USP essay- Symmetry

I was digging around my laptop, to see what kind of old relic I could find(Old computers tend to become cluttered like any other worktable desk, unless you put alot of effort into keeping things in order), and I found this! My entry essay into the USP scholars program in NUS. I'm not sure how it impressed the people there into granting me and interview and subsequently accepting me, but I'm reasonably impressed with it myself. Here it is:

On Symmetry

There are many interesting and intriguing ideas out there but in my opinion the most intriguing concept around, is that of symmetry. Perhaps it is Man’s natural obsession to find order amongst chaos as well as our natural eye for symmetric objects, I found myself hooked to the idea of symmetry. When first introduced to the topic in our Mathematics textbooks at Secondary 1, I was among those students who found the topic useless. We were scolded by our teacher who was irritated that we were not interested to engage in the topic. He said that it was immensely important topic that would have many applications elsewhere. I did not believe my teacher at that time, but my perception of this particular concept was to change later, when I read more about symmetry from other popular science and math books.

Etymologically, the word symmetry can be broken to 2 parts, ‘sym’, which means together, or same, and ‘-metry’, meaning measure. Taken together, symmetry implies things that measure together. Geometrically, an object exhibits symmetry, if its parts measure the same, or if the whole can be partitioned into identical parts. Such objects frequently show themselves in Nature and man-made art and objects. In art, symmetry is a beautiful concept to apply. Some of us may have tried before a novel way to produce art when we were younger, by splattering different colours of paint on to a piece of paper, and folding the paper in half. When the paper was unfolded, it revealed a butterfly-like specimen exhibiting bilateral symmetry.

However, the power of symmetry is more than just to produce works of art, for it proved to be an extremely nifty tool to introduce order into a situation. This concept works just like the strong and broad brushstrokes of Van Gogh, for when symmetry is discovered in a particular phenomena or situation, it always proved to be an encompassing concept, one that provides the big picture. In physics, symmetry is closely associated with the conservation laws. If 2 things measure the same, then on the balance beam, x = y. Even though x and y may appear to be different on the surface, we know they must in reality be the same thing, through symmetry. In physics, there have been several occasions where we make use of the fact that physics laws remain the invariant in all frames of reference that are not accelerating to solve problems, greatly simplifying the equations required to solve the problem.

Symmetry thus also includes the idea of how one thing can translate to another. It may provide a set of rules to such that 2 things equate. For example, we can say there is some form of symmetry in language, because we have a set of instructions about the grammar and vocabulary that allow some arbitrary symbols to be equated with some physical meaning. In doing so, we can attain compactness in conveying information, achieving more with less. The use of mathematical symbols to express meaning to come up with so many theories is another example of symmetry at work. If we were to express our theories entirely in verbal means, or through only pure use of English words, we would find our theories a lot more unwieldy to use. To those who are new to the particular language, we usually find that we need a set of instructions, a kind of dictionary to explain how this language works. Just as a mirror allows you to find your image within, this dictionary is the mirror where 2 separate objects measure the same.

Order turns up around us in the most unexpected of ways, frequently hiding just deep enough to frustrate us who are trying to tame a chaotic system. But when it is discovered, there is an elegance that makes scientists and artists alike step back and admire the big picture. With symmetry, we can set out to understand the whole universe. Even in everyday life, one can see the broad strokes of symmetry around us, and appreciate the beauty and elegance that symmetry have on the grand scheme of things.