I recently came upon a tweet by Kathy Sierra. Here it is:
So I went ahead and downloaded the PDF file and read it through. Man did it resonate! Here’s a quote that practically captured the essence:
Mathematics is an art
– Paul Lockhart
Lockhart was describing how the current education in America was eroding the sense of wonder, discovery and thrill of mathematics in children and young adults. First, go download his article Mathematician’s Lament (about 25 pages) and read at least the first and last few pages if you’re in a hurry.
I don’t know much about the American education system, but the way it’s described, it’s bad. And the Singapore education system (at least with regards to math) is similar (well, at least from what I remember when I was studying). The sense of discovery just wasn’t there.
When I was about ten (I think), my parents bought me an encyclopedia set, Childcraft. The first book I went for? The one on mathematics.
I gorged myself on the puzzles, stories, thought experiments in the book. For example, there was that crossing of river puzzle, with a farmer and a sheep and a wolf. There was a story excerpt of Flat World, where Points and Lines meet the 2 dimensional Squares and Pentagons. And there’s a “proof” of the non-existence of vampires. And … wait, what? You want to know the proof?
Ok, suppose vampires suck blood out of victims and the victims become vampires themselves. Suppose there’s only 1 vampire in the beginning. On the first night, he bites one person. By the next day, there are 2 vampires. 2nd night, each vampire bites another person. So there are 4 the next day. I’m sure you can see how this goes… at some point, the doubling vampire population simply overshot the entire world population. But we’re still here, aren’t we? Hence no vampires.
Of course, that proof goes out the window if vampires don’t need to bite every night… or if they can control who to turn into a vampire… ok, moving along…
Oh yes, with this encyclopedia in hand, I learnt about the fun parts of mathematics. I learnt about the magic numbers of 3, 4 and 5 forming a standard 3^2 + 4^2 = 5^2 Pythagorean triangle long before I actually knew what Pythagoras’ Theorem was. I read about how the ancient Greeks were racking their brains for how to get a right angle, and they used a length of rope with evenly spaced knots. They found that a triangle with sides of 3 knot length, 4 knot length and 5 knot length, created a right angle at one of the corners. That was fascinating.
There was also this section on Fibonacci numbers, and a story about rabbits. The algorithm behind the sequence was presented with an interesting back story of an expanding bunny population. I remember in university, my professor mentioned the sequence and I exclaimed, “Fibonacci sequence!”. And my friend, who’s sitting beside me, turned to me and asked, “You know about this?”. Really? A math university student who don’t know about Fibonacci sequences?
I don’t know about you, but for all the talk about Asians being better (at math) (here and here), I think most of us still don’t get to see math as an art, as something beautiful to contemplate. I started out seeing math as fun, then later on as something scientific and not-so-fun. And after my service in the military, I went to university, and suddenly it’s fun again. I guess it took me a fresh perspective to view math once more…
And I think programming is like math. No, I’m not bringing in the meta-blogging type of “This blog topic is something like that” and go off on some far out analogy. I mean programming, like math, requires one to see the abstract, manipulate pieces of information in the mind’s eye, come up with solutions in the ether, and then bring forth the solution into the world.
Right now if you ask me about math, like really hard core math, I’d probably stumble. Partly from a long disuse of the principles, but mostly because unconsciously, I’m trying to capture that sense of wonder again. That requires me to shed some undesirable shackles and discipline, and allow myself to not know everything on the topic. Math fun is back in vogue.
P.S. The next book in the Childcraft encyclopedia I pounced on? The one with stories. I guess I’m a sucker for fiction. *smile*