Beauty in the rough: the mathematics of Benoit B. Mandelbrot
"The reasonable man adapts himself to the world;
the unreasonable one persists in trying to adapt the world to himself.
Therefore, all progress depends on the unreasonable man"
- George Bernard Shaw
It was not long after publishing a review of Nassim Nicholas Taleb's Antifragility — who called Mandelbrot "his mentor" until the mathematician recently passed away —, that I became interested in the peculiar story of a man who may be the single most influential pluridisciplinary scientist on matters pertaining to collaboration, probability theory and complexity of the late 20th and early 21st century.The Fractalist: Memoir of a Scientific Maverick is his autobiography.
An education like no other
Born in Warsaw in 1924 of Jewish parents, Mandelbrot has had a childhood that could be best described as unstable, moving from Warsaw to Paris, to Tulle, to Lyon, with an education split between various institutions of varying degrees of thoroughness. That such an unusual start would see the rise of a great genius is, in itself, a surprise.
After the war, Mandelbrot returned to Paris where, under guidance from his uncle Szolem — also a famed mathematician chaired at the Collège de France — he entered exams for Polytechnique and École Normale Supérieure, and was received as "the best math student in the country that year" at both schools.
An outlier in his own right
A maverick, Mandelbrot's book describes how he chose a path of dissent and marginality, exploring the boundaries of various disciplines that shocked his peers, colleagues and the institutionalized research establishment in which he navigated.
From the onset, the mathematician's obsession with roughness, irregularities and long-tail distributions led him to a variety to research areas, covering issues ranging from language (on words' decreasing frequency as rank increases being logarithmically linear), to finance (on the evolution of prices following a 'stable Paretian' probability law), coastlines (nature-induced fractal "roughness"), to visual arts and music.
After receiving his PhD in the late 50s, Mandelbrot was recruited by IBM Research, where he held a permanent position for thirty years, eventually being made an Emeritus Fellow. Along the path, Mandelbrot worked with many other prestigious scientists, including John von Neuman, Paul Lévy, Jean Piaget, lecturing in prestigious institutions like Harvard, MIT and Yale, where he finally took a tenured professorship.
In the academic circuit, he jumped from one discipline to another, a feature that led him from being dropped out of appointment opportunities alternatively for "lack of focus" or, inversely, for "working on problems too-narrowly defined".
"In fact, a common thread of my work is that values far from the norm are the key to the underlying phenomenon. In many fields, I remained far from the norm, so in that way too I am an outlier", he writes.
It is never too late
Most stunning is the fact that contrary to the majority of scientists, Mandelbrot's major findings weren't published before his 40s and 50s — his most significant lifetime achievement, the Mandelbrot Set, dawned on to him at age 55. He was intellectually active well into his 80s, and wrote "The Fractalist" a few months before his death. He made an entire career taking advantage of "special resources that had become available in one corner or another of a very large institution", he writes, always in the interstitial spaces between academic monoliths.
The book encapsulates a story over two continents, encompassing nearly a full century of scientific, sociologic and economic change. In the last pages of the book, under what he calls the "Balzar-Bohr-Bialik Syndrome", Mandelbrot describes his own creative process, a chaotic, nearly random method of investigation, fed by poor handwriting.
"The result is seen best after it is set in type. It then becomes subjected to a mental process that resembles metallurgical annealing […]. In metaphorical annealing, type reveals unsuspected relationships between words, phrases, paragraphs or chapters. Once I can see these, I am able to adjust them as needed. The paper becomes a new crucible for creativity, a crutch for lesser Mozarts"
And so, with a glimpse of amazing surprise, great ideas emerged, in an instant, but such chance, like Louis Pasteur famously wrote, favours only the prepared mind.
Clearly, from the bottomless wonders of simple mathematical rules repeated without end, Mandelbrot's fractals have opened up a new field, new possibilities, that the prepared and enthusiastic mind may chose to seize, as outsiders, outliers, or "scientific mavericks".
Images: Fractal Science Kit, Balzac's second draft of "Les Employés".