The Fractalist: Memoir of a Scientific Maverick, Benoit B. Mandelbrot, Pantheon Books, 2012. $30.00 (352 pp.). ISBN 978-0-307-37735-7
Before I first talked to Benoit Mandelbrot, my impression of him was shaped by reading his epic book, The Fractal Geometry of Nature (W. H. Freeman, 1982), which is not only ambitious and revolutionary, but formidable and serious. His memoir The Fractalist: Memoir of a Scientific Maverick reflects the man I spoke to, a man enjoyed by his colleagues, friends, and mentees. It paints the picture of a man who was cultured, humorous, open-minded, and reflective.
Memoirs that look back on long and eclectic lives are often several books strung together, each capturing a distinct phase of the author’s journey. Born in 1924 and still putting the final touches to his memoir when he died in 2010, Mandelbrot divided his 86-year tale into 3 parts. The reader doesn’t need to have a specific interest in Mandelbrot or his research to enjoy each part. His experiences serve as windows into history, and his life’s trajectory reveals how an influential career took shape.
In part 1, “How I Came to Be a Scientist,” Mandelbrot begins with his childhood in depression-era Warsaw, Poland, and takes us through his experiences as a teenager in France during its occupation and liberation. Mixed in with his amazing adventures of escaping the Nazis, he tells of his early combat with mathematics: “I always started with a quick drawing…. This playful activity transformed impossibly difficult problems into simple ones. The needed algebra could always be filled in later.” His childhood preference for pictures over equations emerged from a family talent for freehand drawing and went on to fuel his later discoveries of patterns in nature.
Part 2, “My Long and Meandering Education in Science and in Life,” maps out an erratic early career spent criss-crossing from Paris to Caltech and back. Mandelbrot aspired to be a modern-day version of his hero, Johannes Kepler, by discovering “a degree of order in some real, concrete, and complex area where everyone else saw a mess.”
Searching for major interdisciplinary challenges to conquer, Mandelbrot was painfully aware that some colleagues and relatives never forgave him for apparently squandering his mathematical talent on practical problems. How did he weather such criticism? “A blessing throughout my life: I never wonder who I am.” Unrepentant about his quest to merge different fields, he came to accept that “scientific purists fear a new alloy.”
Mandelbrot begins part 3, “My Life’s Fruitful Third Stage,” with his midlife-crisis move in 1958 to IBM’s research division in Yorktown Heights, New York, and takes us through to his twilight. “I remember these years [1958–93] as a golden age—for IBM, for me, and for the sciences,” he writes. “Let me go further, raise my voice and add: and also for the human spirit.”
His adventure into fractal exploration began with a chance discovery. Invited to give a talk at Harvard University on patterns he’d explored in people’s income, he saw a similar pattern in cotton price variations sketched on his Harvard host’s blackboard. How could those two patterns be so similar? Soon after, he saw analogous patterns in the rise and fall of the Nile River and in the meandering coastline of Great Britain. By spotting the universal character of nature’s patterns, he arrived at his “Kepler moment.”
In 1975, Mandelbrot made his first attempt to catalog the rapidly expanding number of similar shapes found in nature by publishing a book with the tentative title, Concrete Objects of Fractional Dimension. A colleague advised him to liven up the title, so he introduced the term “fractal,” which has since spread through many disciplines.
The title of one of his closing chapters lists the disciplines he journeyed through: “On to Fractals: Through IBM, Harvard, MIT, and Yale via Economics, Engineering, Mathematics, and Physics 1963–64.” He acknowledges that “this chapter title seems to make no sense… . Very often when I listen to the list of my previous jobs, I wonder if I exist. The intersection of such sets is surely zero.” When describing how his opportunistic character allowed him to cover such diverse ground, he cites Louis Pasteur’s observation that chance favors the prepared mind. “Halfway through each discovery … I experienced a marvelous and exhilarating surprise” that triggered the next adventure.
Mandelbrot wrote The Fractalist to understand himself, so he deliberately waited until his final years to do so. “You have heard my story. Does not the distribution of my personal experiences remind me of the central topic of my scientific work—namely, extreme fractal unevenness?” We can all learn from the fractal unevenness found within these pages.
Richard Taylor is a professor in the department of physics at the University of Oregon. He conducts research in experimental condensed-matter physics and biophysics and also studies fractals in the visual sciences and the visual arts.
