Tuesday, February 27, 2007

Stop Global Warming Now

By doing things on this list, and sharing this list:


Monday, February 26, 2007

Friday, February 23, 2007

What if...

An asteroid crashes Earth. It is possible. Should we be worrying? Should we be preparing? When I say 'we', I mean the entirety of the human race.

Everything we've done would be wasted.

Wednesday, February 21, 2007

A collection of science jokes: Part 1

There was once 3 scientists on the beach: a biologist, a chemist, and a physicist.

The biologist said: "I want to study the coral structure of the sea". So he went into the sea never to be seen again.
The physicist said: "i want to study the physics of the sea wave".' So he went into the sea and was carried away by the current never to be seen again
The chemist took out a pen and paper and wrote down: "Both biologist and physicist are soluble in water."


An pair of atoms are walking down a street. One says to the other "I think I've lost an electron!" "Are you sure?" said the other. "Im positive!"
Another atom finds the electron and says "I'll keep an Ion it for you"


An atom says to a shopkeeper, "How much are these neutrons?" He replies "Oh them, they're free of charge"


My names Bond. Ionic Bond. Taken, not shared.


There is this farmer who is having problems with his chickens. All of the sudden, they are all getting very sick and he doesn't know what is wrong with them. After trying all conventional means, he calls a biologist, a chemist, and a physicist to see if they can figure out what is wrong. So the biologist looks at the chickens, examines them a bit, and says he has no clue what could be wrong with them. Then the chemist takes some tests and makes some measurements, but he can't come to any conclusions either. So the physicist tries. He stands there and looks at the chickens for a long time without touching them or anything. Then all of the sudden he starts scribbling away in a notebook. Finally, after several gruesome calculations, he exclaims, "I've got it! But it only works for spherical chickens in a vacuum."


Q: What is the name of the molecule CH2O?
A: Seawater


To end with a historical note:

In the 1980's, in an effort to increase public awareness about the importance of chemistry, the American Chemical Society posted billboards with a picture of C6H10 and the title, "It takes alkynes to make a world."

Saturday, February 17, 2007

Happy CNY!

Happy Chinese New Year!

Wish you all a safe and healthy year!

Friday, February 16, 2007

Derivation of the most beautiful identity

I want to share this with you. The derivation of one of my favourite identites in mathematics so far:

Let f(x) = cos x = a + bx + cx^2 + dx^3 + ex^4 + fx^5 + ...

(don't mix up e in ex^4 with e = 2.7182821828...; in this case e is just any constant)


f(0) = cos 0 = 1 = a, thus a = 1

f'(x) = -sinx = b + 2cx + 3dx^2 + 4ex^3 + 5fx^4 + ...
f'(0) = -sin0 = 0 = b; thus b = 0

f''(x) = -cosx = (2*1)c + (3*2)d + (4*3)ex^2 + (5*4)fx^3 + ...
f''(0) = -cos0 = -1 = (2*1)c; thus c = -1/(2*1) = -1/2!

f'''(x) = sinx = (3*2*1)d + (4*3*2)ex + (5*4*3)fx^2 + ...
f'''(0) = sin0 = 0 = (3*2*1)d; thus d = 0

f''''(x) = cosx = (4*3*2*1)e + (5*4*3*2)fx + ...
f''''(0) = cos0 = 1 = (4*3*2*1)e; thus e = 1/4!


and so on.

Therefore substuting the constants into the original polynomial equation,

(i) cos x = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! + ...

You can check this by substitution a value in x, such as 1 (radians).

Similarly, you can work out an expansion for

(ii) sin x = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! + ...

(iii) e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! + ...

Now using expansion (iii), you can expand e^(ix), where i = √(-1)

(iv) e^(ix) = 1 + ix + (ix)^2/2! + (ix)^3/3! + (ix)^4/4! + (ix)^5/5! + ...

= 1 + ix - x^2/2! - i(x)^3/3! + x^4/4! + i(x)^5/5! + ...

Separating the imaginary parts and real parts,

e^(ix) = (1 - x^2/2! + x^4/4! - x^6/6! + ...) + i(x - x^3/3! + x^5/5! - x^7/7! + ...)

= cos x + isin x


so you get Euler's identity

e^(ix) = cos x + isin x

And a special case of it, is when x = π

e(iπ) = cosπ + isinπ = -1 + i(0) = -1

Rearrange, then you get

e^(iπ) + 1 = 0

an equation connecting the fundamental numbers i, π, e, 1, and 0 (zero), the fundamental operations +, ×, and exponentiation, the most important relation =, and nothing else.

Wow! Wow! Aren't you excited? (Nerd... if you actually read through all of the above and understood it.)

Gauss is reported to have commented that if this formula was not immediately obvious, the reader would never be a first-class mathematician.

It doesn't stop here though.

This opens a lot of branches in mathematics. One example is the hyperbolic function, which links circular and exponential functions - something you usually think as very separate branches of mathematics.

Friday, February 09, 2007

Fried rice kung fu!


If only I could produce that fried rice everyday, I could save money at university (+ avoid eating crappy food). I could also sell my fried rice. I could take over the university canteen. Hahaha

I better start cooking now! Hai ya! Hai ya! Hai ya!

Video from averagebetty.

Get the fried rice recipe from the fried rice demon.

Thursday, February 08, 2007


Can you see that 1^3 + 2^3 + 3^3 + .... + n^3 = (1 + 2 + 3 + ... + n)^2?

Tuesday, February 06, 2007

Tutoring - Day #1 and #2

Well it was (Feb 6, 2007) officially my first day of tutoring, i.e. I get paid for it. My tutoree/student is my neighbour, and it is going to be on a daily-one hour basis.

And, well so far it was crap. Better than expected. Actually you know what - maybe for a nine year old, it's quite good. He's polite but extremely hyperactive - so it seems that more than half of what I say to him goes out the other ear. What I mean by hyperactive: throwing basketballs, blowing air with his basketball pump, playing with his sportsband - you love basketball - I get it!

Right now, I am teaching him English, Maths and General studies. Wow! I must say kids these days learn a lot of things! Too much too soon, in fact. For example, in general studies, he already learns about annular solar eclipses and refraction of light! And in maths - manipulation (addition/multiplication all of that) of decimals and fractions? That's what we did in secondary school - not in primary?!

My rule of thumb: Less is MORE.

So yeah, he's not doing very well - and I can understand why. Duh? How can he absorb all that information. There must be something wrong with the syllabus. And the teaching at school too. He says (let's call him David from now on) that he must follow exactly what the textbook (word for word) says or else the teacher will mark him wrong. What kind of learning is that? Copy and paste? Okay, you might be smarter than most people your age (compared to say, the ones in international school - he goes to a local school) in terms of lots of knowledge - but as soon as I change the wording of a question (from the textbook) he would be like "Huh? I don't know! It's not even in the textbook!" And by the way, I am not blaming the students - I am blaming the teachers and education board in general.

Maybe I am expecting too much. But maybe I'm not. Education nowadays is getting worse, and creativity and thinking-out-of-the-box are deminishing. A lot.

No wonder why most children nowadays don't want to go to school.

Well, I guess this is where I come in. We'll see how things go.

Saturday, February 03, 2007

Uneventful day?

Today was supposed to an uneventful day. Nothing to do, nobody at home - brother's playing tennis then birthday party afterwards, my dad is also playing tennis with his friends, my mother's playing mahjong in her friend's house. Also, they will not be coming back home for dinner. So today was supposed to be all by myself. And that's supposed to be a good thing.

And I was planning to stay at home. Watching TV, taking a very very long bubble bath, whatever.

But then my neighbour, whose son I tutor, called me to go to her place to help her son with some homework. So I left home, sigh, but I thought to myself this should be quick. And sure it was quick.

Joyfully, I went back home. And then crap! I forgot to bring the keys! And usually there was somebody at home! But NOBODY this time! CRAP! I was at that moment the unluckiest person on earth! This unlocking-myself-out-of home-accidentally actually happened a few times. But come on - a weekend. For the whole day?!?

And.... well nothing good after that.

I walked around to pass time...

and froze to death.