# Mandelbrot the Magnificent

Benoit Mandelbrot finished his autobiography shortly before he died in 2010. After some editing, it was published as a book entitled *The Fractalist, Memoir of a Scientific Maverick* in 2012 with a foreword by his wife Aliette. In that book he describes in three parts (1) his youth in prewar Warsaw and Paris and later in Tulle (France) during WW2 (2) his education and scientific life in the period 1944-1858 and (3) his life after recognition, i.e. the period 1958-2004.

Liz Ziemska is a Polish born literary agent who came to the US when she was seven. She earned a Bachelor of Science in Biology and a Master of Fine Arts in creative writing and she has written several stories that appeared in fantasy and science fiction collections. What do you think will come out as a story if she first read Mandelbrot's *The Fractalist* and then, impersonating a juvenile Mandelbrot, she would re-tell the first five chapters using the facts provided by Mandelbrot and mix these with her own fantasy? You do not have to guess because that story has been written and it is called *Mandelbrot the Magnificent*.

The facts: Benoit Mandelbrot is born in Warsaw (1924) in a family with a long Russian-Jewish tradition. His mother was a dentist and his father was a business man who became also a tailor, forced by the circumstances. His father's younger brother, uncle Szolem, was mathematically gifted and introduced Benoit to mathematics at a young age. When Szolem got a position in France in 1936, Benoit together with his younger brother Léon and his parents, moved first to Paris and three years later, when Szolem was appointed at the university of Clermont-Ferrand, they moved to the nearby village of Tulle. After the Germans invaded France, Tulle fell under the "Free" France of the Vichy Régime headed by Marshal Pétain. Szolem escaped the war because he got an appointment in Princeton and migrated with his wife to the US. When also the Vichy France was invaded by the Germans, life became pretty dangerous for Jews and Benoit and his brother narrowly escaped from being arrested. Tulle is infamously remembered for the Tulle massacre in 1944, three days after D-Day, when civilians were executed and many taken captive by an SS tank division as revenge for a successful action of the French Résistance. That is a summary of the first five chapters of *The Fractalist* and these are also the facts that Ziemska uses in her story.

If she were only repeating these facts, then there would be no point in writing her novella since also the original text is well told, and it is first hand. So, Ziemska adds some fractal imaginative detail-adornments and some more large-scale fantasies. Examples of the latter are certainly the Mandelbrot family hiding from the Germans in a fractal structure invented by Benoit. She also introduces the *sefirot* as an essential element in Benoit's life. It is a densely but well structured esoteric graph from the Kabbalah with ten nodes that represent all manifestations of an infinite God (or of "G-d, the Mathematician" as Ziemska writes). In Ziemska's view it gave Mandelbrot the insight of iterated function systems, an essential tool for the generation of fractals. To increase the narrative tension, she also added the character of Emile Vallat, a student in Benoit's class in the Tulle period who is another bright student, competing with Benoit for the best grades in mathematics, but Emile's family (his mother is the local librarian where Benoit finds his Book of Monsters, a ficticious book on mathematical objects) is sympathizing with the Germans and so, he is constantly teasing and humiliating Benoit and his brother who try hard to be discrete and hide their Jewish background.

Of course fractals and more generally mathematics are well represented announcing Mandelbrot's future career as the inventor of fractals and their omnipresence in nature. So several names of mathematicians are mentioned: Kepler, Poincaré, Gaston Julia,...; and mathematical terms, not really mathematics, just some name dropping without explanation: Zeno's paradox, Fibonacci numbers, Hausdorff dimension, the volume of a sphere as a multiple integral, the golden section, and of course the Mandelbrot set; and there are the illustrations from The Book of Monsters: the Sierpinski triangle, Koch's snowflake curve, Peano's curve,.... These are all very curious elements to embed in an imaginative novella, making it literally "extraordinary". The beginning and the end of this story is Mandelbrot finishing his memoirs while his wife Aliette is serving him cauliflower for his eightieth birthday, his favourite dish in which he admires the fractal structure.

This is a well told story, with many Jewish elements like for example the role of the *sefirot* and the dreadful situation of Jews during the war, and the atrocities that in fact any war does to a society. The latter is unfortunately very real, but, although based on facts, it is not a biography of Benoit Mandelbrot's youth. For that component it should be taken for what it is intended to be: a mixture of facts and fiction. Somewhat disappointing from a mathematician's point of view is that geometry is illustrated by "monsters" (and not by "gems") but Ziemska blames Poincaré for that. She uses one of his well known quotes where he claims, referring to an example produced by Weierstrass of an everywhere continuous function that is nowhere differentiable (a typical property of fractals) that "logic can sometimes make monsters that would have to be set grappling with this teratologic museum". But it is certainly Ziemska's fantasy that makes mathematics seem to be some Kabbalistic pseudo-science placing it in the same category as a magician's magic, with the magician anxiously hiding the secrets of his tricks from his public, so that he can perform disappearing tricks in some Hausdorff dimension, impenetrable for ordinary people. But of course this works out very nicely when used in a fantastic story.

**Submitted by Adhemar Bultheel |

**10 / Apr / 2018