`Give a Name to Its Harmony'

Dedicated readers develop sub-genres of interest among the books they read. For example, I enjoy biographies of mathematicians. I’m strictly a hobbyist, and reading about Euler, Riemann and Ramanujan is a recreation like solving math puzzles. For fifteen years, Amir D. Aczel has been entertaining dilettantes like me with such titles as Fermat's Last Theorem and The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity. His latest book is A Strange Wilderness: The Lives of the Great Mathematicians (Sterling, 2011), and in a chapter titled “Italian Shenanigans” he writes about one of my favorites, Leonardo of Pisa, better known as Fibonacci (c. 1170 – c. 1250), who lent his name to a number sequence, the Fibonacci numbers.

Starting with 0 and 1, each number in the sequence is the sum of the previous two numbers. Thus: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, and so on. Aczel notes: “As it turns out, the ratio between each term and its predecessor approaches 1.618…, the golden ratio, which appears commonly in nature and art.” More than a tedious parlor game, the Fibonacci numbers suggest, at least to non-mathematicians, the presence of design principles in the universe, perhaps one of nature’s structural default modes. The notion, I know, appealed to Guy Davenport, from whom I first heard of Fibonacci almost forty years ago in “The Dawn of Erewhon,” the final story in his first collection, Tatlin! (1974):

“The Fibonacci number following thirty-four is fifty-five. A set of thirty-four helix curves radiating from a common center clockwise crossing a set of fifty-five helix curves rotating counterclockwise from the same center gives the finely meshed honeybrown redgold spiral net panier of the Grote Zonnebloem, Helianthus annuus.

“Adriaan had one on his desk, others in a wicker basket at his feet. If one spiral is a rotation of thirteen helices, then the counterspiral is twenty-one. Fibonacci, both. And he [Fibonacci] had brought the ancient Indic naught, the Arabian number unoccupied by quantity, to be our zero.

“Fibonacci harmonies ran through the pinecone which he kept on his table, through the snail shell.”

Helianthus annuus is the sunflower, in which each floret is positioned toward the next at an angle of about 137.5 degrees, the golden angle. This produces the pattern of interconnecting spirals described by Davenport. Botanists speculate that the arrangement results in the most efficient packing of seeds.

In his essay on the fiction of Eudora Welty, “That Faire Field of Enna” (The Geography of the Imagination, 1981), Davenport says that for the artist “event is pattern and essence melodic.” He extends the musical/mathematical metaphor:

“Art is the attention we pay to the wholeness of the world. Ancient intuition went foraging after consistency. Religion, science, and art are alike rooted in the faith that the world is of a piece, that something is common to all its diversity, and that if we knew enough we could see and give a name to its harmony.”

[Go here for an entertaining video about Fibonacci numbers in the design of pineapples, pine cones and other flora, and here and here for more discussions of the Fibonacci sequence in nature.]