“A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals.”

— Benoît Mandelbrot

A Theory of Roughness (2004)
Context: Do I claim that everything that is not smooth is fractal? That fractals suffice to solve every problem of science? Not in the least. What I'm asserting very strongly is that, when some real thing is found to be un-smooth, the next mathematical model to try is fractal or multi-fractal. A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals. Since roughness is everywhere, fractals — although they do not apply to everything — are present everywhere. And very often the same techniques apply in areas that, by every other account except geometric structure, are separate.

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Benoît Mandelbrot 56

Polish-born, French and American mathematician 1924–2010

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“I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

As quoted in Encyclopedia of World Biography (1997) edited by Thomson Gale

“It is time to employ fractal geometry and its associated subjects of chaos and nonlinear dynamics to study systems engineering methodology (SEM). Systematic codification of the former is barely 15 years old, while codification of the latter began 45 years ago… Fractal geometry and chaos theory can convey a new level of understanding to systems engineering and make it more effective”

Arthur D. Hall (1925–2006) American electrical engineer

A.D. Hall III (1989) "The fractal architecture of the systems engineering method", in: Systems, Man and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on Volume 28, Issue 4, Nov 1998 Page(s):565 - 572

“I find enough mystery in mathematics to satisfy my spiritual needs. I think, for example, that pi is mysterious enough (don't get me started!) without having to worry about God. Or if pi isn't enough, how about fractals? or quantum mechanics?”

Tom Lehrer (1928) American singer-songwriter and mathematician

Interview at celebathiests.com (June 1996)

“My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

A Theory of Roughness (2004)

“The American mainstream news media have so far steered well clear of the subject because the phenomenon has been enthusiastically embraced by the talk radio fringe, leading to a death spiral of diminishing credibility.”

Charles Stross The Laundry Files

Source: The Laundry Files, The Annihilation Score (2015), Chapter 14, “Infected” (p. 266)

“Because of the economic crisis, China and the United States are bound together. This is a totally new phenomenon, and nobody will fight for ideology anymore. It’s all about business.”

Ai Weiwei (1957) Chinese concept artist

2000-09, Who Is Ai Weiwei?, 2009

“Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory, and besides were my love when I was a young man. Cauliflowers exemplify a second area of great simplicity, that of shapes which appear more or less the same as you look at them up close or from far away, as you zoom in and zoom out.
Before my work, those shapes had no use, hence no word was needed to denote them. My work created such a need and I coined "fractals."”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

A Theory of Roughness (2004)

“Words are such thin shavings of the fractal fruit,
tiny scraping of the skin that holds
these joyously determined swirls of history
inside their juicy turbulence.
Talking itself westward after the day's feast,
each little word with its meaning strapped to its back
falls down the swell of tomorrow
like a hiker with hopeful new shoes.”

Karen Press (1956) South African poet

Purposefully peeling footsteps (Home, 2000)

“An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role remained unrecognized and waited for me to be uncovered.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

A Theory of Roughness (2004)
Context: My book, The Fractal Geometry of Nature, reproduced Hokusai's print of the Great Wave, the famous picture with Mt. Fuji in the background, and also mentioned other unrecognized examples of fractality in art and engineering. Initially, I viewed them as amusing but not essential. But I changed my mind as innumerable readers made me aware of something strange. They made me look around and recognize fractals in the works of artists since time immemorial. I now collect such works. An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role remained unrecognized and waited for me to be uncovered.

“A branch of physics that I was working in for many years has lately become much less active. Many problems have been solved and others are so difficult that nobody knows what to do about them. This means that I do much less physics today than 15 years ago. By contrast, fractal tools have plenty to do. There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable. The hammer I crafted is the first effective tool for all kinds of roughness and nobody will deny that there is at last some roughness everywhere.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

A Theory of Roughness (2004)

“A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals.”

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Benoît Mandelbrot 56

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