Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas

COINCIDENCES, CHAOS, AND ALL THAT MATH JAZZ: MAKING LIGHT OF WEIGHTY IDEAS by Edward B. Burger and Michael Starbird W. W. Norton and Company, 2005, 276 pp. ISBN: 0-393-05945-6 Come on, babe, We 're gonna brush the sky; I betcha lucky Lindy Never flew so high 'cause in the stratosphere, How could he lend an ear To all that jazz? ("Velma," All Thai Jazz, from Bob Fosse's musical Chicago; Marshall, 2002). Mystery, curiosity, chaos, beauty, jazz music, and - math? Yes! Like Velma, Burger and Starbird invite their audience on a whirlwind tour of a world not often seen by the average individual. In this case, it is the world of truly jazzy mathematical ideas that reveal often astounding patterns and truths. But readers, unlike Lindbergh in the song above, will soar through the stratosphere of fun and fascinating facts and concepts while attuning their ears to the earthly mathematical riffs that underpin our abilities to make our planes and our imaginations fly, swoop, and barrel roll through the universe ... and maybe even beyond. First and foremost, while maintaining a lighthearted, humorous, and extremely accessible sense about the beauty and wonder of mathematics, Burger and Starbird do an excellent job of instructing the reader about how fundamental concepts produce startling observations. Readers learn how small variations can result in chaos; about Fibonacci numbers and nature; what a big number really is; fractals and art; cryptography; the fundamentals of computing; the transcendence of the fourth dimension; and many other fascinating mathematical concepts. In their Opening Thoughts (preface), the authors state: Many people think mathematics is the mechanical pursuit of solving equations. In truth, mathematics is an artistic pursuit .... But no-one should be fooled into believing that the lighthearted tone implies that we are not pursuing lofty goals. Within these pages is authentic mathematics, often of a rather advanced kind, but presented in a way that enlists the help of our (and your) everyday experiences, (p. viii) It is the lofty goals of engaging and educating the reader that the authors do achieve, early and often. By the end of Chapter One, I was convinced that math is fun. I wanted to learn more - and soon became convinced that I had been taught mathematics in the wrong way my entire academic life! As a developmental/educational psychologist, I couldn't help but wish that teachers would use the examples set forth in this book to introduce children in the third grade to the fascination of Fibonacci pineapples, coneflowers, and golden ratio rectangles. These ideas are very engaging and could be easily taught to young children, providing ideal opportunities for hands-on discovery learning activities that could be completed in cooperative groups. The noted developmental psychologist Jean Piaget [3] (and many others - e.g., Gelman and Gallistel [1] - who have since expanded, tested, and refined Piaget's initial theories) has shown quite convincingly that children's cognitive development prospers most from concrete activities that are sensorimotor in nature. …