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.”