The more you learn about something, the more detail reveals itself. It’s a bit like walking down a single path of a fractal pattern. Wherever you go, no matter how much you know, new branches open up before you. Within every little thing is an infinity of discovery.
It’s one of the reasons why I don’t accept, “It’s boring,” as an excuse for not wanting to do something. Boredom is when you don’t use your imagination. You can never get bored because of all of the interesting things in world.
To see a world in a grain of sand,
And a heaven in a wild flower,
I still have not tried my fractal writing exercises, but I think I’ll try to work one into the next cycle. Perhaps start with describing a tree, then a leaf (or a section of bark), then cells under the microscope.
Or perhaps a better subject, since we’ll be looking at organ systems, would be a fish.
Mathematics is the language of science. Scientists refine and refine their observations of the complexity of the natural world and try to boil these complex observations down to simple relationships, relationships that are expressed in mathematics. This, I think, is part of the human condition. Our brains are designed to extract simple relationships, heuristics, rules of thumb, from the observations of our senses. It is why Einstein’s equation, E=mc2, has captivated our imagination for so long, why physicists struggle to find the unified theory, and why fractals are so fascinating.
Cristóbal Vila’s short video (found via The Daily Dish) captures some of the magic of the relationship between mathematics and the world.
A few of my students have been complaining that we don’t do enough different things from week to week for them to write a different newsletter article every Friday. PE, after all, is still PE, especially if we’re playing the same game this week as we did during the last.
So I’ve been thinking of ways to disabuse them of the notion that anything can be boring or uninteresting in this wonderful, remarkable world. A world of fractal symmetry, where a variegated leaf, a deciduous tree and a continental river system all look the same from slightly different points of view. A counterintuitive world where the smallest change, a handshake at the end of a game, or a butterfly flapping its wings can fundamentally change the nature of the simplest and the most complex systems.
“Chaos is found in greatest abundance wherever order is being sought. It always defeats order, because it is better organized.”
— Terry Pratchett (Interesting Times)
There are two things I want to try, and I may do them in tandem. The first is to give special writing assignments where students have to describe a set of increasingly simple objects, with increasingly longer minimum word limits. I have not had to impose minimum word limits for writing assignments because peer sharing and peer review have established good standards on their own. Describing a tree, a coin, a 2×4, a racquetball in a few hundred words would be an exercise in observation and figurative language.
To do good writing and observation it often helps to have good mentor texts. We’re doing poetry this cycle and students are presenting their poems to the class during our morning community meetings. It had been my intention to make this an ongoing thing, so I think I’ll continue it, but for the next phase of presentations, have them chose descriptive poems like Wordsworth’s “Yew Trees“*.
