I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
~Benoit Mandelbrot, 1982
“A Greek among Romans” is what author and disciple Nicholas Taleb called him. A fitting label for someone who spent most of his life working on a mathematical philosophy no one else seemed interested in investigating. “Until a few years ago, the topics of my PhD were unfashionable,” claimed Mandelbrot, “but they are very popular today.” In fact, his specialty has blossomed into the field of Complexity Science, branching out with limitless application.
Mathematician Benoit Mandelbrot died earlier this month from pancreatic cancer. The extent to which this particular blog is indebted to his work and ideas is yet to be seen. That vast wealth resides in what Taleb would call the “antilibrary” – what we have yet to learn. However, this much is known: Mandelbrot’s work as a type of evangelist brought about an awareness to a transformative way of observing the world around us.
Over the past week and a half since Mandelbrot’s death, numerous articles about his life and work have populated the blogosphere. Listed below are some of the most informative ones. As for this post, it is only a prelude to some of the things we hope to find in the antilibrary concerning Mandelbrot.
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
As part of our “The Aesthetics of Chaos” series, we’ll be taking a look at the various different forms of art and how the “fractal geometry of nature,” as Mandelbrot called it, gives us an aesthetic guide. One artist in particular, the Australian painter Robert Berry, will be sharing with us some of his insights on the topic of fractals, nature and aesthetics. Many of these ideas stem from what we have learned about fractals from Mandelbrot. While he was a mathematician, Mandelbrot did not see distinctions between fields of study as most of his peers did. One of the reasons he did not continue as a mathematician in France, he claimed, was because of their “rage against images.” Were it not for his openness to images, he would not have discovered the beautiful intricasies of what we now call The Mandelbrot Set. Insights gained from fractals fluidly link aesthetics to science. “Think of color, pitch, loudness, heaviness, and hotness,” wrote Mandelbrot. “Each is the topic of a branch of physics.”
My fate has been that what I undertook was fully understood only after the fact.
In the following 2008 PBS interview, Mandelbrot and Taleb warned about the increasing fragility of our complex world. When asked to make predictions about the future, Mandelbrot simply replied “anything is possible,” while warning about the importance of vigilance. In an up-coming book review, we will be taking a look at the new second edition of Taleb’s The Black Swan: The Impact of the Highly Improbable. Many of Taleb’s ideas proceed directly from Mandelbrot’s work.
An extraordinary amount of arrogance is present in any claim of having been the first in inventing something,
One of the great insights stemming from his study of fractals was Mandelbrot’s view that recurrence is seen throughout nature. Even the above quote is a recurrence of Solomen’s lament “there is nothing new under the sun.” Part of our Chaos Journal project is to chart recurrence at the level of an individual. (If society is truly fractal in nature, then the smallest “pixel” of society is the individual.) At the Potsdam Institute for Climate Impact Research, Dr. Norbert Marwan is a pioneer in studying recurrence in complex systems. Dr. Marwan has graciously agreed to allow The Renaissance Mob to use his CRP toolbox (http://www.pik-potsdam.de/) to study recurrence as a tool for understanding both self and society.
Thanks to Mandelbrot’s study of fractals, roughness and chaos, we continue to learn about aesthetics, addressing fragility, and understanding recurrence in life and society.
Other articles about Mandelbrot
Benoit Mandelbrot (RIP) and the quest for a theory of really everything By John Horgan Oct 18, 2010