Mandelbrot’s The Fractalist, Chapter 13: Life as a Grad Student and Philips Electronics Employee, 1950–52

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“Unlike Szolem, I enjoy intellectual fencing and occasionally showing off. Otherwise—like Szolem—I absolutely stopped having patience for their games.” Like Tversky and Kahneman – there had to be a base rate. Mandelbrot needed to engage with his peers and barb … Continue reading

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Mandelbrot’s The Fractalist, Chapter 12 Growing Addiction to Classical Music, Voice, and Opera

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.

Best Quote(s)

It is a short chapter, both quotes are good. 🙂

Page by Page


“I heard the great diva Lotte Lehmann on one of her “last” tours. As she performed Schubert’s An die Musik, her voice cracked, and she stopped and apologized. Many elderly people in the audience were crying—but I confess wondering if she was not simply behaving like divas are supposed to during their farewell tour( s).”


“What brought the three of us together was a special development—the observation that music has a fractal aspect.”

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Mandelbrot’s The Fractalist Chapter 09: A (Then Rare) Foreign Student at the École Polytechnique, 1945–47

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.

Best Quote(s)

“… 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.

Page by Page, Swipe by Swipe


“The many perks that come with the degree give few graduates an incentive to live outside of France—ordinarily, a prerequisite to renown abroad.”

“But then it became less and less important until it faded into a nice memory of youth.”


“With the exception of a classmate who died, I was the school’s only foreign student over a period of nearly ten years.”


“I had entered the school literally in rags.”


“I was reminded of my serial number (1179) and of the pride I had felt when—shortly after I had trashed my rags—I was measured for a masterpiece of custom tailoring.”


“Marching in grand U, we had performed for Charles de Gaulle, Winston Churchill, and other lesser historical figures. Most oddly—and memorably—we honored Ho Chi Minh!”


“Captain Wolf commented that although my 2/ 20 suggested a willful troublemaker, it only meant that I had no concept of the role of military authority. This was indeed the case—and my whole life’s orbit was to show that professional authority did not awe me either.”


“Gaudeamus igitur, juvenes dum sumus (While we are young, let us rejoice).”


““How come twenty-year-old students in France are so much better in math?” Part of the answer: “Because they are, in effect, bribed.”


“Graduation rank actually predicted future performance very poorly. Yet many of my classmates played key roles in rebuilding France after the war. They faced weak competition because our immediate elders had led largely disrupted lives, were not fluent in English, and suffered other handicaps.”


Future French President Valéry Giscard d’Estaing,

“…He kept telling everyone that he will be a député [national representative] by thirty, minister of finance by forty, president of the republic by fifty, and president of Europe by sixty. How stupid can you get?”


“Students did not attend Carva for quality teaching, but rather for useful classmates and good jobs.”


“It contained Painlevé’s pre-Wright proof that—granted certain “natural” mathematical assumptions—airplanes could not possibly fly!”

“This proof deserves to be republished as a warning ⚠️ to scientists that a theory can be killed by an assumption that looks mathematically “natural” but was not chosen by nature.”


“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.”


“His self-directed boldness and insight cost him much in his career and early recognition, but I found his independence admirable. I felt ready to pay the same price.”

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Mandelbrot ‘s The Fractalist Chapter 11: French Air Force Engineers Reserve Officer in Training, 1949–50

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


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.”


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


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.”


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


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

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Mandelbrot’s The Fractalist 10: Pasadena: Student at Caltech During a Golden Age, 1947–49

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


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


“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.”


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


“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.”


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


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


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


““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?”


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


“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.”


“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.”


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


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


“… 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.”


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

Gossamer Condor, Paul MacCready (1925–2007),


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


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


“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.”


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

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Mandelbrot’s The Fractalist Chapter 08: Paris: Exam Hell, Agony of Choice, and One Day at the École Normale Supérieure, 1944–45

Part Two – My Long and Meandering Education in Science and in Life

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.

Best Quote(s)

“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.

Page by Page, Location by Location



“I wanted to keep close to geometry and to prepare myself to realize in some way that Keplerian dream I had formulated not too long before. The scary exams proved a cinch and brought about the first, the freest, and most agonizing professional choice of my life.”

“… [Mandelbrot’s] mathematics teacher, M. Pons, hailed me in the street, and we had our first and last private conversation. “Let’s talk about the big math problem at Polytechnique. I could not solve it in the time allowed, but examiners say that—in the whole of France—one student did solve it, and he is from my class. Could it be you?” “Well, I did solve the entire problem—including every optional question at the end.” “How did you manage? No human could resolve that triple integral in the time allowed!” “I saw that it is the volume of the sphere. But you must first change the given coordinates to the strange but intrinsic coordinates I thought the underlying geometry suggested.” “Oh!” And he walked away, repeating, “But of course, of course, of course!””


“Plain and simple, not only had I survived the war, but in France I had it made for life. Of course, nothing could guarantee that I would mature into a great scientist—or a great anything. But either school could open every door and provided a kind of automatic lifelong insurance. All this was simply beyond belief. Only nine years since my move to France, only months since the liberation, and still officially residing in that slum of Belleville, I was in no way ready for such choices.”


“Then I moved to the United States—where French credits had no value.”


“Regular schooling identifies sensible ambitions, and my classmates had been preparing over much of their lives.”

“By contrast, I was both underschooled and suddenly overadvised. Only months before, I had been desperately focused on staying alive.”


“The high stakes terrified us all, and my parents did not trust my teachers. So a family “war council” was called to help:…”


“Also, never forget something basic: professors are civil servants. Trouble may leave you somewhere—as it did Mother—with a worthless foreign certification. Keep away from state-certified fields and large national organizations. Education, health, and law are the plague. Go for broad engineering skills that every country will need under every political regime.”


“One hears the same advice today all over the media: don’t count on lifetime protection from one employer.”


Monod – “It reported that as a biologist he would match Pasteur and as a musician he would match Mozart. He chose biology and won a Nobel Prize.”

Von Neumann – who was excellent as a child in both math and chemical engineering also had a ‘war council’ with his family, “The advice was that he should do both. He perfected an alloy whose composition is not expected to ever be encountered again.”


“What am I doing here? This is absolutely the wrong place for me.” Reversing out of Normale – what a courageous decision for a young man to realize he had made a mistake, and to then reverse it.


“It was indeed the absolute worst place for a strong-willed person with already clearly defined tastes.”


“Individual decisions are randomly influenced by history in the making.”


“Having entered Normale, this boy has left on his second day and is about to enter Polytechnique.”

Paul Levy teaching statistics.


“Sierpiński intellectual and political views made Uncle flee Poland, and Bourbaki made me leave Normale in 1945—and France in 1958.”


“Its practical applicability revealed that it reflects the irreducible messiness of where I have chosen to work—the scientific frontier.”


“Many people I know and respect value efficient processing of youths and view “wasted time” as harmful, even threatening, or immoral.”

“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


“A glance at the alumni directory shows that this talk was not followed by action.” What if France did not rebuild? Should they flee afar? Brazil, Argentina


“In the absence of a well-defined set of rules to play by, the very notion of precocity ceases to make sense.”

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Mandelbrot’s The Fractalist: Part 1, “How I came to be a Scientist” – Surviving World War 2

Chapter 1 Highlights

Mandelbrot’s book tells the story in a fractal nature – bouncing big and small and returning to reinforce important topics.  From this first family photo Mandelbrot introduces us to the adults that shaped his young life, helped him survive World War II, and put him in position to excel when life provided him with options.  What a family!

Best Quote(s)

“As observed by a writer native to that part of Europe, Woe to the poet born in an interesting piece of geography in a violent time.”

Mandelbrot’s fractals visual replication of geographic features – coast lines and elevations, was one of the first clear victories of the new field.  Mandelbrot’s life would move about the globe, making big leaps and small.

“Other war survivors describe being in a herd on the way to the death camps, noticing a way out, and taking it instantly. That is the kind of man Father was.”

Little opportunities lead to big changes.  Mandelbrot’s family would face many opportunities where following the herd would have led to a very different life – or even death.  Instead, they found the way out.

“They never shouted at each other but argued constantly about strategy, and they taught me very early that before taking big risks, one must carefully figure the odds.”

Discussion of risks helps mitigate risks.  Identify risks, then address them.

“Like many social customs, it could be defied, but at a cost: not being part of a system of patronage that is pervasive in intellectual and professional groups.”

Mandelbrot’s career would lack the rudder of mentorship – but he made up for it by staying focused on finding a larger calling and harnessing his intellectual capabilities and breadth of interests with hard work.

Chapter 2 Highlights

Warsaw shaped Mandelbrot as his first home, site of his early education and as a way of life that would be completely erased.  His family focused on staying alive and ahead of the Nazi advance at a time when others who were less urgent were murdered.

Best Quote(s)

“For these and other truly unavoidable reasons, Polish history from 1919 to 1939 was rough.”

Rough – just like the fractals that Mandelbrot invented.

“Since diversity cannot be avoided, one may as well like it (as I came to) or at least learn to live with it.”

This is a delightfully modern approach to diversity that is all too common in more integrated, international cultures.

“Before everything they had dreaded became horribly concrete in Poland, my parents’ bold scheme had worked.” Chapter 2, Location 659

His parents craft successful strategies again and again, allowing their family to survive and innovate on behalf of mankind.

“Of the people we knew, we alone moved to France and survived. Most procrastinated—until times turned awful. Only two Warsaw friends survived:…” Chapter 2, Location 663

The eradication of this world is frightening and it pervades Mandelbrot’s view of the world for the rest of his life.  How could it not?

“Others had been detained by their precious china, or inability to sell their Bösendorfer concert grand piano, or unwillingness to abandon the park view from their windows. Mother was horrified by their stories but listened stone-faced.” Chapter 2, Location 668

When the Mandelbrot family needed to act, they did so – unencumbered by the weight of their past.  They moved with focus to achieve their goal, survival.

Chapter 3 Highlights

Pages – ; Locations 675 – 860

Mandelbrot’s youth is about promise and his family’s focus on survival.  In Chapter 3 we find our young student in France with a need to exceed in education, but with the reader knowing that war and atrocity lie in his future.

Best Quote(s)

“By pulling up their deep roots in a community that only a few years later vanished in smoke, my lucid and decisive parents saved us all and earned the utmost gratitude.” Chapter 3, Location 681

Chapter two told us of the wonderful upbringing, education and life lessons that Mandelbrot experienced in Poland – all of which were wiped away with the Nazi invasion and Holocaust.  The lessons of his parents’ focus on survival is repeated throughout the book.

“Each time I recall that successful exam, my heart rejoices. Lady Luck is blind and needs assistance. In 1936, my parents assisted by moving out of Poland. In 1937, I was called to assist—and I did.”  Chapter 3, Location 795

From Mandelbrot’s mind, “My parents kept us alive – and to make the most of it I had to nail that test.  What fortune!”

“A belated benefit from my years of Latin is that they helped me correctly coin new words—like “fractal.”” Chapter 3, Location 833

Mandelbrot’s writing follows his study of roughness – we know where the story is going, and still the book plays out like a mystery.  We know the ending – otherwise who would read this autobiography?  Throughout he foreshadows his contribution to science and math.

Chapter 4 Highlights

Mandelbrot’s family continues to survive as the violence of World War II escalates.  Hard work provides a way out.  Luck breaks for the family again.

Best Quote(s)

“Xenophobia lost, meritocracy won, and she deliberately misplaced my family’s files.” Chapter 4, Location 879

The family survived many challenging times in WW2 – and they did so with some lucky breaks and a commitment to hard work.

“When I was nearing forty, my work became devoted to the phenomenon called intermittence, present in both nature and the financial markets.” Chapter 4, Location 885

Again, we see Mandelbrot foreshadowing his focus on fractals and the study of roughness.

“The final examination included two very easy problems, which I saw instantly to be a single problem stated in two different ways. Apparently, few students noticed.” Chapter 4, Location 1030

Mandelbrot manages to describe his academic and scientific prowess directly without boasting – that is a communication skill to envy.

Chapter 5 Highlights

Mandelbrot continued to excel in his studies despite the oppression of the Nazi occupation of France.  He studied shapes, and used the basic of geometry in novel ways to solve problems more fitting for older students.

Best Quote(s)

“True to our antiherding instinct, our family decided it was best to split up: the boys on their own, and the parents on theirs.” Chapter 5, Location 1068

It is remarkable that parents would make this decision – it had to have been agonizing.  And it was the right one.

“Not unlike sports, the bulk of training consisted of mastering a single but extremely arcane gesture.” Chapter 5, Location 1079

When brilliant minds comment on sport and athletics, the observations are always fascinating.

“Oradour-sur-Glane is a little town where the Waffen SS committed a horrible massacre in 1944, herding 642 villagers into a church and setting it on fire.” Chapter 5, Location 1118

Referring back to the family decision by the Mandelbrot’s to split up – the acts of violence by the Nazis defy the civility of modern life.  As we will see in a later chapter, the Mandelbrot decision saved the lives of their children.

“In a way, I was learning to cheat.”  Chapter 5, Location 1197

By learning to think in shapes, Mandelbrot would teach himself ways to think that even he considered cheating.  His life’s great accomplishment is taking that way of thinking, using it to study roughness and sharing it with the rest of humanity.

Chapter 6 Highlights

Mandelbrot deploys his genius in order to help an aristocrat maintain the family horse farm while a war rages in the background.  Carnegie uses animals to endear the reader to people – and the olfactory descriptions of a young Dr. Mandelbrot amidst equestrians is powerful imagery.

Best Quote(s)

“Nobody ever listens to me, but you did. And you remembered everything. You can’t be altogether bad.” Chapter 6, Location 1242

Mandelbrot takes a page out of the Carnegie playbook from How to Win Friends and Influence People.

“Horse owning Gentry thought Germany would win, “I cajoled them, first to listen to Swiss radio in French, then to France Libre in London.”” Chapter 6, Location 1298

From a persuasion standpoint, Mandelbrot was pacing his gentrified hosts to understand there were more possibilities about what might happen with the war.

Chapter 7 Highlights 

Locations 1312 – 1347

We wrap up the first part of Mandelbrot’s life – with a wonderful preview of the 2nd and third parts.  The family made a bold bet to split up, and it was truly necessary based on the gruesome description of French resistance youths meeting their death hanging from street lamps.

Best Quote(s)

“The bold plan our parents had devised—bless their hard-won survivor skills—had let them and their sons cope with events separately. This bet, the riskiest of our complicated lives, worked better than any realist could have hoped.” Chapter 7, Location 1335

The plan had worked, all four were alive – while other families in similar situations were never to meet again.

“During this second, twelve-year stage of my life, I was not going to manage elegantly—as will be seen. So, in time, I deliberately provoked a belated third stage.” Chapter 7, Location 1347

Mandelbrot’s self reflection is impressive.

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