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An inquiry into the nature of mathematics and why as Indians we excel in its understanding, application and revel in its beauty
[THIS ARTICLE WAS WRITTEN FOR PUBLICATION IN BITS-PILANI'S MAGAZINE. WHETHER IT WAS OR NOT IS STILL A MYSTERY TO ME]
Well, I hope u read the topic very, very carefully, because that’s NOT what this article is about. Then why have such a title you ask? To be honest with you my patient reader, I could not think of one. But do not judge my literary skills as yet, for I have a few words that might be of some interest to you. So without further delay let me delve into the heart of the matter.
Well, I suck at math... and oh well, how do I put it? OK, plain and simple... SO DO YOU. Yeah, you are studying in one of
I'm sure you are all aware of how
Many of you, I am sure have read the book "Surely you are joking Mr. Feynman". It is a truly humane book which if you’ve not as yet read, I urge you to do so as soon as you can because it reveals many insights into the mind and environment of the genius. Well, that was the book that got me all hooked into quantum physics, Schrodinger kittens (sorry... was that a cat?) string theory and what not, but my ID number at the end of this article would show you that I am an Economics major with a Comp Science dual. Yes, that interest in physics died somewhere along the way (to those few who do have the interest, kudos to you... lucky you). For someone who did not attend any IIT coaching, the idea of solving 3-10 page long differential equations was too much of a terror. Economics sure felt like a safer option.
Coming back to the book, didn't you get the feeling that there always was a sense of lightness and ease that Feynman had whenever he referred to 'work' as such. No cribbing about exams, tests, assignments, work load, deadlines – EVER!! . Ok, you can argue that he was old when he wrote the book and was nostalgically looking back at his younger days, however, he does mention early on that he did not like trigonometry in his younger days. But it is the reason for his dislike that is the most thought provoking. He claimed to always make the mistake of cancelling out the n’s while dividing sin and tan!!!! Well, well... now how many of us would ever dream of doing that? Definitely not in the exam, oh, we've mugged up the problem all too well to commit such a blunder. Hmm, how about at our study table a couple of days before the exam... no way!! I guess we'd be too busy cheering Sachin or Kaka to score their next 100 or goal.
Coming back to the word that I had drawn your attention to - ‘play’. Don't you realise the fundamental difference between us and Feynman... HE PLAYED!! He played during what we'd call 'studying'. He played with Math, Physics, Biology and what not. All work and no play sure makes Jack a dull boy, but what if it was all play and no work? Wouldn't that make Jack an ultra productive creative machine in the eyes of the commoner?
Another thing that I'd like to draw to your attention to is the extremely low number of original research papers that are being published by the IIT's, BITS and other such leading universities of India. Now, let’s eliminate all the lack of funding, low industry support, limited access to technology and the other crappy excuses that are given in their defence. Maybe the experiment based papers are hard to come by, but how about the ones that involve you, the internet, a pen and papers. Where are the original theoretical papers that we should be churning out?
Well, here's my explanation ... we suck at math. Consider this, ever since class 3 we have been asked to mug up tables. "Learn this now, it'll help you in your higher classes" is what we were told, and we blindly obeyed. Typical middle class attitude don't you think? But did it ever occur to you at that age as to what these things might actually represent? Did any of your early schooling ever really mean anything to you? Did you ever express yourself using the knowledge that you learnt in school? Did you ever see a tree or plant in your neighbourhood and go "Hey, I saw that plant in my text book" or ever see a movie/ documentary and go "That was there in our science/history/geography text book" I guess most of us wouldn’t. Alright given the schooling system is bad, there's too much pressure on kids to perform, no time to stop and smell the roses.. blah blah.. but aren't we missing the essential point here? We are NOT being educated and in this competitive world, we need the ability to be creative with our knowledge to even survive. Remember, the Chinese are fast catching up to us, and if we want to retain our jobs and standing in the world, we need a huge upsurge in the number of new products and patents and coming from our country.
Until now I guess I haven't yet said anything significant. I'm sure you would all have come across these thoughts somewhere or the other. But here's my solution, at least with regard to math.
MATHEMATICS SHOULD BE TAUGHT AS A LANGUAGE
Yes, I mean it, a language, just like Hindi, Sanskrit, English, at least in the lower classes. Students should be asked to express themselves mathematically. The student ought to be asked to model every phenomenon that they see/experiences in a mathematical way.
I am no educationalist, but let me sight a few examples that have been lying around in my mind for a while. Let me start at the primary classes, taking the example of students eating an ice cream. Every student must be asked to rate the happiness he/she felt while eating the first ice cream, on the second, on the third and so on. That way a child is sure to understand the meaning of providing weights to goods, and if I may be so ambitious as to suggest maybe even an intuitive understanding of the law of marginal utility of economics. This exercise could be carried out anytime, maybe even in the break time.
Furthermore the importance of mathematics in everyday life should be highlighted (even though may not be really necessary). Take for example an awareness program telling children to conserve electricity. During the course of the lecture, the participants should be asked to do the maths that is required for them to understand the importance of conserving electricity. They ought to be taught at a young age how to read meters, and do the simple math involved to calculate the total expenditure, amount of pollution generated and so on. Why must students wait for their parents to teach them these basic skills?
Young minds must also be encouraged to come up with innovative means of expressing the world around them. Take for example the Ignobel awards. I believe that this should be made a compulsory event in every school and college. When asked to mathematically ‘model’ the most absurd of things they observe, the process is sure to ignite the creative spark in them. Students would learn to use mathematics in ways that they never dreamt would be possible.
Another plausible exercise might be to ask the student to create mathematical problems rather than simply be asked to solve them. This way the young minds would be moulded to think of ways and means to solve physical problems. A spirit of competition amongst classmates would lead them to come up with newer and more innovative problems, and in the process develop more novel and exciting ways to apply the mathematical principles available to them to justify the solutions for the problems they create. I'm sure a text book filled with such problems would be far more interesting than those written by boring professors who may have forgotten what it means to be a young person.
I am sure that if students become as comfortable in using mathematics to describe their surroundings as using their mother tongue, the young minds of tomorrow (and today) will be able to develop a plethora of significant and far reaching innovations. Our minds are queer, throwing out the weirdest of ideas (like this article for example) at all odd times. It requires a firm grip of mathematics to convert these abstract forms, ideas and images to a form that is comprehendible by our fellow man. I sincerely encourage you all 'play’ with the knowledge that you gain. And remember, no idea is insane or useless, if communicated properly.
P.S. Einstein's path breaking paper on special relativity was 5 pages long... but our textbooks... ahem...