erasing clouds

Book Review: Mario Livio's The Golden Ratio

by david kraut

Subtitled “The Story of Phi, The World’s Most Astonishing Number,” Mario Livio’s The Golden Ratio may initially strike browsers as a two hundred-fifty page oxymoron. After all, for most non-mathematicians, numbers surround us and perhaps represent noteworthy features of other things (prices, ages, batting averages), but rarely astonish us on their own. Yet Livio, an astrophysicist and cosmologist, brings this particular number to life and into our lives, showing even the most math-phobic of readers that “mathematics is, in some sense, the language of the universe.” The most impressive feat of the book, however, is how it shows that whether we’re aware of it or not, it is a universal language in which most of us are already fluent.

The book explains Phi’s astonishing qualities by chronicling its discovery and use. Just as much a biography of the number as an explanation of its importance, The Golden Ratio illustrates each fascinating aspect of this “most irrational” of irrational numbers with stories of the people who worked with it over the years. From the ancient Egyptians to current computer scientist Steven Wolfram, Livio illuminates a broad spectrum of individuals who may have discovered or employed various properties of Phi. He brings the reader into the agora with Plato, Euclid and the Pythagoreans, behind the lens of Kepler’s telescope, into the workrooms of Descartes and Fibonacci, inside Newton’s cramped cloister cell, and among the works-in-progress of Durer, DaVinci, DeBussy and Bach.

Like Pi, Phi is known to thousands of decimal places, but for the purpose of enjoying this book the approximation 1.618… suffices. If you divide one number by another and the quotient is 1.618…, then the two numbers are said to be in “the Golden Ratio.” This particular relationship between two values is found in an astounding number of natural forms. Pineapples, pinecones, sunflowers, planetary orbits, and the chambered nautilus (showcased on the book’s cover) all display Phi in some way. With this in mind, it is no wonder that human-made forms incorporate the ratio as well. Ever imitating life, art through the ages has reflected this mysterious relationship.

While Livio presents the possibility of great artists, architects, musicians and poets intentionally designing works around Phi, he consistently and vehemently reminds readers that such associations are most often forced onto pieces of art by those who he calls “Golden Numberists,” or people obsessed with Phi and determined to prove its universal presence and potential for application. He carefully points out, however, that many artists have cultivated a deep interest in the Golden Ratio which prompts him to wonder, “Does this ratio…truly contain some intrinsic, aesthetically superior qualities?”

Like most good work, Livio’s book raises more questions than it purports to answer. For example, if these artists did not intentionally incorporate Phi into their work, but many of their highest quality pieces coincidentally reflect the proportion (or something very close to it), does that imply that superior artistic quality is connected to Phi on some level that the artists themselves are not in touch with? Does Phi exist as an objective reality, or is it a human creation ascribed to what we perceive as real? Similar questions can be (and have been) asked about Pi, resulting in just as frustratingly hazy conclusions. Answers elude us because they are questions about the relationship between humans and their place in the universe, a relationship that may or may not be expressible in terms of any language.

The Golden Ratio shows us that the language of mathematics is infused into our world. If we enjoy the sight of a field of sunflowers or the sound of Bach’s Suites; if we investigate empty mollusk shells on the beach, poking around in there to see where the spiral goes; if we can’t avert our eyes from the Mona Lisa’s face and aren’t sure why; if we live in a culture that designed its most important building in a pentagon, the most “Golden” of shapes; we may well be conversing in a language so ingrained into our being, so buried in our evolutionary history that we do not even realize it exists. This well-written and highly enjoyable book alerts us to the presence of that language and the degree to which it pervades our existence.

{Broadway Books, 2002}

this month's issue
about erasing clouds

Copyright © 2005 erasing clouds