Thinking Aloud

I feel like Forrest Gump. Eating chocolates by the bench, and telling my life’s story to an old lady. A little feather floats down from the sky. Life is simple, it’s just a story.

But I’m not Forrest Gump. I am who I was made to be. Just that I am now in the process of discovering. On one life’s journey, only one life to live. What would it’s character be?

There are about a million and one ways one can prove that 1=0 and hence that all numbers are equal.

But after two years of algebra and a course in set theory. One knows that the notion of ‘equality’ is imprecise. After all in the trivial ring, the multiplicative identity and the zero of its underlying abelian group are equal, hence that 1=0.

1 and 0 are just symbols after all. Numbers are just symbols. One ought to know that the effort to find the hundred billionth digit of pi should know that they are calculating symbols, not doing mathematics. (Ok, that’s condescending, but don’t tell them that).

Even from a set theoretic point of view 0 is the empty set, i.e. nothingness. 1 is simply a set containing nothing. 2 is a set containing a set that contains nothing and so on…bleah…nonsense rite.

But this construction aquires its power when we impose a ’structure’ on it. And then and only then does numbers become useful. I.e. an ordering. 0 ought to come before 1. This is perhaps one of the simplest structure one can impose on a set.

I guess laymen ought to know that numbers used in everyday life makes sense because of this natural ordering. But otherwise, mathematics is NOT about studying numbers. It uses numbers much like an engineer or an accountant needs to use numbers to convey information. For mathematics, that information is mathematical knowledge.

It’s 12:40. Will be sleeping soon. But watch this space. As they say, you’ll never know what God can do. Fulamak, trying to build up willpower aka positive thinking (trying to bend reality through the force of my mind)

Come on lah…

But its real right? God really does work right? Or is he sleeping. Maybe I need some kind of Elijah to jeer at the Baal worshippers. To jeer at my God. Oh hell, it’s not me. I’m not being me. I’m being…

I’m usually like this when I’m not in control of my life. So don’t worry. I’ll get to grips soon.

The majestic rooster crows. I wake up every morning and stare…and just stare.

The semester is ending. It didn’t go as well as I had wanted it to end, but there are many, and I say many things to be thankful to God for. It feels strange being in final year. You float.

The weather is beautiful. Raining for two nights in a row already.

Studies, continue? Where? Scholarships? Money…accomodation. Detachment. Am in a foreign land. It is not my true home after all. But then again, on this side of eternity, there is not one place where we can truly call home. Only when He comes to make all things new.

The red rooster crows again. Truly the red rooster keeps on crowing day after day. Its just the same old me, the same of stuff, the same old computer monitor that I stare at every damned day.

He plays Debussy.

Thank God for Debussy. Otherwise, I would have long died from oppressive silence.

Nothing beats Debussy after a long day. Wish I had more time to blog. (and not to mention more ideas too)…

It rained today.

But I slept off the beautiful afternoon. Too tired.

I enjoy mathematics, I enjoy what I study and I certainly am thankful to God for making it possible for me to study mathematics. I really hope to make a career out of it. Gosh, I actually feel nostalgic about my first year; sitting in a linear algebra class, wondering what the big deal is about gaussian elimination. I feel the excitement of learning what groups actually were. I guess it was at that moment that I actually fell in love…

And talking about love…I’ve had my crushes-and heartbreaks- but all of them were for the better. I am a better person because of those experiences.

3 1/2 years in NUS have been eventful.

I’m feeling particularly evil today. So I’ll do something I’ve never done before. Start a tagging chain!

*Kill me*

1. What are your favourite hymns?
Great is thy faithfullness, What a friend we have in Jesus

2. Writers that have greatly influenced your spiritual journey?
JI Packer, John White, Philip Yancey, Francis Schaeffer

3. Clean or shaven?
Shaven definately, fuzz makes me feel unkempt.

4. MacD or KFC?
I don’t know, I grew up with KFC. But since MacD is just in campus, I would think MacD. But either way, hardly step into a fast food restaurant.

5. One famous person who shares the same birthday as you?
Raphael, the renaissance painter. 1483.

6. Greatest mystery of the universe?
Where does all those hair in my room come from!!??

7. Attached?
No.

8. Tell me who should do this quiz?
Zhi-Yong, Zhi-Zheng, Aurelia, Faith, Marcus Khoo.

Haven’t been blogging regularly. Just too busy with homework assingments. (Refer to the previous post.) In fact I’m definately not much freer this week. And so the axiom of regularity doesn’t apply to this weeks worth of blogging.

Can’t talk about much now. Have a great week!

It was a moment to remember. The second last hurdle has been crossed. There’s left only to show the existence of a group G = HK such that H and K are both not normal (in G) but yet each of them solvable. G should not be solvable.

I can only start by considering nonabelian groups, yukk!!

This is how doing group theory for one whole week feels like:

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

I dream of sweet smelling coconut trees,
the salty tang of the bay soaked wind,
and the cool drip of dew on my glass of lemonade.
Hawaii, where lovers go.

Oooh, how I love the emerald hills,
the verdant sea and setting sun;
how she bathes in the swaying waves,
and spills the yolk of the evening into the bay.
Hawaii, where lovers go.

I would give a million, to be where you are,
To be in Hawaii, where the orchids are fresh.
To sip the milk of gods, and eat the flesh of the earth.
Oooh, Hawaii, where lovers go.

Ooh Hawaii, it is a sigh upon my lips…
Ooh Hawaii, it is a sigh upon my lips…
Ooh, Hawaii…

The ironic thing about natural disasters is that our home, has become our enemy. We are of this nature, but at the same time, when nature destroys our livelihood, our families, our jobs, alienation sets in. The place we once made our home, the land we thought we owed now has turned against us. Who owns nature, really? Who owns this earth? Is it not the Maker?

Lord, have mercy.

Not been blogging consistently.

I guess life’s been bland, like plain water. So nothing to say, really.

I must admit. My prayer life sucks.

I read His word, but I don’t pray. I guess, deep down inside, I can’t fully bring myself to ask Him to fulfill my desires. I am afraid to ask. I am afraid of being dissappointed. Probably why I ask other friends to pray for me, but I (almost) never go to Him and ask him personally.

Why, why, why?

Where have I gone wrong?

I was browing through friendster when I came across a photo of Kayjin with Dr. Tan (my honours sup) taken during his convocation.

Feeling super guilty right now.

*Hangs head in ultimate shame*

The view is vast,
Scarce the eye can take it in,
I love my window,
It takes me places,
even imagination cannot reach.

Not all is within the mind’s eye,
something beautiful, somethings sublime,
Sometimes somethings, somewhat breathtaking.

The view in the window is vast,
Life looks east, and waits till dusk.

What’s going on?

Over at limkitsiang.blogspot.com, he has dedicated 3 posts to the issue of a setting up of a Department of Parliament within the Government and the creation of a post of DG to oversee this department.

When I check the national news…what dominates is the earthquake.

What’s going on? Why is nobody saying anything else about this important development? Why are people not informed, and why are they not making their views heard? Are M’sians so ignorant?

CNN.com - Death toll in Asian quake tops 800 - Oct 8, 2005

One must pray…

NECF Malaysia
Given the sophistication of polemics mounted against Christianity we can no longer rest content on the simple preaching of the gospel. This calls for a systematic and sustained effort to train Christian thinkers and activists who can defend the integrity of the Bible, the plausibility of the Christian worldview, and demonstrate Christianity as a holistic way of life in cross-cultural apologetics.

Hmm….wonder why I feel a little…disconcerted.

Spend the whole day thinking abour Steiner’s Porism. It really felt a little cheating it proving it using complex analysis, somehow the proof (which I think is correct) seems like using a chainsaw to cut sticks.

But I’ve proved it. And I hope the argument holds water. It better…after dying in the midterm, this better be good!

If anything, I really wish sometimes that life is like geometry. Nice and straight, curving at right places and heading of to infinity. What’s more, geometry is beautiful.

That’s just wishful thinking. Unlike mathematics, real life decisions are not cut and dried. One cannot see all ends. Geometry is like Michaelangelo, Rembrant and Picasso. Real life is like Pollock and Koonig.

Baa baa black sheep, have you any wool?
Yes sir, yes sir, three bags full!
One for the master, one for the dame,
And one for the little boy who lives down the lane.

I’m dreaming of lamb actually. Lamb steak, yummy.

I’m not making much sense am I.

Sorry Faith, yet another mathematical post.

Category Theory (that’s what I’m learning now) is really sticks and dry bones. Its interesting, but difficult to see why its so important in modern mathematics.

The e-mail from home was timely indeed.

Thanks.

It’s been a long time since I made a personal rant here on this blog.

I wish…

*let’s out a long, long sigh*

CNN.com - Bali terrorist blasts kill at least 36 - Oct 1, 2005

Please pray for the victims. Although the death toll is lower than the last time, it’s still a horrible, horrible thing.

Here’s something to go with your coffee and eggs in the morning.

Do you know the answer to this?

1) If you have 3 odd prime numbers, is it always true that there is at least one of the three that divides the product of the other two leaving remainder one. ( Let p,q,r be three distinct odd primes. Is it true that at least one of these cases happens? qr = 1 mod p, pq = 1 mod r or pr = 1 mod q.)

I think it’s true, but can’t prove it.