There is a grace and tact to Mandelbrot’s writing instilled from his upbringing – he has not written a ‘final’ part, simply ‘Part 3.’ Condensing the life of someone that unlocked so much knowledge starts to feel hopeless – he did so many impressive things and wrote about them with modesty and elegance.

Fractals For When Things Are Not Smooth

“What I’m asserting, very strongly, is that when some real thing is found to be unsmooth, the next mathematical model to try is fractal or multifractal. Since roughness is everywhere, fractals are present everywhere.” Location 4460

Dr. Benoit Mandelbrot, Chapter 29, Location 4460

Before Mandelbrot, mathematics and models dealt with a world that was smooth. Interest rates compounded continuously, and graphs were full of straight lines, slopes and curves. But this did not fit the world as it was seen. Mandelbrot’s creation of fractals allowed models and graphics that created images that reflected the roughness shown in nature, finance, and so many other fields.

For a ‘Fractal Life Strategy’, we could say:

• You know how things behave if the world is smooth.
• When the world is not smooth, it is rough. And when it is rough, we anticipate things using our knowledge of fractals.

Wild, Mild and Slow

“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

Any form of enumeration is enlightening – Mandelbrot’s study of fractals established that probabilities can shift between three states – mild, wild and slow.

Branding

“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

Mandelbrot contributed to many different fields, all building from his first work with Zipf’s Law. As he matured, he realized that he needed a name for this field of study – he needed to market his accomplishments. ‘Fractals’ were born.

Writing

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

Benoit Mandelbrot, The Fractalist, Chapter 24

Mandelbrot succeeded in his Keplerian dream because he was outside of the academic establishment; by being with IBM he could see many problems, and by having a broad focus for his work, he was forced to make his writing more accessible than his peers who had a narrower, more learned, target audience.

Team Building

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

Mandelbrot, Chapter 21

Mandelbrot joins IBM at a time when the business is going through a massive post World War 2 hiring binge to promote a much needed culture changes. They hire for brilliance, ignoring quirks, and in so doing develop a world class research center. The camaraderie and stability of IBM enable the birth of fractals and fulfillment of Mandelbrot’s Keplerian dream.

Opportunity, Impact

“I had often demonstrated the capacity to formulate big dreams that everyone else held to be odd and unreachable—but that I managed to fulfill.” 4253

Mandelbrot’s The Fractalist, Chapter 27

Mandelbrot had a grand dream – to impact to humanity along the lines of what Kepler brought by studying, calculating, and predicting the structure of the universe. His dreams were big. Others though them unattainable, but he continued to work and was successful in reaching them.

Part 3, Chapter by Chapter Summary – 34 Mandelbrot Quotes

Chapter 21

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

Chapter 22

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.

Chapter 23

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.

Chapter 24

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.

Chapter 25

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.

Chapter 26

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.

Chapter 27

Mandelbrot’s time at Yale is punctuated with the institution’s highest honor. He observes twice, both in his life and in the goals identified by Yale’s math department that there was a strategy for setting out on goals that were ‘odd and unreachable’, that can lead to great things. Yale hired him based on a desire to be ‘different’, not ‘lesser’.

Best Quote(s)

“THE ART OF RECEIVING new offers and fast promotions has always baffled me, but I have been lucky on a few occasions.” 4200

Benoit Mandelbrot, The Fractalist, Chapter 27, Location 4200

Mandelbrot’s name is now well known and distinct, but his life is full of big offers and promotions that go unfilled. There is a fractal nature to his life – rarely smooth, and often rough. How many autobiographies are smoothed out in the re-telling and remembering of a life?

“I had often demonstrated the capacity to formulate big dreams that everyone else held to be odd and unreachable—but that I managed to fulfill.” 4253

Benoit Mandelbrot, The Fractalist, Chapter 27, Location 4253

Mandelbrot’s self aware comment matches his insight about his new academic home, Yale, earlier in the chapter, “… they had decided to replace “lesser” with “different”—in particular, by expanding less abstract topics.”

Chapter 28

With two chapters left to go, Mandelbrot’s reflections on his life and accomplishments make every passage notable. Picking ‘Best Quotes’ feels like an affront to the pearls of wisdom dispensed but not chosen.

Best Quote(s)

“An important turn in my life occurred when I realized that something I had long been stating in footnotes should be put on the marquee.”

Benoit Mandelbrot, The Fractalist, Chapter 28 (Location 4278)

Mandelbrot didn’t set out to study roughness; he instead found a series of problems across seemingly unconnected fields that focused his mathematical skills on an area that was universally present, but not always acknowledged.

“Before my work on roughness, it was either undefined or measured by too many irrelevant quantities. Now it can be measured by one, two, or a few numbers.”

Benoit Mandelbrot, The Fractalist, Chapter 28 (Location 4289)

I’m reading John Urschel’s Mind and Matter with my son; Urschel played in the NFL and afterwards completed a PhD in math at MIT. At times his statements of fact seem boastful, but they are true. How wonderful a statement from Mandelbrot! Is he boasting? Perhaps, but how could he state the truth and not be boastful.

Mandelbrot’s Keplerian dream inspired him to organize a theory of roughness from work across many fields and make a great contribution in mankind’s understanding of the world around us.

Chapter 29

With only the Afterword left, these are the final words written by Mandelbrot. He begins with a weighty reflection about his 86 years of life, and closes with a wink to the reader, that the ‘fractal’ hints that were sprinkled in the book about his own life were intentionally inserted. Like the other chapters in Part 3, there are a number of outstanding quotes that provide insight to his strategy for life and models for explaining the world around him.

Best Quote(s)

My favorite quote from this chapter may be my favorite overall for the whole book; it is usable in real life. If things aren’t smooth – they are probably rough. There is a model for how rough things work – fractals.

“What I’m asserting, very strongly, is that when some real thing is found to be unsmooth, the next mathematical model to try is fractal or multifractal. Since roughness is everywhere, fractals are present everywhere.” Location 4460

Dr. Benoit Mandelbrot, Chapter 29, Location 4460

How best to explain one concept of fractals – self-similarity – with examples;

“A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Another example of this repeated roughness is the cloud.” Location 4456

Dr. Benoit Mandelbrot, Chapter 29, Location 4456

If fractals are so new as a field of study, how many other similarly obvious fields await the focus of the right mind?

“Fractal geometry is one of those concepts which at first invites disbelief but on second thought becomes so natural that one wonders why it has only recently been developed.” Location 4422

Dr. Benoit Mandelbrot, Chapter 29, Location 4422

If other obvious fields exist for study – if fractals were waiting for the right circumstances to be unlocked, how was it that our story’s hero, who had fled the Nazis in Part 1, was the person to find them?

“One reason is my personality—I don’t seek power or run around asking for favors. A second is circumstances—I was in an industrial laboratory because academia found me unsuitable.” Location 4460

Dr. Benoit Mandelbrot, Chapter 29, Location 4460

And lastly, a wink and a nod to those who have noted that fractals have surely filled the life of Dr. Mandelbrot:

“Does not the distribution of my personal experiences remind one of the central topic of my scientific work—namely, extreme fractal unevenness? All counted, I have known few minutes of boredom.” Location 4480

Dr. Benoit Mandelbrot, Chapter 29, Location 4480

Afterword

Mandelbrot achieved a great deal, but felt his whole life that there was much more discovery that he could have given the world. The afterword closes out with the topics he had hoped to touch on, but was unable to develop – negative dimensions and lacunarity, and also provides some closing observations on his life.

Best Quote(s)

“Like fractals, life is better understood as a process than as a result.”

Afterword

Use processes to understand the world.

“A fractal is defined as well by what has been removed as it is by what remains.”

Benoit Mandelbrot

Absence defines as much as presence.