The Island of the Colorblind

(Another unique cycad, a female Ishi, Cycas multipinnata, has recently been found in a temple garden in China; no other specimens are known to exist. It is portrayed, with others, in a set of postage stamps issued in May 1996, commemorating cycad species native to China.)

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In the northern part of Guam, there is a tropical dry forest, dominated by cycads; in Rota the cycad forest is wetter, ‘mesic,’ though not true rain forest such as one sees on Pohnpei. The last few years have seen the destruction of Rota’s unique forests on a fearful scale, most especially with the building of Japanese golf courses. We encountered one such development as we were walking through the jungle – huge bulldozers tearing up the earth, mowing down an area of several hundred acres. There are now three golf courses on the island, and more are planned. Such clear-cutting of virgin forest causes an avalanche of acidic soil into the reef below, killing the coral which sustains the whole reef environment. And it may break up the jungle into areas too small to sustain themselves, so that within a few decades there will be a collapse of the entire ecosystem, flora and fauna alike.

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Chamberlain, in The Living Cycads, described how he estimated the age of a Dioon edule, which reaches maturity (in the wild) around the age of fifty, and then puts out a new crown of leaves every other year on average. By counting the number of leaf scales on the stem, and dividing by the number of leaves produced each year, he arrived at the age of the tree. He described one beautiful specimen which, by this criterion, was 970 years old, even though less than five feet in height. Indeed, Chamberlain wondered whether some cycads might approach the sequoias in age.

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The cones of cycads vary in character and shape and size: the vast cones of Lepidozamia peroffskyana and Encephalartos transvenosus may weigh more than a hundred pounds, and the cones of the smallest Za-mias no more than thirty milligrams. But all of them exhibit, in the arrangement of their cone scales, intricate geometric patterns similar to the corkscrew spirals or helices we see in pinecones, the leaf arrangement of cylindrical stems, or the whorling florets of sunflowers. The study of these patterns, this phyllotaxis, has intrigued botanists and mathematicians for centuries, not only because the spirals themselves are logarithmic, but because there are numbers of accessory helices (or parastichies) running in the opposite direction and these two sets of helices occur in a fixed ratio to one another. Thus in cycad cones, as in pinecones, we almost always see spirals in five and eight rows, and if we express as fractions the number of parastichies, we find a series of 2⁄1, 3⁄2, 5⁄3, 8⁄5, 13⁄8, 21⁄13, 34⁄21, and so on. This series, named after the thirteenth-century mathematician Fibonacci, corresponds to a continued fraction which converges to 1.618, the numerical equivalent of the Golden Section.

These patterns probably represent no more and no less than an optimum way of packing leaves or scales together while avoiding their superimposition (and not, as Goethe and others thought, some mystical archetype or ideal), but they are a delight to the eye and a stimulus to the mind. Phyllotaxis fascinated the Reverend J.S. Henslow (professor of botany at Cambridge, and Darwin’s teacher), who discussed and illustrated it in his Principles of Descriptive and Physiological Botany, and it is pondered at length in an eccentric (and very favorite) book, D’Arcy Thompson’s On Growth and Form. It is said that Napier’s discovery of logarithms at the start of the seventeenth century was stimulated by a contemplation of the growth of horsetails, and the great botanist Nehemiah Grew, later in the century, observed that ‘from the contemplation of Plants, men might first be invited to Mathematical Enquiry.’

This sense of the mathematical determination (or constraints) of nature, especially of organic form and growth, divested of idealism or idiosyncrasy, is very strong now, especially with the development of chaos and complexity theory in the last few decades. Now that fractals are, so to speak, part of our consciousness, we see them everywhere – in mountains, in landscapes, in snowflakes, in migraines, but above all in the vegetable world – just as Napier, four centuries ago, saw logarithms in his garden, and Fibonacci, seven centuries ago, found the Golden Section all about him.

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