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Mitchell Jay Feigenbaum (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in
chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to hav ...
led to the discovery of the
Feigenbaum constants In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the physicist Mitchell J. Feigenbaum. Histo ...
.


Early life

Feigenbaum was born in
Philadelphia, Pennsylvania Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Since ...
, to Jewish emigrants from
Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
and
Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inva ...
. He attended
Samuel J. Tilden High School Samuel J. Tilden High School is a New York City public high school in the East Flatbush section of Brooklyn, New York City. It was named for Samuel J. Tilden, the former governor of New York State and presidential candidate who, although carryin ...
, in
Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...
, New York, and the
City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...
. In 1964, he began his graduate studies at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of th ...
(MIT). Enrolling for graduate study in
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, he changed his area of study to
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
. He completed his doctorate in 1970 for a thesis on
dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given t ...
s, under the supervision of Professor
Francis E. Low Francis Eugene Low (October 27, 1921 – February 16, 2007) was an American theoretical physicist. He was an Institute Professor at MIT, and served as provost there from 1980 to 1985. He was a member of the influential JASON Defense Advisory Grou ...
.


Career

After short positions at
Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...
(1970–1972) and the
Virginia Polytechnic Institute and State University Virginia Tech (formally the Virginia Polytechnic Institute and State University and informally VT, or VPI) is a public land-grant research university with its main campus in Blacksburg, Virginia. It also has educational facilities in six regi ...
(1972–1974), he was offered a longer-term post at the
Los Alamos National Laboratory Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
in
New Mexico ) , population_demonym = New Mexican ( es, Neomexicano, Neomejicano, Nuevo Mexicano) , seat = Santa Fe, New Mexico, Santa Fe , LargestCity = Albuquerque, New Mexico, Albuquerque , LargestMetro = Albuquerque metropolitan area, Tiguex , Offi ...
to study
turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
in fluids. Although a complete theory of turbulent fluids remains to be established, his research led him to study
chaotic maps Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids ...
. In 1983, he was awarded a
MacArthur Fellowship The MacArthur Fellows Program, also known as the MacArthur Fellowship and commonly but unofficially known as the "Genius Grant", is a prize awarded annually by the John D. and Catherine T. MacArthur Foundation typically to between 20 and 30 indi ...
, and in 1986, alongside Rockefeller University colleague Albert Libchaber, he was awarded the
Wolf Prize in Physics The Wolf Prize in Physics is awarded once a year by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Mathematics, Medicine and Arts ...
"for his pioneering theoretical studies demonstrating the universal character of non-linear systems, which has made possible the systematic study of chaos". He was a member of the Board of Scientific Governors at
the Scripps Research Institute Scripps Research, previously known as The Scripps Research Institute (TSRI), is a nonprofit American medical research facility that focuses on research and education in the biomedical sciences. Headquartered in San Diego, California, the instit ...
. He was Toyota Professor at
Rockefeller University The Rockefeller University is a private biomedical research and graduate-only university in New York City, New York. It focuses primarily on the biological and medical sciences and provides doctoral and postdoctoral education. It is classif ...
from 1986 until his death.


Work

Some mathematical mappings involving a single linear parameter exhibit the apparently random behavior known as chaos when the parameter lies within certain ranges. As the parameter is increased towards this region, the mapping undergoes
bifurcation Bifurcation or bifurcated may refer to: Science and technology * Bifurcation theory, the study of sudden changes in dynamical systems ** Bifurcation, of an incompressible flow, modeled by squeeze mapping the fluid flow * River bifurcation, the ...
s at precise values of the parameter. At first, one stable point occurs, then bifurcates to an oscillation between two values, then bifurcating again to oscillate between four values and so on. In 1975, Dr. Feigenbaum, using the small
HP-65 The HP-65 is the first magnetic card-programmable handheld calculator. Introduced by Hewlett-Packard in 1974 at an MSRP of $795 (), it featured nine storage registers and room for 100 keystroke instructions. It also included a magnetic card re ...
calculator he had been issued, discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692...'' A New Kind of Science'

/ref> He was able to provide a mathematical argument of that fact, and he then showed that the same behavior, with the same mathematical constant, would occur within a wide class of mathematical functions, prior to the onset of chaos. This universal result enabled mathematicians to take their first steps to unraveling the apparently intractable "random" behavior of chaotic systems. The "ratio of convergence" measured in this study is now known as the first Feigenbaum constants, Feigenbaum constant. The
logistic map The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popula ...
is a prominent example of the mappings that Feigenbaum studied in his noted 1978 article: "Quantitative Universality for a Class of Nonlinear Transformations". Feigenbaum's other contributions include the development of important new
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...
methods in
cartography Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an i ...
, starting when he was hired by Hammond to develop techniques to allow computers to assist in drawing maps. The introduction to the ''Hammond Atlas'' (1992) states:
Using
fractal geometry In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
to describe natural forms such as coastlines, mathematical physicist Mitchell Feigenbaum developed software capable of reconfiguring coastlines, borders, and mountain ranges to fit a multitude of map scales and projections. Dr. Feigenbaum also created a new computerized type-placement program which places thousands of map labels in minutes, a task that previously required days of tedious labor.
In another practical application of his work, he founded Numerix with Michael Goodkin in 1996. The company's initial product was a software algorithm that dramatically reduced the time required for
Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...
pricing of exotic
financial derivatives In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be u ...
and
structured products A structured product, also known as a market-linked investment, is a pre-packaged structured finance investment strategy based on a single security, a basket of securities, options, indices, commodities, debt issuance or foreign currencies, and ...
. Numerix remains one of the leading software providers to financial market participants.Numerix Website
/ref> The press release made on the occasion of his receiving the
Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of nati ...
summed up his works:
The impact of Feigenbaum's discoveries has been phenomenal. It has spanned new fields of theoretical and experimental mathematics ... It is hard to think of any other development in recent theoretical science that has had so broad an impact over so wide a range of fields, spanning both the very pure and the very applied.


Works

* * * *


See also

* ''Theory of Colours'' (book)


References


External links

*
Feigenbaum's webpage at Rockefeller
*

* ttps://chaosbook.blogspot.com/1993/05/acceptance-speech-1993-nkt-research.html Cvitanović, P. "A not so short history of Universal Function" {{DEFAULTSORT:Feigenbaum, Mitchell 1944 births 2019 deaths Scientists from Philadelphia 20th-century American mathematicians 21st-century American mathematicians American people of Polish-Jewish descent American people of Ukrainian-Jewish descent 21st-century American physicists Chaos theorists City College of New York alumni Jewish American scientists Jewish physicists MacArthur Fellows Members of the United States National Academy of Sciences Scripps Research Wolf Prize in Physics laureates Mathematical physicists Los Alamos National Laboratory personnel Samuel J. Tilden High School alumni Mathematicians from New York (state) Cornell University faculty MIT Center for Theoretical Physics alumni