To remember and to honor Benoit Mandelbrot, Edge is pleased to present several pieces:

"A Theory of Roughness: A Talk with Benoit Mandelbrot", an Edge feature which previously ran on December 20, 2004

Response to the 2005 Edge Question, "What Do You Believe Is True Even Though You Cannot Prove It?

"A remembrance on behalf of the Edge community by Dimitar Sasselov;

"Benoit's Dangerous Life" by George Dyson

"The Father of Long Tails", a 2008 interview conducted in Paris by the Swiss art curator andEdge collaborator Hans Ulrich Obrist, currently the Curator of the Serpentine Gallery in London.

Response to the Edge-Serpentine Gallery collaboration "Formulae For The 21St Century: What Is Your Formula? Your Equation? Your Algorithm?"

Photograph: Budapest, 2003. "Benoit's Dangerous Life": A report on the photograph by George Dyson

Photograph: With John Brockman, Cambridge, Massachusetts, December 29, 2010

BENOIT MANDELBROT, who died on October 14th, was Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T.J. Watson Research Center. His books include The Fractal Geometry of Nature; Fractals and Scaling in Finance; and (with Richard L. Hudson) The (mis)Behavior of Markets.

A THEORY OF ROUGHNESS [12.20.04]

A Talk with Benoit Mandelbrot

A recent, important turn in my life occurred when I realized that something that I have long been stating in footnotes should be put on the marquee. I have engaged myself, without realizing it, in undertaking a theory of roughness. Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics. Chemistry is filled with acids, sugars, and alcohols — all are concepts derived from sensory perceptions. Roughness is just as important as all those other raw sensations, but was not studied for its own sake.

Introduction

By John Brockman

During the 1980s Benoit Mandelbrot accepted my invitation to give a talk before The Reality Club. The evening was the toughest ticket in the 10-year history of live Reality Club events during that decade: it seemed like every artist in New York had heard about it and wanted to attend. It was an exciting, magical evening. I've stayed in touch with Mandelbrot and shared an occasional meal with him every few years, always interested in what he has to say. Recently, we got together prior to his 80th birthday.

Mandelbrot is best known as the founder of fractal geometry which impacts mathematics, diverse sciences, and arts, and is best appreciated as being the first broad attempt to investigate quantitatively the ubiquitous notion of roughness.

And he continues to push the envelope with his theory of roughness. "There is a joke that your hammer will always find nails to hit," he says. "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 least some roughness everywhere."

"My book, The Fractal Geometry of Nature," he says, 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 soon changed my mind.

"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 had remained unrecognized and waited for me to be uncovered."??

—JB

Inflation does not provide a natural explanation for why the early universe looks like it does unless you can give me an answer for why inflation ever started in the first place. That is not a question we know the answer to right now.  That is why we need to go back before inflation into before the Big Bang, into a different part of the universe to understand why inflation happened versus something else. There you get into branes and the cyclic universe. ... I really don't like any of the models that are on the market right now. We really need to think harder about what the universe should look like.

SEAN CARROLL, a theoretical physicist, is a senior research associate at Caltech. His research interests include theoretical aspects of cosmology, field theory, and gravitation. He is the author of a Spacetime and Geometry: An Introduction to General Relativity; and From Eternity to Here: The Quest for the Ultimate Theory of Time. And he is cofounder and contributor to the Cosmic Variance blog.

We have decided, as a scientific endeavor, to extrapolate as much as we can from our knowledge of the individual processes that we can measure: evaporation from the ocean, the formation of a cloud, rainfall coming from a cloud, changes in wind patterns as a function of the pressure field, changes in the jet stream. What we have tried to do is encapsulate those small-scale processes, put them together, and see if we can predict the emerging properties of that fundamental complex system.

THE PHYSICS THAT WE KNOW 
A Conversation with Gavin Schmidt

Introduction

There is a simple way to produce a perfect model of our climate that will predict the weather with 100% accuracy. First, start with a universe that is exactly like ours; then wait 13 billion years.

But if you want something useful right now, if you want to construct a means of taking the knowledge that we have and use it to predict future climate, you build computer simulations. Your models are messy, complicated, in constant need of fine tuning, exacting and inexact at the same time. You're using the past to predict the future, extrapolating the very complicated from the very simple, and relying on an ever-changing data stream to inform the outcome.

Climatologist Gavin Schmidt explains:

How do you ask questions about expectations in the future? Obviously, you have to have things that are based on the physics that we know. You have to have things that are based on processes we can go and measure, that has to be based on our ability to understand the climate that we have now. Why do you get seasonal cycles? Why do you get storms? What controls the frequency of these events over a winter, over a longer period? What controls the frequency of, say, El Nino events in the tropical Pacific that have impacts on rainfall in California or in Peru or in Indonesia? How do you understand all of those things?

We approach this is in a very ambitious way.

What we have decided, as a scientific endeavor, is to extrapolate as much as we can from our knowledge of the individual processes that we can measure: evaporation from the ocean, the formation of a cloud, rainfall coming from a cloud, changes in the wind patterns as a function of the pressure field, changes in the jet stream. What we have tried to do is encapsulate those small-scale processes, put them altogether, and see if we can predict the emerging properties of that fundamental complex system.

— Russell Weinberger

GAVIN SCHMIDT is a climatologist with NASA's Goddard Institute for Space Studies in New York, where he models past, present, and future climate. His essay "Why Hasn't Specialization Led To The Balkanization Of Science?" in included in What's Next? Dispatches on the Future of Science, edited By Max Brockman.

Gavin Schmidt's Edge Bio Page

Already the impacts are obvious in the extreme north, where melting Arctic sea ice, drowning polar bears, and forlorn Inuit hunters are by now iconic images of global warming. The rapidity and severity of Arctic warming is truly dramatic. However, the Arctic, a relatively small, thinly populated region, will always be marginal in terms of its raw social and economic impact on the rest of us. The greater story lies to the south, penetrating deeply into the "Northern Rim," a vast zone of economically significant territory and adjacent ocean owned by the United States, Canada, Denmark, Iceland, Sweden, Norway, Finland, and Russia. As in the Arctic, climate change there has already begun. This zone — which constitutes almost 30 percent of the Earth’s land area and is home to its largest remaining forests, its greatest untouched mineral, water, and energy reserves, and a (growing) population of almost 100 million people — will undergo one of the most profound biophysical and social expansions of this century.

LAURENCE C. SMITH is Professor and vice chairman of geography and professor of earth and space sciences at UCLA. He studies likely impacts of northern climate change including the economic effects in the Northern Rim.

Laurence C. Smith's Edge Bio Page

REALITY CLUB: Stewart Brand, Alun Anderson, Laurence Smith

From WHAT'S NEXT?
Dispatches on the Future of Science
Edited By Max Brockman