Let God be X
I was reading the newspapers early this morning and a couple of things about religion riled me up. But I'm not going to succumb to the temptation of ranting about it again. I've said enough. Today, I'm going to write about learning.
This is a topic that has intrigued me every since I was a kid. I've always observed that each one of us is born with a certain aptitude for specific areas and not others. I noticed that in my class then, there were those who were hopeless when it came to subjects like mathematics, but excel in languages.
What makes a person pick up maths easily but flounders when it comes to stringing a simple sentence in English? In my case, I certainly wasn't a math whiz and I even disliked the subject during my primary years, but then I learned to like the subject when I entered Form Four.
I've always loved subjects like history and geography but was also scientifically inclined. Which made me neither this nor that. If there had put me in the Arts stream, I would have been bored by the way in which there teach the subjects. Humanities require good, inspirational teachers, which are few and far between.
Like all reasonably good students, I was of course put in the Science stream. And that was a revelation, akin to a religious awakening. The subjects of Physics and Chemistry suddenly opened to me what real science was all about--that the universe itself could be understood and expressed in beautiful mathematics. Mathematics became to me, the language of God.
I fell in love with mathematics. But I realized at that time, I did not perform as well in the subject as some of the other students who came from Chinese schools. I was curious. What was their secret that made them excel in the subject?
As I spent more time with them, I noticed that their minds were more logical. There's no vagueness in everything they say or do. It was the 'dullness' of their logical minds that made them think clearly when it came to solving math problems.
This clear logical style of thinking is something that my young mind was not accustomed to. I had the mind of an artist--prone to passionate bursts of emotion and poetry. A romantic, if you will. And when it came to solving mathematic problems, I was careless and always making silly mistakes. And I noticed that I did not bother to understand the underlying concepts with the thoroughness and clarity of a logician.
To achieve that precision and clarity of thinking, I realized that I had to slow down my mind. As an artist, I value my flights of fancy--the flurry and passion of thoughts as they whiz through the mind. But this is like painting in broad impressionistic strokes of impasto. You can fill the canvas up very quickly but leave out a lot of details.
When it comes to mathematics, you have to be a Pointillist. One dot at a time. One logical conclusion after another. State a fact, and then ask yourself, what's the next logical step. Put that down on paper, clearly. Clarity and precision are key. Always, one statement of truth at a time. Break a large problem into smaller parts. Tackle them independently, and then put the pieces together. By following this principle, you will always arrive at the inevitable conclusion: the right answer.
I began to perform a lot better in maths after that. I was thoroughly in love with the subject because it opened up a world of beauty to me. Every problem, can be broken down into simple parts, by the application of specific mathematical techniques--a deft substitution, a transformation or a geometrical approach. And when I saw how mathematics were used to expressed the laws of Nature, I was ecstatic because I finally could catch a glimpse of God's genius.
It is funny how I use the word "God" so often when I discuss mathematics but in everyday life, I try to make my language secular. You will never find me saying "God bless you". But when it comes to mathematics, I am unashamedly 'religious'.
I am veering dangerously back into the subject of religion, which I am trying to avoid because I have written too much about it. But I just want to register this point: it was applied mathematics that made me understand why people find the concept of a personal God, even an impersonal one, appealing.
For instance, in the subject of Statics Mechanics, there's the concept of centre-of-gravity. You are always given a weird looking object with various weights or forces impinging on it and instructed to calculate where is the centre of gravity for this system of forces. You will define a point X somewhere in the middle of object and then you write an equation that balances the moments caused by the forces clockwise and counter-clockwise. When the point X is found, you can forget about all the other details. Everything reduces to a single force acting on point X. Point X is where you would put your finger, to hold the entire object in balance. A complicated problem is reduced to an extremely simple one, by finding X.
God is like X. We always need mental stepping stones to figure out the problems in life. As humans, we deal with people. We know how to love or be loved by someone. Our minds work with people-related metaphors. If God is a fictitious lord, invented by superstitious people, it is perhaps a necessary one. We know how to obey or respect a person of authority. And that streamlines all our subsequent actions. A centre-of-gravity 'exists' because all forces act in a resultant manner on that particular point.
We can debate the ontological truth of God, but we will never transcend the limitations of human understanding, which sees the world in terms of people, 3-dimensional space and time which moves from past to future. We are, in other words, 'naive'. But even a naive understanding of the universe is useful, as long as we understand it as a model, and not the ultimate reality, if ever there was one.
To tackle mathematics, I had to modify my model of thinking. When I understood mathematics, I saw metaphors that helped me to under other concepts like God. Without labels like "God" or "center-of-gravity", we would find it difficult to express anything that is useful. Is there such a thing as a "center-of-gravity"? It's not important. It is a property of the system that has a certain utilitarian value.
Always define the unknown as X. Put it in an equation. Sometimes there are more than one variable: X, Y, Z or X1, X2, X3.... There's no harm in polytheism as long as it serves some useful purpose. But remember, they are there because we need them to think and act. As long as we are clear with the metaphors that serve us, we'll never run into delusions about their reality. Beyond that, there's nothing more to be said.
