

I got bored of framing the table with spirals and heart shapes, and moved to squares. I stared with a long straight line. At one end of this line, I drew a second line perpendicular to the first. Then, at the end of the second line, I drew another line perpendicular to the second line. Just as I was about to prepare for the fourth line, I noticed that the square was already complete and closed, with three lines and three corners!

I was so freaked out I dropped the pen.





Narrations

PMS-ish rant about F1 coverage in Australia

Sometimes, female bloggers cite PMS and rant rant rant about nothing and everything.

No, I don’t have bloody PMS (pardon the pun).



The Formula One season ended on Sunday in Shanghai. The TV coverage on Australia’s Channel Ten was shit. They take usually their TV feed from ITV in UK which provides excellent commentary, but on Sunday decides to mute out ITV’s commentary and use their own talking heads. What the fuck are you thinking Channel Ten? Lost your rational capacity? I'm not surprised.

[A silver McLaren rumbles along the pit lane, and dives into the swarm of waiting mechanics. A text label on the screen says ‘Montoya’.]

“That’s Montoya into the pits”

[duh… like I’m fucking blind or illiterate]
[a white car enters the pit lane]

“And that looks like Kimi Raikonnen pitting as well”

[Stupid! Who the hell calls two cars into the pit lane simultaneous under normal racing conditions? And that’s a white BAR Honda, not a silver McLaren.]
[Tell us about fuel strategies, and compare the fuel strategies of Alonso, Raikkonen and Fisichella. Oh wait, I think I’m asking too much of you.]


They also made a lot of mistakes in identifying drivers. If you can’t tell one helmet from another helmet then you should damn well shut up instead of acting like you know a lot by saying “And there’s Trulli in the Toyota” when the camera is in fact pointed at Ralf Schumacher.

Did I mention that they knew nothing about the sport? They pass time by orally informing us of what’s happening when we can already see it on screen.

So, in conclusion, Channel Ten should just ask Neil and whatever the other lardy arse’s name is to shut up and use the ITV feed. The commentary feed too, idiots! It makes the viewers very much less miserable, and it probably makes Niel and friend feel better too. It was so bad that I turned the TV off and went back to work instead of watching your advertisements. And another matter, too many ads!

And don’t pretend you didn’t buy ITV audio feed. You cut to Louise Goodman’s interviews with Michael Schumacher and Narain Karthikeyan after their races ended prematurely.

Dramatic silence explained

Early this morning at about 3.30am, I had a supper of two slices of toast. Curious about the ambient temperature, I heaved open one of the windows for a whiff of outdoor nocturnal breeze.

As soon as the glass panes parted company, the silence from outside floored indoors like a surging wave of thick, transparent, lumpy, luminiferous porridge. Like pouring cheesecake mix into an intricately shaped mould, the curdled syrup of silence rapidly filled the large open spaces in my apartment before slowly seeping into the tapering nooks and narrow crannies. It was awe inspiring.

It was also shocking, to say the least. It would not be surprising if noise crept in from an open window, but to see the same effect with silence is an eye opener. After all, silence is just no-noise, not anti-noise or noise-inverse or negative-noise.


Here are some conjectures and fantasies designed to help explain the phenomenon of the surging syrup of silence.


Dramatic silence occurs when quiet noises can be heard. The situation does not need to be absolutely devoid of noise to qualify as dramatic silence. For example, late at night in Melbourne, the streets are devoid of traffic. Sometimes I can hear a motor vehicle, but it’s usually far away. Other times, rebellious birds make themselves known by chirping recklessly at 4am. It is these muted sounds that elevate silence to dramatic silence. In the afternoon, these sounds would certainly be drowned out by constant drone of traffic and aged trams rattling on their rails.

The phrase “so quiet you can hear a pin drop” is often used to describe silence. However, if a pin actually dropped and you do hear it go “plink”, the silence would be even more dramatic.

In a room, silence is usually exaggerated by a clock’s ticking, or another person’s breathing. If you were alone, and there was no clock, it would simply be a quiet but boring room.

Going back to the phenomenon of the surging syrup of silence, I can only conclude that the apartment was in a boring state of silence with only the annoying whine of computer fans as company. Opening the window let in the sounds of far away motor vehicles, highlighting that there were no other noises that usually masks these sounds.


Applications of the phenomenon of the surging syrup of silence

The most obvious manner to take advantage of dramatic silence is to manufacture dramatic silence. If you could make loud noises that sound like they are far away, or amplify sounds that are naturally soft, you can possibly make the area sound like it is quiet.

The simplest application of this manufactured silence is in the sale of enclosed spaces. If quiet is a good selling point (usually valid for luxury cars and residential property), then it might pay to install clocks with exceptionally loud ticking to trick the potential buyer. The salesperson could go something like, “Ooo…do you hear that? This car/place is so quiet you can actually hear the clock/my watch tick!”

And since clocks generally tick ahead with minimal noise, the unaware buyer might be in for a royal screw.





Personal

Applied science

Geometric proof of Pythagoras’ Theorem

Squaring the triangle

[The illustrations' colours are a bit messed up in the BMP to JPG file conversion. Just squint and hope you can discern the black from the blue. If you can't, it is no problem anyway.]

The ancient Greeks did it with whatever tools they had. I’m repeating it with AutoCAD 2006 as an illustration aid.

Pythagoras’ Theorem states that for any right-angle triangle with side lengths a, b and c, such that c is the length of the hypogenous,

a^2 + b^2 = c^2

Start with a right-angle triangle, with the hypogenous (the longest line) coloured red as illustrated in Figure 1.


Figure 1


Attach squares to each side of the triangle (Figure 2). If Pythagoras was right, the area of the red square is equal to the sum of the area of the black and blue squares.


Figure 2


All subsequent operations will be purely shifting, dividing and rotating (by 90 degrees) areas.

Shift the red square upwards as shown in Figure 3.


Figure 3


The black triangle protruding out from the left of the red square is equivalent to the original right-angle triangle since all lengths are the same (squares have sides of equal length). This triangle can then be rotated into the space where the original triangle is located, as performed in Figure 4.


Figure 4


The blue square is shifted upwards to upper black triangle, Figure 5.


Figure 5


The blue and black triangle above the red square can then be rotated to fit into the empty area in the left portion of the red square (Figure 6).


Figure 6


The areas are shown to be equivalent, and Pythagoras is correct in his theorem (Figure 7).


Figure 7




Mathematics

Fifth Gear is back!

Fifth Gear is back on Channel 5 BBC! They have started with the new season, the first episod aired on 10 October. Now I’m eagerly awaiting 17th October for my next fix.

With fantastic cars, inspiring commentary, generally impartial reviews, stimulating content and wonderful camera work, Fifth Gear comes highly recommended. And there’s Vicky Butler-Henderson too.

If you are in the UK, tune in to 5 on Mondays 8pm, or Tuesday midnight for a repeat screening. For those of us poor sods outside of BBC’s benelovent reach, there is always the option of downloading the episods via Bit Torrent. Here’s the 10/10/05 episod.






Vicki Butler-Henderson...

Click here for large size image






...in a Noble M400

Click here for large size image



I thought getting an image of VBH (as she is sometimes referred to) from the web might be a bit tricky. I was wrong. The first site from Google's search was “A Vicki Butler-Henderson appreciation site” with loads* of pictures. How surprisingly convenient.



* loads = much, much more than absolutely nessecary

The Autobiography of a Pencil

This is a Chinese language post designed to help me rediscover some lost linguistic skills.
English translation below.




上次提起了几个作文题目，有人要铅笔的自诉刚，也有一个朋友要上巴刹记与倒霉的一天。从三个选一个不容易，所以打算了把两个作文题目合起来。那么就把“三选一”的问题硕成了“三选二”。请别跟我说“三选一”和“三丢一”是一样的。

两个作文题目“倒霉的一天”和“铅笔的自诉”就合成“铅笔倒霉的一天”。

铅笔倒霉的一天

陈一维

我是一枝铅笔，性 Staedtler，无名。2B 级，长6.9寸，外色鲜黄涂黑斑，再加上金色的文字看起来十分健美。好可惜饮用者不只靠美观购买用具，否则用具商业就被我们Staedtler 一家完全控制。

如果饮用者把铅笔的纸盒观察一下，最引人注意的就是印上的六种语文。六语有包英文，法文，德文以及其他无名的欧洲语文。详细地观察下去，在一个小小的角落可找到四行马来文字：

12 Batang Pensel
Staedtler (M) BHD
6/6A Jalan Kilang
80350 Johore Baru

不知是开玩笑，看小亚洲，或是注重出口，但虽然是大马产品可是并没有马来文及华文。

我和同盒友的主人是个工程师名叫丽俐。她只用铅笔，不摸钢笔，所以时常购买一盒一盒的铅笔。主人的男朋友是个画家，也是个常用铅笔的人。男友呢，他用的笔跟我这种不同。他的画笔都是5B或6B级，十分的软，画出来的线黑得很，价钱也不便宜。

一天，丽俐有必要用枝笔，就损手夺了男友的一枝6B。男朋友不耐烦地说：“别用我的画笔。写了字不好画。”这一件事就很快地爆炸成大喊大叫的架。

吵了不久的架便有碗碟花瓶茶杯左丢右破。不只骂铅笔的架，还吵起过去了的事。

“你时常小便不冲水！”
“我妈的生日你连一张卡都没送！”
“你很懒，常要我用车子载上载下！”
“你用我的画笔！”
“只写下个电话号码！”

不知如何，吵架变成了打仗。丽俐从桌上抓了一枝笔（我），便把我当武器要插她的男朋友。插了几插成功了，插穿了他的肚。我感到很多层的东西。插过了外衣，皮肤，薄薄的一层肥，才终于穿入了胃胀。

这时候，我半身在男友的胃里，另一半还被丽俐的手抓着。丽俐很猖狂的，葱满狠毒，把我一手就折断，把我前半身留在男朋友的肚里。

血和早餐不停地流到地面上。







From my essay topics presented in the previous post, there were a few recommendations. Adrian suggested the Autobiography of a Pencil (he thought a pencil can be sexy) while Sonia wanted either Market Trip or a Dreadful Day. Choosing one from the three was not going to be easy, so I choose two instead. Now please do not point out that choosing one from three is equivalent to rejecting one from three.

The fusion essay would be A Pencil’s Dreadful Day.

A Pencil’s Dreadful Day

Tan Yee Wei

I am a pencil, surnamed Staedtler and nameless. Graded 2B, 6.9 inches long, finished in bright yellow paint and black stripes, and printed with gold lettering, I look robustly good. It’s a pity consumers do not buy stationery based on looks alone, otherwise the stationery business would be completely dominated by the Staedtler company.

If the consumer were to scrutinise a box of pencils, the first thing one would notice is that there are six languages printed on it. They include English, French, German and some other unnamed European languages. On further inspection, one can find 4 lines of Malay hidden away at a little corner:

12 Batang Pensel
Staedtler (M) BHD
6/6A Jalan Kilang
80350 Johore Baru

Either they must be joking, underestimating Asia, or concentrating on the export market, but it is a little strange to find a Malaysia manufactured product without Malay, nor Chinese.

Me and my boxmates were purchased by Lilly, an engineer. She prefers pencils to pens, and rarely ever uses pens, but buys boxes and of boxes of pencils. Her boyfriend was an artist, another great consumer of pencils. His pencils though, were different. They were either 5B or 6B grade, with soft tips, dark marks and an expensive price tag.

One day, Lilly needed to jot down some details, and grabbed one of her boyfriend’s 6B pencils. “Don’t use my drawing pencils; they are not good to sketch after you write with them,” he snapped at her impatiently. This matter rapidly exploded into a major argument.

A short moment of arguing later, dishes, vases and glasses were being flung around. Not only were pencils were involved, but they also fought over past issues.

“You never flush after using the toilet!”
“You didn’t even send my mother a card for her birthday!”
“You’re lazy, always asking to be brought here and there in my car!”
“You used my pencil!”
“Only to take down a telephone number!”
And so on…

Somehow, things turned violent. Lilly grabbed a pencil (me) from the table, and tried using it as a stabbing weapon against her boyfriend. She made several stabbing attempts before succeeding in piercing his abdomen. I felt myself piercing through several layers. There was the shirt, then the epidermis, a thin layer of fat, and then into the stomach itself.

At this moment, half of myself was in the boyfriend’s stomach, and the other half in Lilly’s grasp. Savagely, with poisonous hatred, she snapped me in half and left my front half in the boyfriend’s abdomen.

Blood and breakfast endlessly poured out onto the floor surface.








Personal

(s)he was buried in sand

I'll be busy for a while. In the mean time, do enjoy the following photograph of a few of my friends.





Two Boobies and a Penis

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Pulau Perhentian, July 2004.



As you can see, the penis was very well detailed. Maybe not anatomically accurate, but nonetheless it manages to shout "I am a KKC!" at the viewer.




Photography
Personal

How I started writing; how I am restarting.

After a particularly memorable trip to Redang, I started writing in August 2002. This was spurred by an accepting (niche) market of about 6 to 10 people. I was writing for an audience, but mostly for pleasure. It was all very hedonistic.

I learned plenty. Not enough to earn a living by crafting sentences, but enough to be happy with. What a good lot of change has occurred in three years.

***

Now I’m going to try something similar with Chinese. Every once in a while I’m going produce an essay, narrative, monologue, or whatever. I’ll probably start with primary and secondary school essay topics, maybe written with a slightly more mature flavour. We’ll see. And from the Chinese essay, a simple English translation will be generated.

Boring topics which I hope to spice up with needless violence, sexy mature themes and maybe a chase scene or two. Who knows…

***

What should I start with? Or rather, what would you want to see? Other suggestions?

上巴刹记 – Market Trip
描写文- 雨天 – Descriptive essay: Rainy Day
铅笔的自诉 – Autobiography of a Pencil
倒霉的一天 – A Dreadful Day
我的狗 – My Pet Dog




Personal

Children doing their thing- a series of portraits

Subjects are cousins and siblings.








In a New House

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An aunt moved house recently. Many relatives went to 'help', although it was more like lunch while watching the hired professional movers do their thing.
January 2005.








Little Black Eyes

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She's a cheerful little girl.
February 2005.








The Green Photographer

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Batu Ferringhi, Penang.
December 2003.








Guardian of the Palace Gates

Sierramas West clubhouse.
January 2005








Take That!

An evil monster in disguise.
January 2005.

Photography

Personal

Another tag

I must have annoyed Pamela by tagging her the last time. She counter attacked!


Ten years ago I was
12 years old.

Five years ago I was
In a school I did not really feel comfortable in. I was glad to be out of that place. However, I cannot deny that there are were some very good teachers.

One year ago I was
Not doing a lot of productive things.

Yesterday I was
Extremely cross at myself for forgetting to bring my keys out with me. Upon returning to find that I was locked out, I had to take a walk back to the university to get Adrian’s keys from him, then trudge back home to let myself in. I had actually intended to drop my things home and walk over to Safeway to get some ice cream, but the lack of keys screwed the plan up. Stupid me keys.

Good thing I got the ice cream this morning on my way back from the library.

5 snacks I enjoy:
Coffee, preferably with a bit of Bailey’s Irish Cream
Ice cream
Chocolates
More coffee
Coffee beans coated with dark chocolate

5 songs I know all the words to:
Happy Birthday
Negaraku

If there are n words in the song, and I know m words of the song, then I know all the words in the song if and only if n=m.

This being the case, I know the all the words to these songs, since n = m = 0

The Moment, Kenny G
Riverdance
Exodus, Maksim Mrvica
Matsuri, Kitaro

:p



5 things I would do with 100 million dollars:
Count them to make sure its 100,000,000 dollars as opposed to 99,999,999 or 100,000,001 dollars.
Then change them all into coins.
Really, I don’t know what to do with 10^8 dollars. Yet.

5 bad habits:
Procrastination
Procrastination
Procrastination
Procrastination
Procrastination

5 biggest joys:
My family and friends
Managing to snap a decent photograph
Reading
Writing something I am happy with
Driving a ‘difficult’ manual vehicle smoothly

5 places I would runaway to:
Rowden White library
Architecture library – lots of large windows for wonderful natural light
Murni SS2
Blogs

5 things I would never wear:
High heeled espradrilles and platform shoes
Leather briefs
Stockings
G string
Cancer sticks/ cigarettes

Notice I did not mention lacy lingerie?

5 favourite TV shows:
Telecasts of the Formula 1 Grand Prix races


5 fictional characters I would date:
Mini Me, clone of Dr. Evil in the film “Austin Powers”
Trinity, “Matrix Trilogy”
The Architect, “Matrix Trilogy”
月飞 (‘Moon’- what a horrid English translation. Can’t she be Yuet Fei or something?), “Hero”
Pinocchio from “Shrek 2”- he wears women’s underwear!

People I’m tagging:
None. It’s a long task.



Note[added 9 October 05]:
More rubbish in the comments.


Personal

今日看到弟弟的网上日志以華文表達，感得十分的可惜。可惜我浪費了學好華文的機會。不是一个機會，不是兩个機會，而是數千數萬個好機會。

六年在華小求學並學得不很多。課本里得字，有很多读都读不出，別說要我把它写出來。我平時读英報，中文報不摸。六年級同考，成績英文數學兩個Ａ，國語（馬來文）兩個Ｂ，而母語包尾考得兩個Ｃ。失望得很。

四至六年級的華文与級任老師是陳美珠。我還記得她最明顯的語病是：“我听沒有。”有時要粗口的例子，她會說起：“你媽的他媽的。”以前不明，所以把她的例子当耳边風。

初中二、三的兩年，我的華文教師是個陳美麗老師。雖然上課多次看起來都很輕鬆很爽，但陳老師並沒忘了教书的責任。記得中三接近大考的那段時間，我們全班被老師大骂一頓因為有几位學生沒有专心溫习听写。沒記錯的話，我和渊沆就是這几條懶惰虫。少見中學的老師因為學业而生氣。副班長可能還記得這件事。

本人就停在這兒。下次再談吧。




大家請多多批評我的語文之長短处。謝謝。




Personal

Time Machine

Time Machine

Click here for large size image
Click here for Deviant Art entry






Photography

Word verification is now on

That’s it. I’m retiring from this mess.

In the past, I tolerated the odd spam comment or two. It was too much work to have to do the word verification thingy every time someone wanted to make a remark.

It was also a bit of fun coining insults to throw at those spam automatons.

However, they seem to be rather prevalent of late. As such, word verification will be turned on.


Sample insults I’ve come up with:

Illegitimate half-bred child of a hairless goat... go sodomise yourself with a fork.

I have a FREE tip for you. Train your pet iguana to sew with blunt, rusty needles and coarse nylon thread. Then, request that the cold blooded creature sews up your anus. Subsequently, recruit a horse to forcibly rip it open with its huge horse dick. Repeat.

You wank using 2 fingers.


[Edit 6.17pm 4th October 05]

The party responsible for all my recent problems has the following details:

Country: Canada
City : Ruchmond Hill, Ontario
Organisation : Rogers cable inc. mtnk
IP address : 69.196.38.11
Visit length : 00:00:15
Referrer URL : bookmark
Species : hairless androgynous goat

The number of elementary operations to calculate the determinant of a real, k-by-k matrix

The pleasure of (self) discovery is great.

This post is a hedonistic repetition of something I played with on Thursday night. There are no jokes in today’s entry.

Contents:

Introduction- the matrix determinant
Counting the number of elementary operations needed to find the determinant
Expressing the number of elementary operations as a non-recursive function
Proof by induction that the two expressions are equivalent
Cite this article
End note

Introduction- the matrix determinant

The determinant of a matrix A can be expressed as the following:



Where Cij is the cofactor of aij, and Mij is the minor of A formed by removing row i and column j.

The number of elementary operations required to calculate the determinant of a k-by-k matrix will be denoted by f(k).


Counting the number of elementary operations needed to find the determinant
As the definition shows, |A| is a sum of k terms. Each term consists of a multiplication of an element with its cofactor. To count the operations required: summing k terms would require (k-1) addition operations; there are k multiplication steps, and there are k different cofactors to determine. Each cofactor is the determinant of a (k-1) by (k-1) matrix. Note that the step (-1)^(i+j) in the cofactor has been neglected because it is a computationally simple operation of sign flipping.

Thus f(k) = (k-1) + k + k*f(k-1)
f(k) = k[2+f(k-1)] -1.

The trivial case for this recursive equation starts at f(1)=0. Knowing this, all other values of f(k) can be determined by recursion.




Expressing the number of elementary operations as a non-recursive function

Calculating f(k) algebraically for several cases of k, it appears to take the following non-recursive form:



Proof by induction that the two expressions are equivalent

To show that g(k) is an alternative representation of f(k), g(k) = f(k) will be proven by induction. The first case g(1) = f(1) will be proven. Then, assuming that g(k)=f(k) is true, g(k+1) = f(k+1) will be proven. By showing that g(1)=f(1), the second argument can be applied to show that since g(1) = f(1), then g(2) = f(2). Applying the second argument again, it can be shown that since g(2) = f(2), then g(3) = f(3)…

First, show that g(1) = f(1).


*Note that 0! is defined to be 1.

Now prove that if g(k)=f(k), then g(k+1)=f(k+1).



*Pay attention to the factorial signs. They are sometimes not quite visible.


Thus the number of elementary operations required to calculate the determinant of a k-by-k matrix is shown to be



Cite this article

Tan Yee Wei(2005), "The number of elementary operations to calculate the determinant of a real, k-by-k matrix", from "Snippets of This and That"
http://tanyeewei.blogspot.com/2005/10/number-of-elementary-operations-to.html


End note:

A mathematician, a physicist, and an engineer were trying to show that all odd numbers greater than 1 are prime numbers. The mathematician says, “3 is a prime, 5 is a prime, 7 is a prime. By mathematical induction, it follows that all odd numbers greater than 1 are prime.”
The physicist gives his explanation, “3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime.”
The engineer then says, “3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime, 13 is a prime, 15 is a prime.”





Mathematics

The connection between Mathematics and Street Fighter

Yesterday, I acquired what looked like an interesting book, “Foundations of Real and Abstract Analysis”.

The first few pages of chapter 1 were perfectly fine. Fields, unary and binary operators, limits, sets...

Ah makes sense.
Yes, yes. Brilliant expression.
That’s new; I didn’t know that.

Then Section 2 of Chapter 1 came up with a mass of utterly unfamiliar material. Crap. Good thing mathworld.com has a search engine.

The sensation is somewhat like playing a perverse game of Street Fighter.

You seem to be doing rather ok, doing damage faster than you are receiving it. The round appears to be in the bag. The life bars at the top of the screen seem to indicate that you have the advantage.

Then opponent pulls something unethical out of the bag. Equivalent to 3 Cold War era hydrogen fusion bombs, he executes the ultimate move when you least suspect it; the opponent’s Ken goes into an autopilot sequence. A mass of kicks to the head and knee levels are flung out, and finished off with a jumping helicopter kick. The end result: a massive 11-hit combo, and a dead self.

Turns out you have neglected to check the power meters at the bottom of the screen.

Turns out I did not see that the book was from a series “Graduate Texts in Mathematics”, the difficulty being marked by ‘graduate’. Yes, it was right there at the top of the front cover printed in large, friendly letters.

Enough blogging; back to my essay preparation. There’s a Human Resources Management essay due on Monday morning at 9.00am, length of 2500 words, worth 25%. I have yet to make any substantial advances.

On a more positive note, it’s perfectly doable. Pamela is living proof:

I can do my assignments (and NOT fail them) in one nite.. hahahahaz.. This is not something to be proud of but I know many ppl who will die of stress and high blood pressure if they attempt to squeeze out 3500 words in one nite..

End note:
Adrian recently got hold of an emulator that had Street Fighter Alpha 3 in it. I keep getting trashed, by Ken.


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Mathematics