Mandelbrot Makes Sense : A Book Review Essay

ers of chaos theory as it generated pictures of ever increasing complexity using a deceptively minuscule recursive rule, one that can be reapplied to itself repeatedly. You can look at the set at smaller and smaller resolutions without “ever” reaching the limit; you will continue to see the recognizable shapes. The introduction of fractals was not initially welcomed by the mathematical establishment. This method of pictorial presentation did not seem to correspond to what seemed “to be mathematics” in the selfdefining discipline. It is thanks to its popularity with physicists and other applied scientists, themselves following the lead of the general public (mostly computer “geeks”), that fractal geometry vindicated its way into the now-broadened field of mathematics. For The Fractal Geometry of Nature made a splash when it came out a quarter century ago. It spread across the artistic circles and led to studies in aesthetics, architectural designs, even large industrial applications. BM was even offered a position at a medical school! His talks were invaded by all manner of artists4, earning him the nickname “the rock star of mathematics”. The computer age thus helped him become one of the most influential mathematicians in history, in terms of the applications of his work, way before his acceptance by the ivory tower. We will see that, in addition to its universality, his work possesses an unusual attribute: it is remarkably easy to understand. A Polish-Lithuanian Jew who found refuge in France as a child, BM is also a refugee from the French mathematical establishment protective of the “purity” of mathematics. To borrow from the late probabilist and probability thinker E. T. Jaynes (a man who went deeply into the subject), it was said that “the French did quite useful mathematics before Bourbaki” – as the secretive guildlike organization installed a truly top-down view of the subject matter, insuring no corruption by earthly material. Indeed many physicists have been horrified at the extent and side effects of such purism, with Murray Gell-Mann calling it the “Bourbaki Plague”, and attributing the divergence between pure mathematics and science to the obscure language of the Bourbakists5. In a way, the separation between geometry and algebra can be seen as the separation of images and words in human expression and thought – just imagine a world in which images were barred. The Bourbakiinspired purblindness does not just limit the tools of analysis. Just like blindness, one of its effects is to reduce contact with reality. Platonic top-down approaches are interesting but they tend to choke under the occasional irrelevance of their pursuits. It is telling that BM’s hero is Antaeus, son of Gaia the mother Earth, who needed periodic contact with earth to replenish his strength. Owing to the vicissitudes of a clandestine life during the Nazi occupation of France, the young Benoit was spared some of the conventional Gallic education with the uninspiring algebraic drills, becoming largely self-taught with some assistance from his uncle Szolem, a prominent member of the French mathematical hierarchy and professor at the College de France. Instead, he developed an encyclopedic knowledge of the history of mathematical thought. He also gave free course to his geometric bent. Untrained in the usual equation solving techniques, he passed the entrance exam to the I closed this book feeling that it was the first book in economics that spoke directly to me. Not only that, but the astonishing simplicity, realism, and relevance of the subject makes it the only general work in finance I’ve ever read that seemed to make sense. Benoit Mandelbrot makes sense. Just as he used us common readers outside the ivory tower to force his fractal ideas into science (where they became “part of the scientific consciousness”1); he may just be the one to help turn economics into something real. This first essay is non-technical and general2 (i.e. can be read by someone without a mathematical background) and focuses around the topics covered in this book. The second one is more technical and it goes deeper into the epistemological problems of “fat tails”, concentration, and extreme events. What do fern leaves, commodity prices, computer book sales, income distribution, the coast of Britain, cauliflowers, and the intricacies of the vascular system have to do with one another? Mandelbrot’s work revolves around the simple practical application of a concept called “fractal” in replacement for more complicated mathematical tools that are universally used without empirical justification. Triangles, squares, circles, and other geometric concepts that caused many of us to yawn in the Mandelbrot Makes Sense: A Book Review Essay A discussion of Benoit Mandelbrot’s The (Mis)Behavior of Markets by Nassim Nicholas Taleb