I've finally managed to come around and finish the diorama for my gundam. I thought the Gundam was bad, but forgivable... The diorama was just outright bad.... Thank God for sucky handphone cameras.... 

Nowadays, I find myself wondering what am I going to do with my Physics degree. If my results turn out good and I manage to land myself in a good university for graduate studies, I suppose it's quite a no-brainer. 

The thing is, whether or not I do well enough for my undergrad is subject to a huge amount of uncertainty.

I guess I've got a number of options. One is that I can do my graduate studies in Singapore. The good part is that I can continue to tutor. It is very good money, but more than that, I really do enjoy teaching.... Of course studying in sg means I don't have to leave the familiarity of home. But then again, I really would like to stay overseas a couple of years, just for the experience.

Another option available to me is that I just screw graduate studies and go next door for TCC (Teacher Conversion Course). I'd then become a full time tutor. This is the most stable choice available, and the one which promises the most income. But so what, I'd be a whore. I'd be betraying the spirit of inquiry. I'd be betraying Science. I'd be betraying Physics. I guess one can say," what do I have to offer to Science that could possibly be labeled as a betrayal at my not deciding to pursue it?". Truth is, I don't think I have much to offer to Science at all. I guess I'd be the poor man trying to win a princess over with nothing but sincerity and love.

Call me a romantic, but I don't want to stop learning, I don't want to stop being in the "scientific community" (though I don't really think I count as being in the "scientific community" at the moment either). In short, I want to pursue Physics till the end. I've done badly in school for physics all my life, but that has never stopped me from liking it. My greatest joy, would be to know that I do have something good to give to Physics. Hopefully, after some searching, perhaps the poor man will find a diamond ring sitting by the road to offer his Princess.....

Sometimes, I get to thinking that, every year, Singapore has about a 100, maybe less, new physics undergrads (including those from NUS). I wonder how many of them will still be doing physics thirty years later. I wonder how many will convert to become engineers, how many will become teachers. I wonder how many will not be doing Physics at all (ie, banking and finance and all that other stuff). 

But most of all, I wonder, where will I be thirty years from now......

On a different note. I'm feeling pretty lousy right now because I just found out that the Final Fantasy: Distant Worlds concert is coming to Singapore and tickets have long been sold out. I've tried purchasing tickets on Ebay, but there's this asshole who's either camping or using some programme to bid 50c higher right after you place your bid. And the highest bidder to all three tickets available on Ebay seem to be by the same guy. 

This sucks.... it looks like I'll be stuck watching the Youtube videos at home.... sigh......

Tuesday is going to be a killer paper. Linear Algebra. In linear algebra, we deal with the concept of a "vector space" (which I don't really understand that well myself). We deal with supspaces of vector spaces, namely, Euclidean N-space, column spaces, rowspaces, nullspaces, eigenspaces, what have you. In his introductory lecture on Classical Physics, the Stanford lecturer Leonard Susskind made a reference to, "an abstract space in which there is are only two laws of physics" (pretty interesting but I am unable to elaborate further, due largely to my lack of understanding for such abstraction).... 

Through it all, I realised one thing... That I have no inkling of what exactly a space is. 

So I wiki-ed it and I realised that the concept of space has been a rather hotly debated topic since the 1600s, maybe even earlier. Two giants of their time who argued as to what a space actually is, were Newton and Leibniz. Newton argued that space was absolute and independent of matter (meaning that there is a universal reference frame, see Newton's bucket experiment, which is pretty convincing). Leibniz on the other hand, regarded space as relational (meaning that the reference frame must always be pegged onto a particular object from which we want to take reference from).

According to wiki, Immanuel Kant's believed that the nature of space was "synthetic" (his working definition of the word "synthetic" still puzzles me, but I now it does not simply mean "man-made" as in the conventional sense). But Kant rejected both the Newtonian and Leibniz(ian?) view of space, concluding that space was not an objective feature of the world, but rather, an unavoidable systematic framework in which people organise their sensory experiences.

Well, I can see the sense in all their views, but these discuss the nature of a space. Not what a space is. After having a discussion with Jason, I guess we've come away with the working definition "for now" that a space is a kind of set. Like a bag that holds things. However (very intuitively), a space is a set that has certain rules, in which the things it holds must be a vector (which means spatially extended). Whether or not the bag has anything in it, it still exists (where in the event it is empty, it is known as a "zero space" or a null set"). Hence, wouldn't the word "general vector space" be slightly redundant? Because the word space itself says that the space contains vectors. 

It's not the best definition, and people may be inclined to disagree, but please, do share your thoughts. 

This is touching the more philosophical aspect of physics/mathematics already. Physics sure isn't easy. But it's definitely not uninteresting....

I realised a number of things during my "study break". First, NTU is absolutely shitty in the sense that they still teach new stuff even though it's the last week of lessons. I'm the most incensed by the amount of content they tried to cram into MAS183, linear algebra and multivariable calculus. We've covered about 80% of our linear algebra text and almost half the entire chapter of multivariable calculus from James Stewart (and that's a lot). I've been preparing "cheat sheets" for every topic as I feel it's good revision. I've managed to cram 112 and 182 into a single A4 paper, but guess what, for 183, I had to use, not one, not two, but THREE whole A4 size papers, filled on both sides. The people who plan the course syllabus for physics really should sit down and think of the quality of learning rather than the quantity.... sigh.....

Second, I've just completed the PAP113 06/07 paper and while checking answers, I realised one thing, I've been made paranoid by "tougher" modules like PAP111 and 112. I come up with a simple answer first, and upon looking at the weightage of the marks, I will overthink things and come up with a more complicated solution that's wrong. And it'd turn out that the simple solution would be correct..... Maybe next time I'll just write both answers down. Prof Sum said that he would mark the cancellations too.... I hope this holds for Prof Shen as well....

God Bless to all Physics students in this coming exams... May you be given wisdom and the clarity of thought.

PS - Walter Lewin is damn cool....

And next, another one of my favourites, the jazz standard Take the A Train by Duke Ellington arranged for guitar by Roland Dyens, performed by Soichi Muraji.