Pixel Grower and the beauty of mathematics
I recently encountered a simple, yet enthralling game called Pixel Grower.
The game's review page at JayIsGames (an excellent site for finding this sort of Flash-based diversion, if you've not heard of it) waxes poetic on the beauty of “the game as art”. A commenter on the review linked to the Wikipedia article on diffusion-limited aggregation, which provoked my Wikipedia exploration of fractals and chaos theory.
If you know me well enough, you've probably endured my rambling on mathematical beauty before, but here it comes again.
Math is beautiful. No, not arithmetic or algebra; real math. The kind inspired by studies of the natural world and how it evolves over time and in response to stimuli. It shows up in things like fractals. Fractals, for those who don't know and are too lazy to read the article, are geometric figures that exhibit self-similarity: they consist of small pieces that, at least approximately, resemble the whole. They show up in all sorts of places: coral reefs, mountain ranges, plants, snow flakes, and much more. They're just one example of what I find awe-inspiring about math — its ability to describe just about anything in the universe, provided someone's taken the time to think about it enough.
At school, I often find myself explaining to my friends how I feel about math, and I always come away with a sense that a lot of people are unable to see this beauty because they've had their curiosity about such things hammered out of them by years of middle- and high-school Mathematics courses. Courses that teach nothing but memorization of formulae for finding the volume of a sphere or the roots of a polynomial, without ever exploring the depths and bounds of how and why these things came to exist, or any of the fascinating things that can be done with them. The result seems to be scads of people who are jaded about math because they never “use” any of what they were taught.
This is wrong. Math can, and should, be exciting. My EECS curriculum required a course in basic signal theory, and I thought it was cool enough to warrant taking an advanced course in signal analysis. This is partly due to the professor teaching these courses, one Babak Ayazifar of the University of California at Berkeley. You can watch videos of his lectures for EE20N Structure and Interpretation of Signals and Systems online if you're so inclined. I highly recommend them. Ayazifar truly understands how math should be taught: by building concepts from basic ideas, proving everything as you go, and with myriad examples of how these things show up in practice. The best example from EE20N is the discussion of how amplitude modulation works, something that should be an immediate reference for anyone who's ever used a radio!
Now that I've said all of these things, I'm not sure where I intended to go with this post. Maybe I meant to make the point that math education is sorely in need of fixing, particularly in primary and secondary schools. It's sad that people lose interest in a subject that is so inherently interesting because it and its applications describe everything in the world around us, and I hope that at least one person who reads this has their eyes reopened to the subject through thinking about what I've written here.