Heads of Laboratories
Mitchell J. Feigenbaum, Ph.D.
Toyota Professor
Laboratory of Mathematical Physics
Mitchell.Feigenbaum@rockefeller.edu
Faculty Bio
The description and prediction of natural events that exhibit erratic behavior, such as whorls in fluids, remain challenges in physics and mathematics. Dr. Feigenbaum’s laboratory helped establish the field of chaotic dynamics, which seeks the understanding of just such phenomena. Its overall thrust is to enlarge the applicability of mathematics to science.
Dr. Feigenbaum is a pioneer in the science of “chaos,” the mathematics of erratic dynamical systems — objects with unpredictable behavior and an attendant “fractal” geometry.
Chaotic motion shows a lack of predictability despite the total absence of any random ingredients. While the various constraints on a system, such as bounded resources, can allow it to move regularly on a smooth space, its chaotic motion lies in a highly complicated subspace — a socalled “strange attractor.” Using computers and inventing mathematics, Dr. Feigenbaum erected a full, precise mathematical description of systems during their transition from order to disorder — for example, a dripping faucet changing from a steady drip into an erratic one. The mathematics that underlies this changeover holds true for all systems undergoing this “period doubling” onset of chaos, with all scaling details identically independent of a system’s precise nature, including fluctuating animal populations, electrical signals in circuits, lasers and various chemical reactions. Dr. Feigenbaum has shown that all these phenomena prominently exhibit numbers determined by his theory, for example 4.6692016…, a constant of nature called “Feigenbaum’s constant,” determining the rate of onset.
A fractal is a complex object built hierarchically of finer and finer details, all similar apart from their successively reduced scales. These intricate formations in space, reminiscent of objects such as mountains and snowflakes, as well as complex formations in time, can be described by mathematical rules, discovered by Dr. Feigenbaum, called “scaling functions.” Scaling functions describe the evolution of an object, whatever its current form or size, and so, unchanged, can be repeatedly reapplied.
In this circumstance, the object produced is scale invariant, meaning that as it evolves from a given size, its details remain loosely proportional to that size, and so, fractal. Looking at systems from this perspective, Dr. Feigenbaum has made important contributions to numerous fields, including cartography: As a consultant to the Hammond Corporation, he developed techniques that allow computers to draw maps of archival quality, with unprecedented accuracy, using a dataset of just one high, fixed resolution. This atlas, published in 1992, contains Dr. Feigenbaum’s “optimal” conformal projections for arbitrarily chosen regions on Earth, and these projections are at least three times more accurate than all previous ones. The computerautomated labeling of maps was also accomplished by a new directedannealing algorithm for dynamical systems.
During his time at Rockefeller, Dr. Feigenbaum has taken part in numerous collaborations, including research into the electrical fluctuations of single neurons to quantitatively determine their chaotic properties; measuring the way fibroblasts travel to the site of injury, observing that as their path appears not to be random, they are moving chaotically; and analyses of the outcome of optical imaging of cortical activity.
CAREER
Dr. Feigenbaum received his Ph.D. in theoretical highenergy physics from the Massachusetts Institute of Technology in 1970, under Francis E. Low. He was a research associate at Cornell University from 1970 to 1972 and a research associate at Virginia Polytechnic Institute from 1972 to 1974. He then moved to Los Alamos National Laboratory, where he was a staff member from 1974 to 1981 and a fellow from 1981 to 1982. (Dr. Feigenbaum, while creating his work on chaos, shared his office with Murray GellMann in 1976.) From 1982 to 1986 he was a professor of physics at Cornell University. Dr. Feigenbaum was a visiting member at the Institute for Advanced Study in Princeton, New Jersey, in 1978 and 1984. He joined The Rockefeller University in 1986. In addition to being the university’s Toyota Professor, he is also director of the Center for Studies in Physics and Biology.
Among many awards, Dr. Feigenbaum received the 2008 Dannie Heineman Prize for Mathematical Physics for developing the theory of deterministic chaos and a 2005 New York City Mayor’s Award for Excellence in Science and Technology for his pioneering studies in chaos theory. In 1986 he was awarded Israel’s top scientific honor, the Wolf Foundation Prize in Physics. He was presented with a John D. and Catherine T. MacArthur Foundation Fellowship in 1984, the Ernest O. Lawrence Award by the United States Department of Energy in 1982 and the Los Alamos National Laboratory’s Distinguished Performance Award in 1980. He was elected to the American Academy of Arts and Sciences in 1987 and the National Academy of Sciences in 1988.
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