Random Ramblings

Back in 1999, when my dear sister Melissa was diagnosed with Leukemia and in her honor I had dedicated myself to train for a century bike ride with the Leukemia Society to raise funds for the foundation. I put together a donation mailing package which included an origami swan. The symbol of the swan originated from Japan where a young girl was stricken with the cancer and started folding swans as therapy. After she had passed, thousands of people folded swans in her honor for the message of hope. My co-worker than, Zepha, had mentioned she had known of a person who is able to demonstrate and solve mathematical equations by the art of origami. This information and concept was interesting and was filed away in my gray matter.

Fast forward to July, 2004. TheaterWorks, a local regional performing theater opens its house to the public for dress rehearsal. On this day, they were showing Arcadia by Tom Stoppard. In the play, it introduces fractal geometry, second law of thermodynamics, chaos theory. The play is set in two time periods, the 1800's and the present. Thomasina, a thirteen year old, is a mathematical genius far ahead of her time. Septimus, her tutor encourages her to work on a solution to Fermat's last theorem.

Each week I plot your equations dot for dot, xs against ys in all manner of algebraical relation, and every week they draw themselves as commonplace geometry, as if the world of forms were nothing but arcs and angles. God's truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose? Do we believe nature is written in numbers?

She later on wrote in her workbook:

I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone.

Now in the present, a mathematician Valentine discovers Thomasina workbook and profuse enthusiastically about the mathematical chaos theory.

The math isn't difficult. It's what you did at school. You have an x and y equation. Any value for x gives you a value for y. So you put a dot where it's right for both x and y. Then you take the next value for x which gives you another value for y......what she's doing is, every time she works out a value for y, she's using that as her next value for x. And so on. Like a feedback....If you knew the algorithm, and fed it back say ten thousand times, each time there'd be a dot somewhere on the screen. You'd never know where to expect the next dot. But gradually you'd start to see this shape, because every dot will be inside the shape of this leaf.

Further more, Val goes on to explain the chaos theory, where random events intervene to shape lives. Nature is written in numbers.

If you knew the algorithm and fed it back, say, ten thousand times, each time there'd be a dot somewhere on the screen. You'd never know where to expect the next dot. But gradually you'd start to see this shape, because every dot will be inside the shape of this leaf. It wouldn't be a leaf, it would be a mathematical object. But yes. The unpredictable and the predetermined unfold together to make everything the way it is. It's how nature creates itself, on every scale, the snowflake and the snowstorm.

Then onto September 17, 2004, I came across this post by Ivan on his CreativeBits weblog. (BTW, this is a weblog I read everyday.) He wrote about the Fibonacci's numbers, which lead to the famous Phi number and the golden mean. The theory of the Golden Ratio explains how nature works. The rules and laws that govern growth. You will never look at artichoke the same way again.

Everything in our universe, such as the shape of hurricanes, the way the trees grow, the way the petals are arranged in a flower and even the structure of the human skeleton are all arranged by the golden means.

This last weekend, I went to the Belmont Art Festival, it was rather paltry. I was stumbling around the community center and came upon a local artist gallery. They were exhibiting Counterparts: Art from Mathematics on, you guess it, number theory! It featured three artist: Dale Seymour, Nancy Macko, and Robert Lang.

Dale Seymour's work brought together the amazing patterns and the relationships in math by using geometric forms: tessellations, polyhedral, the golden ratio. Nancy Macko presented two versions of The First Ten Prime Numbers, images about the building block of mathematics. Robert Lang, now his was of interest. He made geometric origami from a single-sheet of paper without cutting. This is the Golden Ratio explained through origami. Zepha, you are so right.

Now, I've always had a skill to pick up and decipher patterns rather effortlessly. I've always love to look at patterns for its art form, but nothing ever was put to me so scientifically. This was a theory that I've practiced and performed in everyday life but never before explained, understood, or looked at in a scientific way.

Poles apart, yet inseparable, art and mathematics are the Oscar Madison and Felix Unger of world culture. Mathematics is "counterpart" to art in both senses of the term: something that closely resembles something else, something that is a natural complement to something else. Patricia Albers, curator

Thanks to all for a lesson learned.

To read more about Arcadia and it's mathematical ideas visit this website.

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