Novelist and math professor Manil Suri penned a lovely op-ed yesterday advocating studying math for the beauty of the experience, as one might take a course in music appreciation or enjoying art.
“As a mathematician, I can attest that my field is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall. Perhaps the most intriguing of these is the way infinity is harnessed to deal with the finite, in everything from fractals to calculus. Just reflect on the infinite range of decimal numbers — a wonder product offered by mathematics to satisfy any measurement need, down to an arbitrary number of digits.”
Even though I’m hardly any wiz at math (he would likely furrow his brow at the phrase), it was mostly my favorite subject, and I took a lot of it, somewhat to the surprise of my journalist parents. What caught my interest were just these interesting and sort of unfathomable ideas, but which you could work with despite not being able to “get your head around them.” Suri mentions infinity, and my elementary school apprehension (in both senses of the word?) that you could just “keep going” out there in whole numbers without ever stopping was amazing. Later, realizing that there was an infinity “in between” any two fractions–getting smaller and smaller and smaller–was also head spinning, and even later that it was possible to talk about sizes of different infinities, some were bigger than others, well, that one still keeps me going.
Another idea, picked at random, was n-dimensional space, which a teacher or a book simply illuminated for me as adding more coordinates to the plane old Cartesian grid provided that same fizzy head spin. Two coordinates get you up and over, three (z) adds dimension “out”, the fourth maybe time, but no reason to stop there, even though we can’t visualize (or at least I can’t visualize) past four, you can have 9-dimensional space, it’s a coordinate grid where a point is described by 9 coordinates.
It’s all wonderful ideas once you get past the paperwork: non-Euclidean geometry, about which I wanted to write a play in college (didn’t). And then there is catastrophe theory, the subject of an intriguing little book, Mathematics And the Unexpected, by Ivar Elkund, which I only half-understood, but that engrossed me totally. (It had a Bruegel on the front cover, keeping with the theme of art and mathematics that Suri started with.)
Recently there was a post about catastrophe theory by Steven Strogatz, a math blogger for the NYTimes who wrote about it as applied to, among other things, sleep. I’ll let him explain it and leave you with an intriguing animation from his article, demonstrating why things that seem to be working in an orderly, predictable way based on clear rules, can have unexpected outcomes.
As one of the comments on Strogatz’ blog post puts it:
“Easy to see why Mathematicians fall heads-over-heels in love with their subject.”
A Few Reasonable Words 