Fractals

Posted on Thursday 17 April 2008

This morning after my Thursday Iron Men study class I raced over to Greathouse Elementary School to meet Cyndi and climb on board one of her charter buses headed toward Lubbock. Last year Cyndi applied for and received a grant from the MISD Education Foundation to take all three 5th-grade classes from Greathouse to the Science Spectrum, and she invited me to come along as an additional adult sponsor. I told my morning study guys three things about the day: (1) the good thing about being self-employed is that I can go with Cyndi on a field trip; (2) the bad thing about being self-employed is that I am always on-call to help supervise a bus full of 5th-graders; and (3) if I am still standing up in front of the study group at 7:25 AM, keep me out of dutch with the misses and tell me to leave now so I won’t make the entire field trip start off late.

In truth, I enjoy watching Cyndi and her fellow teachers, Patty and Pam, do what they do. I like to watch them teach and corral small kids because they are so good at it and I know I will learn something from watching them.

When they tell stories about teaching, it is always about how hard it is or how they have to administer yet another standardized test or about some particular young hoodlum who snuck into their class pretending to be in the 5th grade. I like hearing their stories because I like them as people and I want to explore their lives, but watching them in action is better still.

I always learn something useful and worthwhile whenever I observe an expert practicing their craft – and that is true whether the craftsman is a teacher or an engineer or a carpenter or a drummer or a stand-up comic.

Now, I know my three teachers are rolling their eyes even as they read my assessment of them as expert craftsmen, but don’t we all do that when complimented? None of us are very good at seeing how well we use our natural strengths. Our talents are so natural to us we forget that everyone else can’t do the same thing, and we tend to make light of what we do best.

Well, back to the Science Spectrum – one of my favorite exhibits was a small computer display that could draw fractals based on user input. The most beautiful group of fractals were Mandelbrot Sets. I first learned about fractals back in 1988 when I read a math book by James Gleick titled: “Chaos, Making a New Science,” and I’ve been fascinated by them since. It is amazing to me how math equations can begin plotting what appears to be random data, and then after hundreds of thousands of iterations, produce beautifully intricate and complex images.

The most fascinating thing about fractals is their complexity. If you take a small portion of a Mandelbrot Set and enlarge it, the resulting image will have the same detail and complexity as the original. And if you zoom in again on that enlarged portion, the new image will be just as complex. And over and over – the same level of complexity and beauty no matter how close you look. This property is known as self-similarity.

Contrast that to a sphere. The closer you look at a sphere the less complex it gets. If you keep zooming in toward the surface of a pool ball, for example, the three-dimensional sphere will begin to resemble a two-dimensional plane. It becomes less complex and less detailed the closer you look.

We don’t want to be people like that. We don’t want to be the sort of person who loses complexity and detail and beauty when someone looks at us up close.

I hope we are the sort of people who look the same no matter how close someone looks. I hope we are self-similar. I hope the peace and love and joy we wear on the surface looks just as good up close - way, way up close – as it does at a distance. I hope we are the sort of people who can live transparent and vulnerable lives, lives that show the heart of Jesus no matter how close anyone looks.

Well, in fact, I had a great time today with the 5th-graders. My sponsor duties were simple: stand wherever Cyndi put me and look friendly and helpful and scary and authoritarian all at the same time. One young man who didn’t know who I was, asked me, “Who are you, the police?”

I said, “No, I’m The Man. Don’t stick it to me.”

Being two generations too young to remember the sixties he didn’t know what I meant, but he stayed in line and stopped punching his neighbor.

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