Mandelbrot, Founder of Fractal Geometry, Wins Honda Prize

YORKTOWN HEIGHTS, N.Y., November 17, 1994 . . . . The 1994 Honda Prize was
presented today in Tokyo to Benoit B. Mandelbrot, IBM Fellow Emeritus at
the IBM Research Division's Thomas J. Watson Research Center and Abraham
Robinson Adjunct Professor of Mathematical Sciences at Yale University.
Dr. Mandelbrot, best known as the founder of fractal geometry, was cited
by the Honda Foundation "for contributing to the establishment of a
harmony between mathematics and science and culture and the environment
that surrounds human activities, and to a better understanding worldwide
of science and for new tools to solve the problems induced by modern
progress."

The prize was conferred at a ceremony in the Hotel Okura and was followed
by a commemorative lecture by Dr. Mandelbrot and a reception. Dr. Norihisa
Suzuki, Director of the IBM Tokyo Research Laboratory, was in attendance
on behalf of the IBM Corporation.

According to the Honda Foundation, Dr. Mandelbrot "has brought geometric
shapes to a new level of science, providing us with an idea that goes
beyond the traditional differential analysis, the primary mathematical
problem-solving tool utilized since the advent of Newtonian dynamics.
Furthermore, the fractal theory has had a tangible impact not only on
natural sciences but also on such areas as social sciences and art. It is
an extremely viable means of bringing social activities, nature and
sciences closer together."

Mandelbrot's fractal geometry provides a mathematical description of many
of the complex shapes and irregular phenomena found in nature. Coastlines,
mountains and clouds cannot be described by traditional, Euclidean
geometry. But those shapes do often possess the remarkable property of
self-similarity: they remain unchanged under varying degrees of
magnification. Fractal geometry quantifies that property.

Phenomena such as the distribution of galaxies in the universe, the
geometrical structure of turbulent fluids, and price fluctuations in
financial markets have all been successfully analyzed using the
mathematics of fractals. The beauty of fractals has even led to
applications of fractal geometry outside of science by visual artists,
designers, movie makers, and musicians.

The Honda Prize, awarded annually since 1980 to an individual or an
institution, was established to promote the concept of "Eco-Technology,"
which "combines ecology and technology to bring about harmony between
human activities and the overall environment." The Honda Foundation
carries out a variety of activities in support of that concept. The prize
consists of an honorary certificate, a medal, and 10 million yen.

Technical and Biographical Background

The great mathematician, physicist and writer Henri Poincare once drew a
distinction between the problems that a scientist poses and the problems
that pose themselves. The work of early "natural philosophers" addressed
itself to problems that nearly everyone could appreciate, see and feel.
But, as mathematics, science, and technology developed, they diverged from
one another, and the problems that pose themselves to the specialists
became increasingly invisible and far removed from the experience of the
non-specialists. Who can see and feel a DNA molecule, a Yukawa meson, a
p-adic field, or the process of combustion in a car engine?

Very few persons now alive have identified substantial bridges over the
chasms that now separate mathematics, science and technology from one
another and from the interests of the common man and the child. One of
these few persons is Benoit B. Mandelbrot, the originator of fractal
geometry, who has given us, not one but a whole collection of such
bridges.

Fractal geometry begins with questions like "What is the shape of a cloud,
a mountain, a coastline, or a tree?" 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 compared with standard geometry.
Nature exhibits not simply a higher degree but an altogether different
level of visual complexity. It challenges us to study forms that Euclid
leaves aside as being "formless," to investigate the morphology of the
"amorphous."

Having raised the question of "What is the shape of a mountain," Mandelbrot
derived his response from multiple directions. He put heavy reliance on
the computer, taming this instrument at an early stage of its existence to
be a drawing machine. He brought back the eye into science by using it as
a co-witness, next to the customary formulas, of the validity of his
theories. He drew from reputedly abstract chapters of mathematics by
revealing the profound simplicity of certain concepts previously judged
"pathological." He revealed (with the computer's help) that a very simple
formula can generate a shape that the eye and the mind both view as
utterly complex. And he revealed that "mountain forgeries" based on simple
fractal formulas can be strikingly beautiful.

Using the computer and the eye, Mandelbrot revived the old mathematical
topic of iteration of functions, which necessarily combines a number of
distinct mathematical structures. Again, he demonstrated the creative
power of simple formulas by showing how an especially simple one yields
the Mandelbrot Set. He revealed beauty that strikes everyone's eye and is
indissolubly linked with the beauty that can only strike the mind of the
well-prepared mathematician. It seems that these two forms of beauty are
two sides of a single phenomenon.

While the above-mentioned investigations have attracted the widest
attention, the bulk of Mandelbrot's work has been devoted to many
questions of physics that are technical but use the same methods as his
works on mountains and the Mandelbrot Set. His work in physics includes
very practical questions, for example, the task of quantifying the notion
of roughness. But he has also studied turbulence, percolation, and fractal
aggregates, and tackled major conceptual issues, such as those raised by
the coexistence in nature of smoothness ruled by differential equations
and of orderly roughness ruled by fractals.

Mandelbrot has shown wisdom in not wanting to create a new profession,
preferring his work to remain influential in widely ranging existing
fields. Therefore, his fractal geometry allowed itself to be subjected to
a very exacting way to judge a field's importance: by its effects on many
other on-going investigations. By this standard, few contemporaries have
been as bold and as fortunate as Mandelbrot. His life work spanning more
than forty years has been harmonious and well balanced.

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