A complex lesson from simple shapes

FLOWERS - of a sort - can bloom from the mathematical mind. My son, whose favorite subject is math, wrings petals from paper by practicing origami, the ancient, Oriental art of paper folding. Given enough paper and time, he can make a garden of intricate shapes. It is the complexity of the art that he loves: a hundred folds for a single design is not uncommon. The result is a wondrous mix of clarity and clutter, a paper knot in the form of a rose, perhaps, or a daisy, a creation that seems light and whimsical, the intricacy relegated to accordion folds hidden away.

I love to watch Matt create the designs under his desk lamp. A yellow glow spills on hands and paper while a familiar shape, a cat or a daisy, emerges. But the concept - this love of complexity - chafes somehow. Americans are encouraged to admire simplicity. Most of us are Shakers at heart, though not in practice, and not sympathetically when we read Thoreau's injunction to ``Simplify, simplify.'' We are comfortable with the legends of our rough-hewn, folk past and enjoy glorifying presidents from log cabins or a computer company born in a garage. We think that the amorphous Pillsbury doughboy is cute and trust our fates to politicians who have the common touch.

But my son's touch is uncommon, though the hand is plain and looks a good deal like yours and mine, and what his hands do with paper is, despite the art's Oriental name and traditions, every bit as American as apples and pie charts. What we, as 20th-century Americans, fail to pay sufficient attention to, perhaps, are the rigors of complexity that govern our lives: our unacknowledged ability to bring many complex activities, from driving a car to writing on the computer, to the level of instinct. The fact is that we are not very good, as a culture, at being simple, no matter how hard we try. Few of us heed Thoreau and fewer still are Shakers. If being simple is a gift, it is not one of ours. What we are able to do well, I think, is quite different: We make complexity look easy.

Matt's struggle with origami teaches this lesson about the American character. He first tried to learn the art by getting a book on the subject - a bad translation from the Korean with sentences like this: ``Through the occlusion of fold `a' angles `b' and `c' emerge simultaneously.'' It was not just the instructions that were baffling; the task itself was complex and difficult. The simplest shape required 10 to 12 folds, any one of which, done wrong, turned up a donkey with two tails or a three-legged giraffe, mutants that found their way, in a wad, to my son's trash can. It is the complexity of the art that infuriated - and, at first, commanded respect.

With practice Matt learned most of what he needed to know. Eventually he met a math teacher and friend who is a member of a national origami society. She taught him the subleties of the art. Now what stuns me as I watch him whip out a turtle or a frog on command is not the complexity of the task but the ease with which the lover of it can harness such a mess and bring it under control. In origami, I have come to see, love and discipline meet, and there is boundless creative energy in the formula.

In minutes now, Matt can turn a sheet of colored paper into a bird, a donkey, or a star. No flat page in the house is safe. Like Noah's ark, his bookshelf is a zoo of birds, animals, and ``everything that creeps.'' A quick inspection turns up a dog, a swan, a camel, a grasshopper, a pig, a panda, and, of course, a dove. A snake slithers down to the next shelf, dragging with it other biblical associations, and pterodactyls - wings clipped snugly to the next shelf up - hover menacingly over the scene. Homo sapiens - a latecomer in evolution and in Matt's menagerie - makes his appearance in a baby carriage, with round wheels (a difficult feat for an origamist, I'm told).

The ancient Greeks knew a good deal about this kind of disciplined complexity. Because he saw a connection between mathematics and shapes, Pythagoras considered numbers holy. With numbers he could uncover relationships among shapes and begin to understand the intricacies that a fold could produce. Seeing that the shape we do not understand is made up of ones we do produces faith. Knowing that the sum is greater than the comprehensible parts produces wonder.

That mix of faith and wonder is what Matt takes in by the finger tips each time he tears a page out of his notebook and begins to fold. He would not put it that way, I'm sure. To him it's just ``neat.'' But to those who can't do it, it is a miracle, the kind that is found everywhere in American life: In the dribbling of a basketball, in riding a bike backward, or - well, name the American pastime and it is there.

Given the intricacies at his, and others', finger tips, it may be time for Americans to redefine simplicity. Grace under pressure, love within boundaries, freedom through form - these are the lessons Matt learns when his hand flutters over paper and a nest with an egg emerges. That is his gift. I watch his fingers produce abundantly within the constraints of his own devising; I see, in his creations, a rough draft for the geometry of lilies. In his hands it looks so simple, but it's not.

We want to hear, did we miss an angle we should have covered? Should we come back to this topic? Or just give us a rating for this story. We want to hear from you.