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MATTHEW PATE | Reality folding in on itself

One of my favorite periodicals is Smithsonian magazine. Like the museums it represents, Smithsonian is a wonderful collection of art, culture, history, science and considered thought. More often than not, a flip through the pages (or the website www.smithsonian.com ) leaves me both entertained and informed. This month’s issue was no exception.

Being too lazy to go downstairs and fetch the magazine off the kitchen table, I pulled up the website and saw something remarkable. Nicole Pannuzo, a graduate student at Arizona State University, has designed a rather remarkable new type of toothpaste tube. Built on principles of the Japanese paper folding art, origami, the tube neatly collapses along spiraling folds. This design answers the age old question of how to get that last little bit of toothpaste out of the bottom.

So maybe this isn’t a cure for cancer, but it’s a very elegant idea. Moreover, it’s an appropriation of techniques that have already found their way into the likes of automobile airbags and spacecraft. Just as transistor radios of the 1960s did, it builds on the apparent Japanese knack for elegantly cramming something large into a very small space.

Origami for most Americans means paper cranes and flowers. These simple models are something we might teach a child how to make. That oversimplification betrays the beautiful complexity and utility that is origami. Even a little study of origami provides all kinds of useful ideas both about nature and the built world.

Perhaps the biggest idea contained in the paper folds is fractal geometry. To describe them in the crudest, non-mathematical way, fractals are patterns that repeat (sometimes indefinitely) at greater and greater scales. They exhibit what is called “self-similarity.”

Peter Engel’s insightful book, Origami: Angelfish to Zen, demonstrates this property in origami models. Engel shows three pages of unfolded models. There are two dozen square diagrams with crease lines that depict growing, self-similar patterns.

If you want a much more “mathy” study of fractals turn to Matila Ghyka’s book, The Geometry of Art and Life. Here you’ll get the bigger picture, namely that the entirety of existence, from the DNA helix to galaxies all exhibit a fractal self-similarity. Snowflakes, cat’s paws, maple leaves, the Great Pyramid at Giza and your own body all contain structure that can be described using fractal geometry.

This brings us back to the Smithsonian website. Another article in the current offering contains winners from the Wellcome Image Awards contest. These are images from science and medicine that explore, “the meaning of medicine, its history and current practice.” These highly detailed pictures demonstrate all that has been discussed here: namely, that there is an obvious ordering of things.

Of course the discerning of order often requires the proper vantage and vocabulary. What looks like chaos and randomness at one level may actually be a well-ordered and predictable system. As is turns out most stable systems actually contain a bit of chaos. Our own social world is evidence of that. We don’t all march in lockstep. We have crime, revolution and disease. Some pull. Some push. Some go with the flow. Like the origami toothpaste tube, finding that perfect flow somehow makes life seem just a tiny bit better.

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