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Why math? - Arvind Narayanan's journal [entries|archive|friends|userinfo]

Why math? [Jan. 11th, 2006|11:07 pm]
Arvind Narayanan

Most people who are bad at math consider it to be meaningless memorization of mundane equations. People who are good at math and who benefit from it simply sneer at them or try to explain why math is fun and important, but in terms that are just as incomprehensible as math itself. Here's my attempt at a simpler explanation of why math is not only fun and important, but can be life-changing.

When you learn math, what you really learn is the art of abstraction. Now what the hell is that?

Think of a 2-dimensional frog that lives on the surface of a lake — not a regular frog, but an imaginary one that exists in, and can perceive, only length and width but not height; its sad life is therefore confined to the two dimensional surface of the lake, and it knows nothing of the world above and below. Suppose further that for some reason, cubical objects fall into the lake from above. We don't care what these objects are and why they fall into the lake, just that they are cubical. The frog of course doesn't know about the cubes: all it can perceive are the two-dimensional intersections of the cubes with the surface of the water.

The frog is at once fascinated and bewildered by this phenomenon. It can see pattern and symmetry in the shapes that the cube makes on the surface, but since the cubes fall at various angles the frog is simply unable to figure out the underlying mechanism that gives rise to these patterns. Its mental apparatus is completely incapable of conceiving the concept of a cube, because its perception throughout its life has been limited to two dimensions. If the frog were somehow given the gift of 3-dimensional thought, it would realize in a flash of enlightenment that it is looking at cubes falling into the water.

Math is that gift. Mathematicians call it abstraction. If you can grok math, your life will change as thoroughly and as wonderfully as that of the two dimensional frog.

In our lives, we see, hear and sense things all the time that are seemingly arbitrary, yet give tantalizing glimpses of underlying pattern, structure and beauty. We feel that if only we had some vital clue, we could understand and control these phenomena far better than we are able to. That, people, is what math enables you to do. Not numbers and figures directly, but the art of abstraction which can only be imbibed through math, will enable you to peirce the veil of complexity that shrouds our daily interactions. From stock markets to music, from computers to food, and absolutely everything in between will become vastly simpler if you are mathematically educated. Further, you will find beauty in everything you see, and you will be constantly thankful for your existence. And if you are the type of person to do so, you would find yourself closer to the mind of God.

Of course if you're reading this blog you probably don't think math is dull, but now, the next time some bitches about math you at least know where to point them :)

[User Picture]From: koyaanisqatsi
2006-01-11 01:49 pm (UTC)
I don't know too much about math. One of my many weaknesses. I remember thinking it was fun in high school--solving equations (and in chemistry, balancing equations) but it's been ages ago.
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[User Picture]From: arvindn
2006-01-11 10:11 pm (UTC)
It's never too late to start!
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From: (Anonymous)
2006-01-12 07:01 am (UTC)
I am Sandeep. I will be senti here. To me abstraction often seems to be more of unlearning than learning; once you reach the soul you find the essential unity between many things. I think someone, probably JP Serre, said that if you want to call one thing many names you may do poetry and if you want to call many things by one name do mathematics. Incidentally, more often than not I find math dull irrespective than whether I understand it or not so your blog has more readership than you thought ;-))
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