Mathematics as a language (07/12/1999) (Now playing Cha1 qu3) If you have realplayer, you can see and hear the lovely Sammi Cheng performing this song here (I think this is a very beautiful song J)
Alas, economics, at the advanced level, is very much mathematics. I have been trying to read up set theory, matrix algebra and calculus for the last month and it is so much like trying to learn a foreign language. But I thank God for convincing me of one thing: before I can even think of crystallizing economics using mathematics, i.e. being creative in the application of mathematics, I must be able to master mathematical concepts of proofs like the back of my hand. It is tough but clearly the rewards are immense.
It is just like the learning of English. Looking at the first paragraph of this article, how in the world did someone like yours truly, who is born illiterate, ever possess the capability of formulating the above paragraph at this date, 07/12/1999? That is because, prior to the typing that I am doing now, I have already understood what do words like, 'convincing', 'crystallization', 'application' etc. and all the various tenses of the English Language, struggling through it from Primary one up to the present moment. As I am thinking of how to be creative in coming up with this article, my subconscious mind already starts to recall all the possible words I can use to formulate this 'creative' article. Imagine yours truly trying to come up with this article in Mandarin! Boy, I will have lots of difficulties due to my limited Chinese vocabulary.
I guess it is the same with mathematics. I am glad that mathematics has revealed itself to me as very much an exercise of logic, in its purest form. I remember Jodie Foster in the science fiction movie, Contact, stating her belief that, should any non-earth being contact us, the language it will use will be mathematics, the universal language.
At this point of time, I suspect my present struggle in understanding the basic concepts of mathematics, such as set theory, is the result of the decisions I have made in Secondary school. I remember struggling in secondary 3 with concepts such as relations, functions, range, domain and all the concepts of derivatives. It was such a pain in the neck to understand all those concepts. Then, in June 1989 if I can remember correctly, the year when I was secondary 4, I happen to chance upon my classmates doing something that is now popularly known as the 'ten-year series'. After trying out those questions, I found out that I could now do all the mathematical questions in the textbook with much greater ease. Furthermore, the subsequent class tests and examinations became so much easier. Being positively reinforced in such a manner, I started relying on such methods on my GCE 'O' and 'A' levels, leading to very good results for mathematics since one cannot fail to notice the similarities of the questions throughout all the years.
Ex-ante, the decision to focus on memorizing the steps instead of taking time to understand and apply it to new situations was a wise one since I was about to give up on mathematics. Ex-post, that decision has very much destroyed my understanding of mathematics and crippled my present study of economics. At this point of time, I need to be able to visualize economics as an optimization process, there are no longer any 'ten-year' series nor any steps to memorize in creatively applying mathematics to economics.
Yet, if I asked myself frankly, I may have no choice then. Would I be better off by continuously struggling through mathematics, doing badly for my 'O's and maybe 'A' levels too, realizing at the end the beauty of mathematics, and yet unable to qualify for NUS because my friends took the short-cut method of learning mathematics? It was a tough call but, as mentioned in an earlier article, I can now understand better why Singaporeans find it so difficult now to move from knowledge absorbing, which we are superb at, to a knowledge creating stage, which is what I am personally facing at this moment. I also understand why, although we keep beating the Americans in undergraduate work and below, the truly creative scientists and engineers are still Americans. As Monica Gwee have mentioned, while Singaporeans have an astonishing breadth in their coverage, we lack depth in anything. Those of us who took the former EC3201 and the present EC4203, the economic theory courses, should be able to identify with that comment.
As a sanguine person, I would say that it is never too late to repent J. I pray to God that he will enable me to meet my 'Paul-like' Damascus in mathematics soon. Once the scales have fallen off my eyes, I believe that I will be able to unleash the true creativity of mathematics in my economics.
Some links to stimulate interest in mathematics