November 2, 2004
When Words and Logic Fail... Let's take five with Moira Gunn. This is "Five Minutes."
I just thought of Leonardo da Vinci's famous line drawing of the man inside both a circle and a square. You know the picture: It's a beautifully proportioned man whose arms and legs are posed in two positions: Outstretched he touches a perfect circle; with arms lowered and feet together, he fits a perfect square.
It's called Vitruvian Man, after Vitruvius, a Roman architect enthralled with the mathematics of beauty, the geometry of proportion, the ideal of the perfection of man. He used these principles as he constructed temples, and his books on architecture survived into Leonardo's time. His drawing exemplifies the specific idea suggested by Vitruvius — that a man — that ideal of perfection — could be drawn to fit into the two perfect shapes: a circle and a square.
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In truth, Vitruvius was inspired by the even earlier work of Pythagoras, yet another famous figure in the long tradition of humans trying to link mathematics, nature and beauty, which includes another Leonardo — one Leonardo Pisano, better known as Fibonacci.
He wrote extensive mathematical treatises in the early 13th century, and he is best remembered today for the Fibonacci sequence. Remember? Start by adding 1 and 1 to make 2, and then add the last two numbers in the sequence to make the next, and so on. This simple little sequence of numbers, astonishingly, can be seen everywhere in nature. From the shapes of seashells to the unfolding of petals on a flower, it appears again and again throughout the natural world.
And so I thought perhaps we might deliberately try to apply mathematics whenever we learn something new and strange — if we can find a familiar footing in the world of mathematics, perhaps we can more easily accept what is new and strange.
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Case in point is the human skeletons recently excavated from a tiny isolated island in Indonesia. Fully grown, they're only three feet tall with heads "the size of large grapefruits"¬ù and much longer arms than we would expect proportionally. While scientists are scrambling for usable DNA to establish just where in the human evolutionary trail this crowd decided to make a right turn, there is even postulation that there may still be such humans in remote and unmapped jungles.
And that's when the thought struck me — what if we find them alive? Will it be difficult to accept them as human? How can we see them as anything but alien? But what if — even with their decided differences in size and proportion — what if they could stand up to the mathematical premise of Vitrurius, if they could be drawn to fit a perfect circle and a perfect square, could we more easily see their beauty?
Let's not forget that the first drawing of a decent Vitruvian man took centuries. Many had tried it prior to da Vinci, but with only awkward, forced results. Yet the timeless beauty of Leonardo's simple drawing, with its excited hand-written notes scribbled around the borders, is undeniable. He had captured the beauty as well as the mathematics — and therein lays the mark of genius.
If we look to math to help us better accept all that is new and strange in our world, we will need modern day da Vinci's and Fibonacci's. But let's remember it's an option, especially when words and logic fail.
I'm Moira Gunn. This is Five Minutes.
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