Mandelbrot’s The Fractalist, Chapter 29: Beauty and Roughness: Full Circle

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

Page by Page, Screen by Screen, Swipe by Swipe – 13 Mandelbrot Quotes

4353

“A MEMOIR IS A LESSON IN HUMILITY. I was born in 1924, and it is now 2010.”

4357

“Of those born in the year 1924, I am sure that many became scientists. What made me seek out a role that others missed or spurned? I have always wondered, and I wrote this book in an effort to understand myself.”

4361

“My refoundation of finance was to occur as I neared forty, and the discovery of the Mandelbrot set came at fifty-five. For a scientist, those are unusually—astonishingly—old ages, as many witnesses have noted. And the number of would-be role models I have considered but not followed has been heartbreakingly large.”

4365

“What has attracted me to problems that science either had never touched or had long left aside—continually making me feel like a fossil? Perhaps a deficit in regular formal education.”

4377

Roughness in Painting and Music

4394

“One mathematical structure I called the Sierpiński gasket, made of several identical parts, turns out to be very common in decoration in Italian churches, either in mosaics on pavement or in paintings on the roof and ceiling.”

4406

“He liked to say he had used a fractal approach to composition for some time.”

4410

“Isaiah Berlin (1909–97), a British philosopher and man of action—whom I met—has written about the distinction the ancient Greek writer Archilochus drew between the fox, who knows many things, and the hedgehog, who knows one big thing. Once, colleagues assigned to introduce me before a lecture kept asking whether I viewed myself as a fox or a hedgehog. The point is that they all saw me as having two faces.”

4422

“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

Koch and Peano

4452

“The cauliflower is the standard example of shapes that appear more or less the same at all scales.”

4456

“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

4460

“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.”

4469

“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.”

4482

“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.”

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Mandelbrot’s The Fractalist, Chapter 28: Has My Work Founded the First-Ever Broad Theory of Roughness?

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.

Page by Page, Screen by Screen, Swipe by Swipe – 8 Mandelbrot Quotes

4278

“HOW CAN IT BE that the same technique applies to the Internet, the weather, and the stock market? Why, without particularly trying, am I touching so many different aspects of so many different things?”

“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.”

“Roughness is just as important as all those other raw sensations, but was not studied for its own sake.”

4285

“I reinterpreted one as the first of many quantitative measurements of roughness.”

4289

“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.”

4320

“Visually examining the Brownian island’s coastline led me to conjecture that its fractal dimension is 4/ 3.”

4341

My Work Reaches a New Audience

4346

“You might have lived shortly after Newton.”

“Uncanny forms of flattery! Each lifted me to seventh heaven! Truly and deeply, each marked a very sweet day! Let me put it more strongly: occasions like that make my life.”

Mandelbrot’s note about his sincere appreciation of the notes he has received over the years follows Carnegie’s guidance to give sincere appreciation.

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Mandelbrot’s The Fractalist, Chapter 27: At Yale: Rising to the University’s Highest Rank, Sterling Professorship, 1987–2004

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.”

Page by Page, Screen by Screen, Swipe by Swipe – 5 Mandelbrot Quotes

4200

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

Adjunct Professor of Mathematical Sciences at Yale

4217

“The Yale mathematics department disliked being ranked below Princeton and Harvard, and they had decided to replace “lesser” with “different”—in particular, by expanding less abstract topics.”

4226

Yale – 17 years more

IBM retire – 2 years of perks, but 13 more.

“So we never moved, and missed much of Yale collegiality—a clear loss.”

4230

“Commuting by car was tedious, and Aliette went beyond the call of duty by being the driver and enjoying Yale while I was working.”

4243

Sterling Professor of Mathematical Sciences at Yale

4253

“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.”

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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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