Fred Lybrand

Mandelbrot pursues love and family life – and does it with the usual cast of exceptional and brilliant people.

Best Quote(s)

“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.

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2825

“Following a custom on its way out, my parents had not married until Father had settled down as a reasonable provider.”

2830

Brother in law

“Years later, the older received the Wolf Prize for chemistry.”

2835

“That mistress was—and is—science.”

2841

“Without her willingness to let me gamble my life—and hers and our children’s—the odd career I undertook would have been unthinkable.”

2863

“We spent a two-year honeymoon there, and it is where Aliette brought Laurent, our older son, home from the maternity.”

2873

His dog, “Bruno Boccanegra de la Boverie.”

2884

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.”

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.

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.

Best Quote(s)

“…. 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

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2749 Pierre Mendès-France (1907–82).

2755

“Indefatigable, he was ridiculed by opponents for keeping a glass and a bottle of milk on his desk. In France? Yes, his constituency in Normandy produced milk, not wine. Besides, he was effective in fighting cheap alcohol.”

2765

Paul Lévy

“Getting to know Paul Lévy was one of my few academic accomplishments in 1954–55. He never had a formal disciple, I never had a formal teacher, and I never thought of becoming his clone or shadow. Yet much of probability theory has long consisted of filling logical gaps in his works…”

2771

“He documented his life, thoughts, and opinions at length in a book well worth reading because of his lack of any attempt to appear better or worse than he was. The best passages are splendid. In particular, he describes in touching terms both his fear of being a mere survivor of the last century, and his feeling of being a mathematician unlike all the others. This feeling was widely shared. I recall John von Neumann saying in 1954, “I think I understand how every other mathematician operates, but Lévy is like a visitor from a strange planet. His own private methods of arriving at the truth leave me ill at ease.”

2782

“One half of the story is part of the mystery the great mathematical physicist Eugene Wigner called the unreasonable effectiveness of mathematics in the natural sciences.”

And the corollary …

2804

Andrei Nikolaevich Kolmogorov (1903–87)

“… he antagonized the notorious Trofim Lysenko, a quack favored by Stalin who destroyed genetics in Russia, and fell into disfavor. He reemerged with a pathbreaking paper on turbulence…”

2815

“John von Neumann seemed to seek the hottest topics of the day.”

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.

Best Quote(s)

“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.

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2610

“This is the worst lecture I ever heard. Not only do I see no relation to the title, but what we have heard makes absolutely no sense at all!””

Otto Neugebauer (1899–1990)

2615

Oppenheimer, “If Dr. Mandelbrot will allow, I would like to make a few comments. … I am impressed, but also fear he may not have given full justice to his striking results. I would like to sketch what I remember.”

2620

Von Neumann, “If he allows me, I would like to sketch some points that Oppie did not mention.”

2631

“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.”

2647

“In truth, I disdained the nature of his interests and the fact that, while multiple unrelated interests made us fellow throwbacks, he was the precise opposite of a self-motivated solo scientist.”

2659

“On the forty-ninth floor of 49 West Forty-ninth Street, in New York City, the receptionist waved me toward Weaver’s secretary, who waved me into his office.”

2664

“No major turn in my entire life proceeded more smoothly.”

2680

“… the observation by the physicist Hans Bethe that “Oppie” could often understand an entire problem after he heard a single sentence, and the observation by the physicist Robert Wilson that in his presence, I became more intelligent, more vocal, more intense, more prescient, more poetic myself.”

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.

Best Quote(s)

“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!

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2489

“I RECALLED THOSE WORDS Gaudeamus igitur, juvenes dum sumus—“ While we are young, let us rejoice.””

2493

Norbert Wiener, MIT, “… Cybernetics, or Control and Communication in the Animal and the Machine. “Cybernetics” was a word Wiener had just coined, and the title defined that word as ranging from brains to telephone switchboards.”

2499

“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.”

2504

“His own account of early motivations was thrilling.”

2509

“To denote this goal before it was even partially fulfilled, he drew on a Greek word to coin “cybernetics.””

2520

“He wanted to “see over the fence” to engineering, biology, and social sciences—but not to narrowly defined economics.”

2533

“All those who knew Jerry can testify that in his “mental movie” he did not view himself as a creator but as a facilitator.”

2538

“He was not himself an accomplished scientist, but was endowed in an unusual way: he had a keen eye for full personal commitment (a large part of scientific value), a highly developed sense of noblesse oblige, and the ability to interact with everyone and get things done.”

“He simply knew how to run an organization without self-aggrandizement, with invisible bureaucracy, and with maximum respect for his charges—including many thoroughly spoiled brats.”

2548

“Northeast of what was Building 20, a neighborhood called East Cambridge is now filled with high-rise industrial labs and upscale housing—where I live.”

2575

“Zipf’s law was the basis of an important physics-like (thermodynamical) aspect of discourse, while grammar is like the chemistry or algebra of language.”

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.

Best Quote(s)

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

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2349

“TAKE THIS REPRINT. That’s the kind of silly stuff only you can like.”

2353

“Oddly but almost ineluctably, that string, that reprint, ended up directing me to some of the main themes of my scientific life: unevenness, inequality, roughness, and the concept of (as well as the word) fractality.”

2364

“…George Kingsley Zipf (1902–50). Independently wealthy, this academic character was a university-wide lecturer at Harvard in a self-invented field he called statistical human ecology.”

2381

“Inequality and Unevenness Are Everywhere:

How long does a book on the best-seller list remain there?”

2387

“Extreme inequality is a familiar pattern in nature and in the works of humans. Such distributions are called long-tailed distributions. For them, no value is typical, and the contrast between short and long tails came to play a central role in my work.”

“My luck was to begin with the distribution of word frequencies—a thoroughly atypical example without any important consequences, and uniquely easy to handle.”

2392

“Statisticians rarely use this method, but there is nothing wrong with it.”

2398

“An odd and hard-to-read pattern emerges. The curve does not fall gradually from most common to least common word.”

“By the very definition of rank, frequency varies inversely with rank.”

2403

“To compare such curves, it is best to replot them more legibly by replacing both the rank and the frequency with their logarithms.”

2408

“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.”

2425

“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.”

“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.”

2436

“A difficulty: a well-defined probability may exist for common words, but what about rare words, especially in multiauthor works or composite files of newspaper articles?”

2441

“Worse, experimentalists try to help by simplifying what they see, and key facts are often unwittingly overlooked.”

2451

“Early on, a shadow was present—the example I worked on was devoid of important consequences. No one could predict that I was to be called the “Kepler of word frequencies,” then more generally the “father of long tails.”

2455

“Had I approached it from a seemingly more “worthy” angle, I am convinced I would have failed.”

2460

“On December 19, 1952, the die was cast. My Ph.D. dissertation loudly affirmed a Keplerian determination to become a solo scientist—the kind my world thought had vanished.”

2477

“So, no, I was not acting spoiled. I did not want to hide—I wanted to find the best conditions to fulfill my Keplerian dream.”

2483

“Had I sought their advice, I am sure I would not have taken it.”

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.

Best Quote(s)

“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.

Page by Page, Location by Location

Locations 1995

“A BLESSING THROUGHOUT LIFE: I never wonder who I am. To the contrary, many successive bureaucracies wondered endlessly.” Location 1995

2024

Mandelbrot finds himself in a repeated “Catch 22” scenario. No one can believe he has his low rank, and because he has his rank no one will believe his educational background.

“But I don’t. Everything I tell you is absolutely true.”

“If it were true, you would not be drafted as a private in rags, but as an officer giving orders.”

2049

“I became an excellent sharpshooter, a skill I am glad never had to be tested further.”

2061

Mandelbrot’s commander had been told that he would be required to advance his reputation with supersonic flight study in order to make general. He goes to ask the young serviceman for his academic advice, and is met several times with the following response:

“Colonel, this is a good beginning, but more work is needed.”

2068

“À vos ordres, colonel.” I never heard from him, or of him, again.

2097

“I take it upon myself to inform the exit visa people that everything is under control and will be fixed shortly.””

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.

Best Quote(s)

“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.

Page by Page, Location by Location

1762

“But freedom of choice was a negative asset; it set me on a wide sea without sufficient guidance.”

1767

“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. Of bringing to a field the element of rational mathematical structure that Kepler had brought to physics several centuries before. But that Keplerian dream remained stuck in a holding pattern. I was aware that the next step after Carva was going to be hard.”

1767

“Roger Brard (1907–77). A naval engineer,”

1778

“But I had a desperate need for someone with broad down-to-earth experience to help me carve a path. Brard was friendly and, to my surprise, made himself available.”

1784

“I viewed aeronautics not as my final field of work but as the best available path toward reaching my Keplerian dream.”

1795

“Their fathers—far more prosperous and worldly than mine—had also insisted that their sons study chemical engineering.”

1801

“Its four propeller-driven engines could not reach Los Angeles without a stop halfway at the TWA hub in St. Louis.”

1817

““Was that preacher any good?” His medical diagnosis was that my eyes were fine except for being overly sensitive to the smog. “What is smog?”

1828

“All too many of the stars who had made the older catalog so attractive were gone.”

1849

“Fluid mechanics as a whole had become an extremely competitive and “mature” field that was growing slowly and splitting.”

“Pure mathematicians and physicists had little to contribute, so it was left to engineers.”

1855

“Ivory tower theoreticians agonized in one world, and adventurers in another made immense amounts of money to fly unproven rocket-powered contraptions that might or might not take off, fly, or land safely.”

1861

“What is the cause and nature of turbulence?” was Fermi’s response.

1866

“Later, the theory of chaos contributed to fluid dynamics and brought me back to it for an important effort: developing a concept called multifractals.”

1894

“… evidence that airplane design has been since 1947 a “mature” field. Spending a lifetime on such details would have been a dreadful experience, and did not tempt me at any point.”

1905

“We always felt in tune but did not see each other often enough. A splendid man.”

Gossamer Condor, Paul MacCready (1925–2007),

1916

“I think you should not start on a Ph.D. with me because you don’t admire me enough.”

1947

“Max Delbrück (1906–81). ….” The father of molecular biology.

1953

“Eventually, molecular biology merged with biochemistry, and genomics took it to an industrial stage. Today’s practitioners complain of it being viewed as a mature field. But in 1949, nothing was further…”

“After the ordeal ended, he relaxed in his chair and, in a completely different tone of voice, concluded, “It was a very nice lecture. I learned a great deal.”

1986

“Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern.”