In Part 1, we watched Mandelbrot’s family survived World War 2 intact. They had a strategy – splitting when others stayed together. Tough decisions were made and they stayed ahead as a wave of Nazi persecution washed over Europe. Strengths were developed, hardships endured.
Part 2 is an incubation period for Mandelbrot. His stories are full of consistent life strategies and goals, but all throughout he feels unfulfilled. There are several components to Mandelbrot’s life strategy that lead to the crescendo that is Part 3, when fractals are a field of study and his Keplerian dream is realized. The accomplishments of Part 3 are built on the foundation laid here in Part 2.
The Habits of Mandelbrot
- Having a goal and continually re-affirming what he does want to do. He names his goal – The Keplerian Dream.
- Small activities are consistent with his larger ambition.
- Associating with the best and brightest – and being open about his ambitions
- Building on his strengths in mathematics.
- Enjoying life – Mandelbrot exhaults in the bureacratic interludes, he finds love with Aliette, rejoices in music.
- Figuring out what he doesn’t want to do. Reversing bad decisions.
- Being comfortable with who he is.
Mandelbrot has now survived World War II, but with survival he is now quickly forced into major life decisions. Which school to attend? His decision to attend Normal – which he does for 1 day before realizing he has made a mistake – is met with a quick reversal. He attends Polytechnique. Uncle Szolem is embarassed, but what courageous behavior for a young man to exhibit at a hectic time of life.
“The high stakes terrified us all, and my parents did not trust my teachers. So a family “war council” was called to help:…” Location 1430
This is more of a statement about me – as the writer of this chapter summary and blog, than it is about Mandelbrot. I’d never heard of a family doing such a formal review before helping a young member make a major life decision. The examples that Mandelbrot shares of the other great scientists – who went on to win Noble prizes and more, shows the wisdom of such a process.
“Good wine or cheese must not be rushed. So why rush good humans by pressing a cookie cutter on a malleable young mind?” Location 1536
By attending Polytechnique, Mandelbrot would enter into a French bureaucratic educational system that would force him to pause his scientific career several times to follow the rules of the state. Rather than seeing this idle time as a waste, he embraced it and believed it to help his ultimate achievements in developing a theory of roughness and fractals.
As noted in his quote below, Mandelbrot enters Polytechnique literally in rags and is one of the few international students. He devours the opportunities in front of him, while also realizing that the degree will provide him golden handcuffs that tie him to France – which may not be the best geography for someone with his Keplerian dream.
“… my whole life’s orbit was to show that professional authority did not awe me either.” Chapter 9, Location 1645
Mandelbrot listens to authority – and is politely interested in its guidance. However, he does not blindly obey.
“Plus, all generally valid rules suffer from deviant exceptions, and I went on to prove that a person profoundly rooted in classics may very well be a successful, yet troublemaking, maverick.” Chapter 9, Location 1746
Mandelbrot was classically trained at Polytechnique, and he had a deep education in geometry – albeit learned in nontraditional ways. It was this domain expertise in these fields that led him to create the study of fractals.
This chapter documents the many remarkable minds and concepts that Mandelbrot encountered in his studies, all while he was searching for a remarkable topic to develop fully as his own. His self reflection while wandering in a field of geniuses makes for great reading.
“But freedom of choice was a negative asset; it set me on a wide sea without sufficient guidance.” Location 1762
Mandlebrot has succeeded and is at the top of the pecking order in France with his success at Polytechnique – and that success has brought freedom. Freedom after the travails of WW2 is paralyzing and gives too much freedom to operate.
“I wanted to feel the excitement of being the first to find a degree of order in some real, concrete, and complex area where everyone else saw a lawless mess.” Location 1767
Mandlebrot curtails his immense freedoms by teasing out a personal and professional goal – and an audacious one at that. This ‘Keplerian’ dream that he has outlined is bold and big. In his autobiography, written later in life, he starts to see visions of this goal early. As the reader, I wonder how much he felt early in life, and how much he portrayed backwards as he enjoyed success in later years. Mandelbrot allows us to feel this mystery along with him without forcing the development of fractals as predetermined.
Chapter 11 could serve as an excerpt from Heller’s masterpiece, Catch-22. Mandelbrot attempts to conform to his military service requirements while the military bureaucracy struggles to make use of a loyal, but atypical, young man.
“A BLESSING THROUGHOUT LIFE: I never wonder who I am. To the contrary, many successive bureaucracies wondered endlessly.” Location 1995
Mandelbroth may have had uncertainty in life as he wandered in pursuit of his ‘Keplerian Dream’ which he would find in his study of roughness, but he knew who he was. He knew he was in pursuit of that goal – even as he knew that the precise goal was not known.
Mandelbrot could tolerate that lack of clarity – and as we’ll see in the chapters about his early family, his wife and children could too. He created a life that let him search for it. Bureaucracies – here the French Air Force, but later IBM – served as stewards of his income, but were themselves confused.
It took a lot of commitment for a young graduate, and later a young father to:
- Admit he did not know the goal with precision.
- Harness the bureaucratic energy of these organizations while it was clear that they were confused about who he was.
Opera and classical music becomes a passion for some – but it has never been so for me. Synthetic, computer generated music on its own has never sounded good to me – but I do like how it can be used to augment the beat or rhythm in dance or techno music. My favorite artist, Bob Dylan, made a legendary transition to the electric guitar and took folk music with him. Perhaps someone is using that with fractal or other digital music now.
“What brought the three of us together was a special development—the observation that music has a fractal aspect.” Mandelbrot, Chapter 12
“Unlike Szolem, I enjoy intellectual fencing and occasionally showing off. Otherwise—like Szolem—I absolutely stopped having patience for their games.”
Mandelbrot, Chapter 13
Like Tversky and Kahneman – there had to be a base rate. Mandelbrot needed to engage with his peers and barb with them in order to realize that the games they were playing were silly. Without the base rate – what it was those peers were going to accomplish – then the prodigy was unable to see that he wanted more. Mandelbrot couldn’t articulate a clear destination, but he could put himself among an exceptional group of peers, hold his own intellectually, and while evaluating their goals say, “More than that!”
Mandelbrot recognized he did not fit, and he developed a system – albeit a loose one – to help refine what he wanted to do to truly excel. He knew what not to do. He trained himself to find the things he should do.
The role of a mentor who has done what you want to do is highlighted by Kastler’s advice in Mandelbrot’s choice of thesis;
“This man was attuned to nuance and comfortable with living between two cultures.” Mandelbrot, Chapter 13 – Location 2324
As Mandelbrot reflects on the lives of his parents following the 1951 passing of his father;
“Their explanation was that less fortunate persons would have perished early in one of the catastrophes that they had managed to sail through.” Mandelbrot, Chapter 13 – Location 2331
Our scientist-hero has identified a goal – creating a ‘Keplerian’ field of study which he can pioneer. Mandelbrot has found a mentor, Kastler, who understood the need to drift between worlds and excelled at it. He has a method to pursue this need – surrounding himself with brilliant peers, and then finding out how to outshine them and realizing that their bureaucratic games of hierarchy hold no attraction for him.
Path dependency matters. Many had noted the trends and methods that Mandelbrot would make into a formal field, but under ‘Important’ areas of study, it was hard to take the intellectual risks necessary to openly discuss their use. Failure would be too painful. By starting in an atypical area that threatened no one, he was allowed room to develop and grow. (On a personal note – this feels like my time in nanofibers.)
“My luck was to begin with the distribution of word frequencies—a thoroughly atypical example without any important consequences, and uniquely easy to handle.” Mandelbrot, Chapter 14, Location 2387
Mandelbrot, Chapter 14, Location 2387
Scaling – ‘being fractal’ – in your activities is one of my personal big take aways from reading this book. Mandelbrot declares that if something is not smooth, then it is rough – and things that are rough have common traits in how they behave. Apply this to life – if things are not smooth, then they must be rough. Do things that scale up and scale down. Much in business is focused on ‘can it scale up’ – but in many ways this avoids the hard challenges of finding ways for activities to be worthwhile if they must scale down. To win in a world of roughness, scaling – both up and down – must be part of the strategy.
“The language—English, French, Latin, whatever—does not matter. Neither—quite oddly—does the writer’s degree of literacy. This is an example of what physicists were soon to call a universal relationship. Another notion in physics, called scaling, is one that underlies fractals.”
Mandelbrot, Chapter 14, Location 2408
If ever a movie is made of Mandelbrot’s life – then the scene where he reads this paper, a gift from Uncle Szolem, and hits this Eureka moment would be a highlight.
“In one of the very few clear-cut eureka moments of my life, I saw that it might be deeply linked to information theory and hence to statistical thermodynamics—and became hooked on power law distributions for life.”
Mandelbrot, Chapter 14, Location 2425
Zipf’s paper was not new – it had first been published 16 years earlier. Mandelbrot would be in a tenuous position – he believed that his mathematical capabilities provided him a unique perspective, but he was alone with this view point. Only as he was able to add to this perspective with advances in topics far afield from word theory would the strength of Mandelbrot’s position improve.
“My good fortune resided in an unfair advantage. I was to be the first—and for an interminable time, the only—trained mathematical scientist to take Zipf’s law seriously.” Mandelbrot, Chapter 14, Location 2425
Mandelbrot, Chapter 14, Location 2425
Mandelbrot heads to MIT (images above from this MIT group), studies under a pioneer and namer of ‘cybernetics’ and continues on his quest to uncover and master a Keplerian field of study.
“Cybernetics” was a word Wiener had just coined…”
Mandelbrot, Chapter 15 Location 2493
Mandelbrot’s definition of fractal and creation of the word as the systematic study of roughness is important to him, and it was something he explored diligently.
“… grammar is like the chemistry or algebra of language.”
Mandelbrot, Chapter 15 Location 2575
This is slipped in as a throw away line about language and Zipf, but it is an elegant way to think of how words are used.
“These two men were the only living proof that my Keplerian dream was not an idle one—that it was possible to put together and develop a new mathematical approach to a very old, very concrete problem that overlapped several disciplines.”
Mandelbrot, Chapter 15 Location 2499
In using Mandelbrot to explore good habits for achieving a goal – here he has set a Goal and identified two living benchmarks. It may be only two – but at least there is someone who has completed his objective!
The Chapter starts with the tale of a public lecture where Mandelbrot is excoriated – but then experiences a classic ‘Oppenheimer’ explanation. Following a fractal pattern, we then find Von Neumann providing another level of explanation on top of Oppenheimer. It is amazing how Mandelbrot’s career was so closely entwined with these brilliant titans of discovery.
“No major turn in my entire life proceeded more smoothly.
Mandelbrot, Chapter 16 Loc 2664
If things are not smooth – then they are rough. Mandelbrot hints here at a ‘Fractal Strategy’ for life. If things are going smooth – then there are a certain set of rules. But when things are rough, be sure that your actions can scale up – and that they can also scale down. Big things build from small patterns repeated with consistency.
“As soon as he heard a field had become hot, he made himself an expert with a competitive edge and identified several key issues he could solve.”
Mandelbrot, Chapter 16, Loc 2631
In Finance this would be a convex strategy, where you follow the winners and keep winning provided they continue to be the winners in the next period.
Young Mandelbrot has completed his PhD and looking for employment, mentors and other problems that will all work towards his goal of a Keplerian type view of a major problem. Zipf put him on the path to Fractals, but Fractals have not yet come to his life.
“…. the unreasonable effectiveness of mathematics in the natural sciences.”
Mandelbrot, quoting Wigner in Chapter 17
“… his fear of being a mere survivor of the last century, and his feeling of being a mathematician unlike all the others.”
Mandelbrot, describing Levy’s autobiography in Chapter 17
Mandelbrot pursues love and family life – and does it with the usual cast of exceptional and brilliant people.
“Without her willingness to let me gamble my life—and hers and our children’s—the odd career I undertook would have been unthinkable.”
Mandelbrot, Chapter 19
Mandelbrot’s approach to risk, and his life’s dream, is linked. He knows that his family took this risk with him, and that without their involvement, he could not have succeeded.
On Citroen, “He tamed front-wheel drive for mass production, and his brilliant engineers rethought every part from scratch so that even some key parts could be duplicated, if needed, in a home garage.”
Mandelbrot, Chapter 19
In a way Citroen was fractal in its approach to manufacturing. The parts were assembled into a vehicle, but then the parts themselves could be easily assembled with ordinary tools.
Mandelbrot was able to assist Piaget’s early work to transform the study of human behavior and human development and also learn from him how to take his own ideas farther.
“… Jean Piaget (1896–1980). He was pleased to hear that I was aware of his fame in trying to bring rationality to child psychology.”
Benoit Mandelbrot, The Fractalist Chapter 19
The number of brilliant minds that Mandelbrot was able to connect with was staggering. Piaget is one of many who was the founder of a major modern field of science.
Piaget, “He promptly changed fields and set out on a lifelong effort to extend proper scientific principles to human behavior.”
Benoit Mandelbrot, The Fractalist, Chapter 19
Before Piaget, the use of data, analytics and rigor was weak in human development. Mandelbrot was to take this same approach to a theory of roughness.
“… telling me that, instead of more papers that looked unrelated, I must write a book.”
Benoit Mandelbrot, The Fractalist, Chapter 19
Mandelbrot put himself near so many people with great skill and was able to position them as coaches and make use of their advice.
In this final chapter before heading into Book 3, we read how an older Mandelbrot looks back on his decisions to pursue his goal and the risks that were required to succeed.
Mandelbrot has a dream – he has a goal. He sees that his life to this point is not getting him to this goal. Without this goal – the Keplerian dream – Mandelbrot has no guiding vision. It is the yardstick by which he measures success.
“Unfortunately, my various enterprises up to 1957 had not gone very far to further my aging but still vibrant Keplerian dream.”
Mandelbrot, Chapter 20
Mandelbrot isn’t sure what he should do – but he is increasingly sure that what he is doing is not a fit for his goals in life. Pursuing a career in French academia will block his goal.
“I saw no compatibility between a university position in France and my still-burning wild ambition and dreams.”
Mandelbrot, Chapter 20
Mandelbrot may not know what to do – but he does know clearly what not to do. Such simple steps as having a goal and avoiding bad decisions keep the dream alive and his pursuit a rationale one.