Mandelbrot’s The Fractalist, Chapter 26: A Word and a Book: “Fractal” and The Fractal Geometry of Nature

Coining the word ‘fractal’ has been foreshadowed from the early chapters – such as Mandelbrot’s study of Latin as a youth and his education in the US near pioneers of newly named fields like biochemistry. He compares his writing style and objectives with that of his uncle Szolem, and summarizes his approach towards writing.

Best Quote(s)

“Throughout my life, it had been my principle never to compete frontally with anybody.” 4087

Mandelbrot’s The Fractalist, Chapter 26 (Location 4087)

Mandelbrot is delighted to find a group that will be publishing a collection of artwork, and with that he writes out a life rule that is unique, and likely colored by the violence that surrounded him in his youth.

“Many scientific articles are completely flat because they are written for people who do not have to be convinced.” 4189

Mandelbrot’s The Fractalist, Chapter 26 (Location 4189)

This is a fantastic insight – if the audience is captive, and if the author knows their information is unique and valuable, then what incentive do they have to make reading a joy?

“Whether it is opera or Greek drama, one must know how to enter into a subject quickly because one cannot assume that the audience will wait to understand. One has to be able to speak to people in their style, to motivate and even amuse the reader a little.” 4193

Mandelbrot’s The Fractalist, Chapter 26 (Location 4193)

Enter the subject to quickly – and the reader is not prepared to receive the message. Enter it too slowly, and they are bored and walk away. How wonderful to enter a topic in conversation, where words can flow back and forth and we can reach the topic at the pace needed in order to achieve our goals.

“Szolem responded, “Yes, there are about fifteen people in the world who read everything I write. That is enough. I find that very comforting.”” 4018

Mandelbrot’s The Fractalist, Chapter 26 (Location 4087)

The humor of this statement, with Mandelbrot’s uncle proudly boasting of his 15 loyal readers, compared to the generations of people who now know Mandelbrot and his fractals, is a great contrast to the anxiety that Mandelbrot faced his whole life.

Page by Page, Screen by Screen, Swipe by Swipe – 24 Mandelbrot Quotes

3984

“NEVER UNDERESTIMATE THE POWER of a word that appears at the right time and in the right context and—let us not forget—accompanied by the right pictures.”

3989

“I also checked in advance that “fractalist”…”

4007

“But I chose to coin a new word—one not directly evocative of anything in the past. I wanted to convey the idea of a broken stone, something irregular and fragmented.” 4007

4018

“Szolem responded, “Yes, there are about fifteen people in the world who read everything I write. That is enough. I find that very comforting.”” 4018

4023

“… But watch out: don’t let yourself be carried away and spend the rest of your life trying to improve it. Go back to something standard and build yourself a reputation that will ease your career.” Advice that—of course—I failed to follow.”

The 1982 Book, The Fractal Geometry of Nature

4029

“I succeeded in persuading W. H. Freeman’s top brass to charge a low price for the book and include a sixteen-page color signature (at a time when color was still perceived as expensive) because I felt it would be a good investment.”

First Fractals Meeting in Courchevel

4055

“The mathematicians were amazed that what they considered to be safe esoterica was in fact part and parcel of nature. The physicists were amazed that many complicated problems could be solved in a simple and transparent way. All the Kepler moments of my life to that day had come together.”

4072

“Then we drove on to Tulle, that hollow in the mountains where I had spent several years during the war, which, after all those years, I still consider my true home.”

4082

Riding the Coattails of a Best Seller from Bremen

4087

Color prints from another publisher

“Throughout my life, it had been my principle never to compete frontally with anybody.” 4087

I Become Known as the Father of Fractal Geometry

4104

“One reason The Fractal Geometry of Nature took off was that an amazing variety of journals reviewed it—in glowing terms.”

4110

“And the book did not become that nightmare of publishers: one that reviewers love but readers avoid.”

4116

Mandelbrot 26.2

4099

I Become Known as the Father of Fractal Geometry

A Shower of Awards

4135

“A specialized award in mathematics is the annual Sierpiński Medal of the University of Warsaw and the Polish Mathematical Society.”

Awards Accompanied by Backlash

4152

“But unfair competition from an outsider is something that no group faces rationally.”

4156

“The third worst, which is what happened, was an uncanny split I had to learn to live with.”

“In addition to the continuing flow of glowing reviews there was a trickle of dismissive comments and virulent diatribes.”

4160

The Balzac-Bohr-Bialik Syndrome: The Tongue, the Pen, and the Eye

“Being an agile writer can be a great asset.”

4165

“Once, having seen in a museum in Paris a page of Balzac’s proofs—and feeling bubbly and flush—I tried to buy a corrected proof for myself.”

4169

“He (Neil’s Bohr) had to be urged by colleagues to stop revising and publish, and his earlier drafts continue to be viewed as better than the last and to circulate in a kind of samizdat.”

4173

“I never begin with a table of contents and then write chapters, sections, and sentences in the order in which they appear.”

4180

“Let me elaborate by expanding on the distinction I see between “seers,” who favor pictures—as I do—and “hearers,” who favor language. Written or printed material is a hybrid that came late in human evolution and some otherwise advanced cultures never produced it at all.”

4189

“The paper becomes a new crucible for creativity, a crutch for lesser Mozarts.”

“Many scientific articles are completely flat because they are written for people who do not have to be convinced.” 4189

4193

“Whether it is opera or Greek drama, one must know how to enter into a subject quickly because one cannot assume that the audience will wait to understand. One has to be able to speak to people in their style, to motivate and even amuse the reader a little.” 4193

4192

A regret?

“And I must confess harboring a sharp regret. Had I been able to get more assistance in the early years, I would have moved faster, and The Fractal Geometry of Nature would have appeared when money for scientific research was flowing, well before 1982.”

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Mandelbrot’s The Fractalist, Chapter 25: Annus Mirabilis at Harvard: The Mandelbrot Set and Other Forays into Pure Mathematics, 1979–80

Mandelbrot was able to take the lessons he learned in financial prices and other wide ranging fields of interest and tie it back to his core area of strength – mathematics. The Mandelbrot set is named. By thinking of fractal math as dimensions defined by fractions, rather than whole numbers, he further extended humanity’s ability to name and study this field.

Best Quote(s)

“And I understood from readings and course material that a field might simply die for lack of manageable and interesting unsolved questions.” 3848

Benoit Mandelbrot, Chapter 25, Location 3848

Mandelbrot thought about fields of study as a social construct, which required the intrigue, interest and commitment of individual scientists to grow and prosper.

“Stephen Jay Gould (1941–2002), a lively paleontologist with multiple appointments at Harvard. Quite independently, we had become two very visible champions of discontinuity—he in paleontology and I in the variation of financial prices.” 3825

Benoit Mandelbrot, Chapter 25, Location 3825

Good products have competitors. Products that don’t have a competitor warrant skepticism in their review. Gould’s framing of discontinuity in the fossil record – known as punctuated equilibrium, explained the fractured lineages of the fossil record by explaining them as bursts of fast moving periods of evolution.

Page by Page, Screen by Screen, Swipe by Swipe

3794

“These pictures were intriguing objects I then called lambda and mu-ma—alternative ways of representing a fundamental new mathematical structure that became known as the Mandelbrot set. It has been called the most complex object in mathematics, has become a topic of folklore, and remains my best and most widely known contribution to knowledge.”

3809

A Luncheon That Changed a Life

“Stephen Jay Gould (1941–2002), a lively paleontologist with multiple appointments at Harvard. Quite independently, we had become two very visible champions of discontinuity—he in paleontology and I in the variation of financial prices.”

3825

Physics in Broken Dimension

3831

“Most of our papers concerned spaces where dimension is not 1, 2, 3, or higher but a fraction, and brought fractals toward the mainstream of statistical physics.”

Amnon Aharony, a physicist from Tel Aviv University

“This led me to put forward a bold conjecture: that solving the usual partial differential equations of physics can yield either familiar and expected smoothness, or fractality.”

3842

“Early in life, I learned that for a scholar, nirvana is to take an unsolved problem that had been stated long before and solve it.”

3848

“And I understood from readings and course material that a field might simply die for lack of manageable and interesting unsolved questions.”

3864

A Turning Point in Mathematics

3887

“Thought wanders to Napoleon’s saying that a good sketch, in all its complexity, is worth a thousand words, or even to the biblical Let there be light.”

3915

“My answer distilled—once again—the already told story of my scientific life: when I seek, I look, look, look, and play with pictures. One look at a picture is like one reading on a scientific instrument. One is never enough.”

3931

Zigzagging Through the First Course Ever on Fractals

“The personal computer had not yet hit the world,…”

3937

“I was expected to pursue and teach my style of using computers, but computers and their use were not welcome at Harvard. Hence, there was a near-total absence of both equipment and skills among the students and faculty.”

Wide Wonder, Complexity, and Mystery

3961

“…for the Mandelbrot set, many view it as extremely—miraculously!—complex. I feel exceptionally privileged that my wanderer’s life led me to be the agent of this discovery.”

3966

Never before described, “The title is “Fractal Aspects of the Iteration of [Quadratic Maps] for Complex [Parameter and Variable].” It appeared in late 1980 in Annals of the New York Academy of Sciences.”

3982

Annual mirabilis? “… was a year of a single miracle that developed slowly over time, while the 1979–80 miracle came on like lightning—as miracles should.”

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Mandelbrot’s The Fractalist, Chapter 24: Based at IBM, Moving from Place to Place and Field to Field, 1964–79

Mandelbrot’s home at IBM is secure, and with that security he continues to search about for interesting problems that fit his growing fractal toolkit. He remains worried that he has started his great work too late in life, and with that worry he remains determined to seek out and pursue new problems which his field of fractals can solve.

Best Quote(s)

“It forced me to gather all I had achieved and fit it into an hour. This effort started me on my 1975 book.”

Benoit Mandelbrot, The Fractalist, Chapter 24 (Location 3706)

Mandelbrot accepts the lecture in France, and by doing so he creates a deadline. This forces him to organize his notes, which become the foundation of the book that would make his name known worldwide.

Page by Page, Screen by Screen, Swipe by Swipe

3673

“It began exceptionally late, so I continually felt in a great hurry and ranged in directions far more varied than I would have thought sensible or feasible.”

3678

“Instead, I was doing what happened to be most desirable given what I perceived as the market for scientific ideas like mine—or, in other cases, what I viewed as easiest to undertake given some special resource that had become available in one corner or another of a very large institution.”

Trumbull Lecturer and Visiting Professor of Applied Mathematics at Yale

3689

“…my various models of “abnormality” in the real world.”

In Paris: A Lecture Not to Be Forgotten

3706

“It forced me to gather all I had achieved and fit it into an hour. This effort started me on my 1975 book.”

“I answered each, briefly but technically. In a sense, I gave a dozen five-minute technical presentations.”

Deciding Not to Compete for the Collège de France

3733

“What I am about to say may sound ridiculous. Burning scientific ambition came first, and I would not think of endangering it.”

3739

Mother Dies in 1973

3755

Visits to the Mittag-Leffler Institute

3766

“The third meeting, in 2002, that my work inspired was on the mathematics of the Internet.”

3777

“To test new Internet equipment, one examines its performance under multifractal variability.”

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Mandelbrot’s The Fractalist, Chapter 23: On to Fractals: Through IBM, Harvard, MIT, and Yale via Economics, Engineering, Mathematics, and Physics, 1963–64

There are times when reading a book that every page, every sentence and every word come together to create a smile on the face of the reader. In Part 1 we’ve followed young Mandelbrot’s survival in the face of Nazi persecution and read with awe the names of the intellectuals he dealt with as he ‘drifted’ in Part 2. In Part 3 the tailor draws the thread, and in doing so we see the design pull together in satisfying way.

Each page in this chapter is great, each turn of phrase is memorable, and it is difficult to not envision an older Mandelbrot working on this document enjoying the time to recall his younger years.

Best Quote(s)

“This chapter’s title seems to make no sense. How can it possibly reflect reality?”

Benoit Mandelbrot, The Fractalist, Chapter 23

Earlier in the book it became clear that the author was attempting to take his field of roughness and apply it to this text. Here he says so directly, implying that the path that took him to study roughness was itself fractal in nature. Of course.

“Numerous additional fields I visited also differ deeply yet share a key feature that to me matters more than any other: roughness.”

Benoit Mandelbrot, The Fractalist, Chapter 23

If things are not smooth, then they are rough. The study of roughness, known as Fractals, shows common patterns to behavior and events that are not smooth.

“The fact that my life’s most productive season came late kept me in a constant hurry, and I could rarely take it easy.”

Benoit Mandelbrot, The Fractalist, Chapter 23

From a life strategy standpoint – Dr. Mandelbrot never shies from the fact that he was late to gain the fame that he seemed destined from at an early age. He admits that this tension drove him and shaped his life.

In fact, a common thread of my work is that values far from the norm are the key to the underlying phenomenon.”

Benoit Mandelbrot, The Fractalist, Chapter 23

In reading Charlie Munger’s Almanack (?) he goes to great pains to justify that his good decisions on ‘big days’ led to his fund performance. Mandelbrot points out that this is true of all things.

“Ultimately, my interests and achievements were viewed in Chicago as absurdly broad, and at Harvard as absurdly narrow! Unfortunately, I had to agree that those opinions were not entirely unreasonable.”

Benoit Mandelbrot, The Fractalist, Chapter 23

Throughout his life – or at least in this autobiographical and elderly reflection – Mandelbrot is comfortable with who he is. He does not force himself into scenarios where he cannot prosper. There is a self confidence in these actions that is crucial to his finding and achieving his Keplerian dream.

“I had not a single identifying brand name for my activity. Ten more years went by until I gave up and coined the word “fractal.””

Benoit Mandelbrot, The Fractalist, Chapter 23

Dr. Mandelbrot – because you haven’t been part of someone else’s laboratory, you really should make up a word and then use that to brand your work.

Page by Page, Screen by Screen, Swipe by Swipe

3439

“This chapter’s title seems to make no sense. How can it possibly reflect reality?”

3443

“Numerous additional fields I visited also differ deeply yet share a key feature that to me matters more than any other: roughness.”

“The phenomena I have studied are elusive and not yet covered by any proper quantitative science—pure or applied.”

3449

“I wanted to provide a consistently more faithful description of known facts—and hence help financial engineering out of its dismal and harmful state. The same goes for the developments that will be described in this chapter: no existing body of science could assist them.”

“The fact that my life’s most productive season came late kept me in a constant hurry, and I could rarely take it easy.”

3459

“A deep unity that had been present in my work all along was gradually revealed, then increased its presence and became my guide.”

3465

“Having worked in many fields but never wholly belonging to any, I consider myself an outlier. It does not hurt that the word “outlier” has an established technical meaning in statistics: it is an observation that is so very different from the norm that it may be due to accidental foreign contamination.”

Astronomical cats…

3465

“To the contrary, I have found that the so-called outliers are essential in finance. In fact, a common thread of my work is that values far from the norm are the key to the underlying phenomenon.”

3470

Title – Hydrology: The Biblical Joseph, Hurst, and Me

3476

“In a 1965 publication, I showed that while Hurst had no clue about what he had discovered, his formula indeed holds—and has unexpectedly far-reaching consequences.”

3481

“The study of rivers brought me to the distinction between two kinds of fractals: the self-similar (shapes scaled by the same amount in every direction, like coastlines) and the self-affine (shapes scaled by different amounts in different directions, such as turbulence).”

3498

“The title of a draft of my first paper on galaxy clusters implied that clustering is an illusion.”

“What you propose is that they may very well be right here.” He pointed to his temple. “Is that right?”

3509

“The point is that in some fractals, clusters are completely real because they have been included by construction; in other fractals, no clusters have been included by construction but the mind sees them anyhow.”

“Below are two images of galaxies: on the left, a real galaxy cluster from the Center for Astrophysics and Space Sciences at the University of California, San Diego, and, on the right, a computer fractal model of galaxies.”

3514

“Helping Lady Luck Through Telephones”

3520

“Louis Pasteur is credited with the observation that chance favors the prepared mind. I think that my long string of lucky breaks can be credited to my always paying attention. I look at funny things and never hesitate to ask questions.”

3526

“As a result, I have sometimes been called the father of long tails. Whether long or fat, those tails are an intimate part of the fractal family. So it makes perfect sense that I have since been called the father of fractals.”

3531

Phone error clusters – “Once again, I brought together a problem from one world and a tool from a far-removed other world. A second major Kepler moment within a year.”

3536

“Of Galileo’s many gifts to scientific knowledge, here is an essential one that requires no formula. His world believed that the heavens were orderly, while everything on Earth was a mess. To the contrary, Galileo found plentiful messes on the moon—its craters. He also found order on Earth—the falling of stones pulled down by gravity.”

3542

“He [Zipf] believed that in the physical sciences, randomness follows the distribution called normal, Gaussian, or bell-shaped, while in the social sciences—word frequencies, personal income—the distribution is the so-called hyperbolic.”

3558

Snatched Up by Harvard Applied Sciences

3569

We rented the house of noted MIT physicist Victor Weisskopf,…

“At lunch, he complained about how hard it was for him to finish his memoir, and urged me not to write mine too early—certainly not as long as I still could do science. I promised, and now can only hope that my wait has not been too long.”

Teaching at Harvard Applied Sciences

Naval Officer compliment,

“I had been told that science was created by humans, but in all my other courses it seemed created by creaky machines. Your course made me watch science being created. Thank you, sir.”

3601

“No Permanent Position at Harvard”

3607

“Ultimately, my interests and achievements were viewed in Chicago as absurdly broad, and at Harvard as absurdly narrow! Unfortunately, I had to agree that those opinions were not entirely unreasonable.”

3618

A Rare Institute Lecturer at MIT

3640

“I contributed to each conclusion by being a truly dismal politician who preferred working to networking.”

“I had not a single identifying brand name for my activity. Ten more years went by until I gave up and coined the word “fractal.””

3645

Lady Luck Against the Mess of Turbulence

3662

“I developed a multifractal model that addressed the intermittence of turbulence and has also turned out to be fundamental to our understanding of the variation of financial prices.”

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Mandelbrot’s The Fractalist, Chapter 22; At Harvard: Firebrand Newcomer to Finance Advances a Revolutionary Development, 1962–63


My first exposure to Mandelbrot was through his joint work with Richard L. Hudson in The (Mis)Behavior of Markets, which was published in 2004 and stands as a testament to the contributions he made to finance beginning with this work in 1962. Mandelbrot follows the rules that led him through Part 2 of his life, and in doing so is presented with a unique opportunity to extend humanity’s understanding of financial markets.  He takes full advantage of the opportunity, but then draws on the lessons learned in Part 1 to realize that the political inertia of this industry will blunt the impact of his magnificent contribution.  Rather than dwell on this, he collects on the cache and karma of his contributions and continues on his life.  

There are several impressive things that Mandelbrot does not do:

  • He doesn’t sever his ties with IBM to become a financier. 
  • He doesn’t dig his heels in to fight the financial establishment – despite his convictions that he is right.
  • He refines his work on his terms, rather than trying to take the theory to far.  
  • He continues to support the next generation of scientists in this area of finance by working with Eugene Fama and Merton Miller.  Mandelbrot does not shepherd his work, he pushes it out and extends its reach.  
  • He misses career opportunities that would be soul crushing and unrecoverable for many, but instead he plots onward.  
  • Mandelbrot does not get stuck on the nature of his contribution to finance, despite its enormous value.  He reads the situation accurately and moves on.

Best Quote(s)

“MY INVOLVEMENT WITH THE BEHAVIOR of financial prices—absolutely unplanned—became a constant of my scientific life.”

Mandelbrot’s The Fractalist, Chapter 22

Mandelbrot’s path to achieving his Keplerian dream is not smooth – it is rough. Encounters with financial prices and their behavior would forever be a part of his life.

“The three states of chance—wild, mild, and slow—can be compared to the three states of matter. Are not solid and gas separated by liquid? Absolutely. In my view, the same is true of chance—the counterpart of liquid being “slow” randomness.”

Mandelbrot’s The Fractalist, Chapter 22

Enumeration of options is always fascinating, and ‘mild, wild and slow’ are wonderful names.

“We’ve done all we can to make sense of these cotton prices. Everything changes, nothing is constant. This is a mess of the worst kind.”

Mandelbrot’s The Fractalist, Chapter 22

There is great freedom in declaring a situation in hopeless. By declaring things a mess, “of the worst kind” the stage is set for Mandelbrot to attempt an explanation. As he benefited from his unique position with Zipf in his PhD, here Mandelbrot benefits from encountering a situation where there is low risk of embarrassment.

“Fractals—or their later elaboration, multifractals—do not claim to predict the future with certainty. But they do create a more realistic picture of market risks than does observation alone.”

Mandelbrot’s The Fractalist, Chapter 22

Telling the future with 100% accuracy isn’t yet possible – but telling the future a little bit better tomorrow than was done today is a great improvement for society. Finance had previously lived in the world of smooth trajectories – when everyone knew that this was inaccurate. Through his study of roughness, Mandelbrot improved the understanding of market behavior.

“But not for a moment did I forget that to remain stable and vertical, a bicycle must move sufficiently fast.”

Mandelbrot’s The Fractalist, Chapter 22

Bicycles are wonderful, but they are safest when moving. Balance is possible with minimal equipment, provided that motion is part of the equation. Velocity and direction are essential to safe operation with a minimalist approach.

“I was acutely aware that my findings would have devastating consequences for the accepted standard theory of speculation.”

Mandelbrot’s The Fractalist, Chapter 22

In Part 1 we watched Mandelbrot’s family deftly maneuver through World War 2 and survive where others misread the political environment and perished. Mandelbrot has recognized that he has done work of great merit, but also sees that the work may not exist in fertile ground. The finance industry’s inertia and resistance to change may prevent this phase of his Keplerian Dream from becoming the early landslide victory that it might have been.

Page by Page, Screen by Screen, Swipe by Swipe

“MY INVOLVEMENT WITH THE BEHAVIOR of financial prices—absolutely unplanned—became a constant of my scientific life.”

“… different states of randomness: the “mild” and the “wild,” and a third state I call “slow.””

3246

“I was acutely aware that my findings would have devastating consequences for the accepted standard theory of speculation.”

3257

“Oh, I am very sorry. I should have started by saying so. The invitation is from Harvard, and their offer is higher than my current salary.”

3263

“If status within IBM had been measurable, mine would have instantly jumped from well under the radar to well above—where it stayed.”

3269

“But not for a moment did I forget that to remain stable and vertical, a bicycle must move sufficiently fast.”

3274

“The sequence that followed, of sociological low points and intellectual highs, could not have been predicted.”

3291

“There were far too many big price jumps and falls. And the volatility kept shifting over time. Some years prices were stable, other years wild. “We’ve done all we can to make sense of these cotton prices. Everything changes, nothing is constant. This is a mess of the worst kind.””

3307

“Moreover, there were too many big price jumps to fit the bell curve.”

3318

“All price charts look alike. Sure, some go up, some down. But daily, monthly, annually, there is no big difference in their overall look.”

3324

“Here, the fractal scaling up and down is not being done to a shape, such as the florets of a cauliflower. Rather, it is being applied to a different sort of pattern, the way prices vary. The very heart of finance is fractal.”

3349

“My first work in finance had brought together two domains of knowledge far removed from one another.”

3355

“By bringing them into all-too-practical finance, I imposed and argued for a deep distinction between “mild” and “wild” states of randomness of chance.”

“The three states of chance—wild, mild, and slow—can be compared to the three states of matter. Are not solid and gas separated by liquid? Absolutely. In my view, the same is true of chance—the counterpart of liquid being “slow” randomness.”

3378

“First, price changes are not independent of each other.”

“Second, the distribution of price changes is not “normal.””

3398

“Fractals—or their later elaboration, multifractals—do not claim to predict the future with certainty. But they do create a more realistic picture of market risks than does observation alone.”

3420

“This left him with a problem that was the bane of my life: my tendency to cross scientific disciplines.”

Mandelbrot encounters current and future greats of finance; Eugene Fama, then a student, and Merton Miller, who would make efforts to recruit him to the University of Chicago.

3425

“Fama conceded, corrected his earlier assertions, replaced the mysterious label “martingale” with “efficient market,” and built his career on becoming its champion.”

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Mandelbrot Part 2: Chapters 8 – 20, “My Long and Meandering Education in Science and in Life”

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

  1. Having a goal and continually re-affirming what he does want to do. He names his goal – The Keplerian Dream.
  2. Small activities are consistent with his larger ambition.
  3. Associating with the best and brightest – and being open about his ambitions
  4. Building on his strengths in mathematics.
  5. Enjoying life – Mandelbrot exhaults in the bureacratic interludes, he finds love with Aliette, rejoices in music.
  6. Figuring out what he doesn’t want to do. Reversing bad decisions.
  7. Being comfortable with who he is.

Chapter 8: Paris: Exam Hell, Agony of Choice, and One Day at the École Normale Supérieure, 1944–45

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.

Chapter 9: 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.

Chapter 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.

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.

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:

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

Mandelbrot, Chapter 12

Chapter 13: Life as a Grad Student and Philips Electronics Employee, 1950–52

“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.

Best Quote(s)

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

Chapter 14: First Kepler Moment: The Zipf-Mandelbrot Distribution of Word Frequencies, 1951

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

Chapter 15: Postdoctoral Grand Tour Begins at MIT, 1953

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!

Chapter 16: Princeton: John von Neumann’s Last Postdoc, 1953–54

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.

Chapter 17: Paris, 1954–55

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

Chapter 18: Wooing and Marrying Aliette, 1955

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.

Chapter 19: In Geneva with Jean Piaget, Mark Kac, and Willy Feller, 1955–57

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.

Best Quote(s)

“… 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.

Chapter 20: An Underachieving and Restless Maverick Pulls Up Shallow Roots, 1957–58

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.

Best Quote(s)

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.

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Mandelbrot’s The Fractalist, Chapter 21: At IBM Research Through Its Golden Age in the Sciences, 1958–93

[About the image – an IBM 1401 mainframe – from the 1960’s – prints a Mandelbrot fractal driven image.]

Mandelbrot would spend the next 35 years employed by an associated with IBM Research. He would serve as a professor at times, but there was always a tie back to industry, giving him flexibility in his pursuits.

Best Quote(s)

IBM was going through a change, and with it they needed to change the kind of people that they were hiring.

“For one thing, relaxed hiring rules brought in many individuals for whom other institutions did not compete: “oddballs,” “wild geese,” scientists whose high-class record was marred by some fault or another or by disputes with faculty advisers.”

Mandelbrot, The Fractalist, Chapter 21

IBM had to change. It had to go through a step change in personnel to create a step change in its own business. It had need of a fractal ‘big change’, which could only occur if it made a series of correct ‘small change’ decisions with its hiring. Mandelbrot again shows examples of fractal activity in his life; if things are smooth – we know how they will behave, but when things are rough, there is a different set of rules.

“The Revolution succeeded because Carnot hired men such as the Corsican Napoléon Bonaparte.”

Mandelbrot, Chapter 21

Looking back Mandelbrot sees that this was the beginning of the ‘Fruitful third stage’ in pursuit of Keplerian dream of pioneering a new field of study. But he at the time the day-to-day activities that were asked of him by IBM didn’t necessarily fit that vision. Again, he shows us a fractal pattern in action – the small steps would come together to create a big shift.

“They appeared at first sight to clash badly—but they really didn’t clash at all. It soon emerged that I was working on the building blocks of my soon-to-be fractal geometry of nature.”

Mandelbrot, The Fractalist, Chapter 21

Page by Page, Screen by Screen

3028

3038

“At work you never have enough time to do what you want, and your wives complain that on Saturday mornings you go to the lab instead of taking the kids to the ball game.”

3049

““Pure scientific research is a very difficult and in most cases unrewarding profession.… You never have enough time to do what you want …”

3055

“A father with a self-assigned and never-fulfilled mission is not a full-time father and can play havoc with his family.”

3075

“So the date June 20, 1958, has come to mark in my mind the midpoint of my life.”

3086

“Neither a great scientist nor an engineering innovator, he was a shrewd operator with a sense of noblesse oblige.”

3108

“My consulting role for “down-to-earth” colleagues was varied and mostly enjoyable.”

3124

A Famous Fred invites him in to IBM – Manfred Kochen (1928–84).

3135

“In 1958, IBM was weighed down by an old and once carefully groomed reputation for extremely provincial and paternalistic human relations: company songs, compulsory white shirt and proper tie, and the like. Out of the blue, it set out to hire an entirely different technical workforce.”

3141

“Therefore, the selection rules had to change, and various old restrictions on inclusion were loosened.”

3146

“The Revolution succeeded because Carnot hired men such as the Corsican Napoléon Bonaparte.”

3161

“For one thing, relaxed hiring rules brought in many individuals for whom other institutions did not compete: “oddballs,” “wild geese,” scientists whose high-class record was marred by some fault or another or by disputes with faculty advisers.”

3167

John Backus

“… John developed a “high-level” programming language dubbed FORTRAN (from “formula translator”), …”

Alex Muller, a colleague, would create the scanning electron microscope (“SEM”) and win the Nobel Prize.

3168

“I can’t be accused of envying those who do well at exams (nor of biting the hand that fed me) by noting that the IBM experiment confirmed my longstanding lack of respect for exam rankings.”

3179

“Yes, there was a time when our computers required no password!”

“Monitoring revealed that I was billed for a mass of tiny programs run by high school students all over the surrounding Westchester County.”

3206

“We were pushing the machine well beyond its original specifications.” Calcomp typewriter

3240

“They appeared at first sight to clash badly—but they really didn’t clash at all. It soon emerged that I was working on the building blocks of my soon-to-be fractal geometry of nature.”

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