I've always loved CNYs. There's just a certain sort of atmosphere that I've loved since young. On CNY's eve, my family went to pay respects to my paternal grandparents. Even though I'm Christian, my parents are buddhist/taoist, and so were my grandparents. And so my mother brought along some vegetarian offerings, and burnables, which mostly include hell notes. When I took a closer look at the thick wad of hell notes, I realised that on each was printed $1000000 (God knows how many zeroes there really were), and this led me to think,"Damn, hell money has got to be worth really little with so many zeros on a single note. That's worse than the rupiah...." And the interesting thing is that, people are burning hell notes all the time, meaning more money is being added into the economy. 

Now I learnt in economics, M . V = P . Y, where M is the amount of money in the economy, V is the rate at which money changes hands (or how fast money is spent), P stands for the general price level and Y stands for aggregate output produced.  Since V and Y are independent of the other variables and are held constants, this means that M is proportional to P. So, if everyone keeps burning hell notes and increases the amount of money in hell's economy, this means P will rise as well, making inflation worse. I wonder what a buddhist/taoist economist would have to say about this practice. I think they would ask their relatives to burn like, paper silver or gold, or paper houses and cars instead of paper money. Maybe the property market is good down under... 

On a different note, I've gained temporary membership in Sargeant Pepper's Lonely Hearts Club Band. Fiona has left on exchange and I won't have her by my side for the next 4 months. I feel like there's a vacuum on my right side where the air is continuously rushing in to fill, but it just doesn't feel right.  I guess I'm going to be a full fledged nerd for the next four months. I used to think that even though I'm a Physics major, otaku, game geek, etc., I don't qualify as a nerd simply because I have a girlfriend... Now that my girlfriend is overseas, I don't have an excuse not to call myself a nerd. Sigh..... Huiheng, hang in there, we'll be expelled from the club soon enough.

I love you baby. I'll be waiting for you. 

I'm a sucker for mathematical ingenuity and neatness. Now, I can't really stand mathematical formalism and rigour myself, but what I mean by ingenuity and neatness is being able to arrive at something profound using simple, yet clever mathematical manipulation. 

The derivation of Euler's formula was like art to me. Upon seeing it, I was rendered absolutely speechless. In my head all I could think of was simply, "Wow".

When dealing with expressions with complex roots, we see in it's solution, a real part and an imaginary part, which comes in the form a+ib. As we are now concerned with an ordered pair (real and imaginary), we can express the solution graphically. Using polar coordinates, we arrive at the expression,

z = r( cos x + i sin x )

Using Maclaurin's expansion, we find that,

Therefore, we find that our complex solution may be expressed as the following,

As

Where n = 2, 6, 10, 14, ...

When n = 4, 8, 12, 16, ... however, the nth power of i would be equal to 1.

Therefore, in attempting to get rid of all the minueses in our complex solution, we have,

Using Maclaurin's Expansion again, we know that,

Hence, we arrive at the following conclusion,

Pure beauty.... 

I had a dream yesterday night. I dreamt that I was visiting this friend's gig and watched them play a song called Steel Machines. I awoke before the song had finished the intro. I got up, and I felt inspired to write a song. So I quickly penned the lyrics before I left for lecture and found appropriate chords when I managed to get back to hall. It's my first time in a long time I've actually attempted to write a song (the last time, the outcome was so absolutely horrible that I blocked it from my memory)... 

Hope you enjoy.

Greetings to all in the New Year and the New Semester. New Year's wishes hope you fulfil all your New Year's resolutions if you're still not jaded enough to stop making new ones every year. 

And no, I am not jaded enough myself as I have once again come up with a number of resolutions myself, which I don't know if I will be able to keep.

So the new semester has started and we had our first two lectures yesterday. Four hours of physics. Non-stop, back to back. At 0830 in the morning to 1230 in the afternoon. And to top it off, the lecturer for waves and optics (the 0830 lecture) has been the most powerful to date. Behold,