Edward Lorenz, father of chaos theory and butterfly effect, dies at 90 Edward Lorenz, an MIT meteorologist who tried to explain why it is so hard to make good weather forecasts and wound up unleashing a scientific revolution called chaos theory, died April 16 of cancer at his home in Cambridge. He was 90. A professor at MIT, Lorenz was the first to recognize what is now called chaotic behavior in the mathematical modeling of weather systems. In the early 1960s, Lorenz realized that small differences in a dynamic system such as the atmosphere--or a model of the atmosphere--could trigger vast and often unsuspected results. These observations ultimately led him to formulate what became known as the butterfly effect--a term that grew out of an academic paper he presented in 1972 entitled: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" Some scientists have since asserted that the 20th century will be remembered for three scientific revolutions--relativity, quantum mechanics and chaos.
Roger Penrose English mathematician, mathematical physicist (born 1931) Sir Roger Penrose OM FRS (born 8 August 1931)[1] is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics.[2] He is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge, and University College London.[3][4][5] Penrose has contributed to the mathematical physics of general relativity and cosmology. He won the Royal Society Science Books Prize for The Emperor's New Mind (1989), which outlines his views on physics and consciousness. He followed it with The Road to Reality (2004), billed as "A Complete Guide to the Laws of the Universe". Early life and education [edit] Born in Colchester, Essex, Roger Penrose is a son of Margaret (née Leathes), a physician, and Lionel Penrose, a psychiatrist and geneticist. As the reviewer Manjit Kumar puts it: Research and career
Boolean algebra Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).[1] According to Huntington the term "Boolean algebra" was first suggested by Sheffer in 1913.[2] Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.[3] History[edit] In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Values[edit] As with elementary algebra, the purely equational part of the theory may be developed without considering explicit values for the variables.[12] Operations[edit] Basic operations[edit] The basic operations of Boolean algebra are as follows. J.
Edward Norton Lorenz Edward Norton Lorenz (May 23, 1917 – April 16, 2008)[1][2] was an American mathematician and meteorologist, and a pioneer of chaos theory.[3] He introduced the strange attractor notion and coined the term butterfly effect. Biography[edit] Lorenz was born in West Hartford, Connecticut.[4] He studied mathematics at both Dartmouth College in New Hampshire and Harvard University in Cambridge, Massachusetts. From 1942 until 1946, he served as a meteorologist for the United States Army Air Corps. After his return from World War II, he decided to study meteorology.[2] Lorenz earned two degrees in the area from the Massachusetts Institute of Technology where he later was a professor for many years. He was a Professor Emeritus at MIT from 1987 until his death.[2] Two states differing by imperceptible amounts may eventually evolve into two considerably different states ... Awards[edit] Work[edit] Lorenz built a mathematical model of the way air moves around in the atmosphere. See also[edit]
Gravitoelectromagnetism Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles. The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton's law.[1] Background[edit] ...or equivalently currentI, same field profile, and field generation due to rotation. Physical analogues of fields[2] Indirect validations of gravitomagnetic effects have been derived from analyses of relativistic jets.
Cybernetics Cybernetics is a transdisciplinary[1] approach for exploring regulatory systems, their structures, constraints, and possibilities. Cybernetics is relevant to the study of systems, such as mechanical, physical, biological, cognitive, and social systems. Cybernetics is applicable when a system being analyzed incorporates a closed signaling loop; that is, where action by the system generates some change in its environment and that change is reflected in that system in some manner (feedback) that triggers a system change, originally referred to as a "circular causal" relationship. Concepts studied by cyberneticists (or, as some prefer, cyberneticians) include, but are not limited to: learning, cognition, adaptation, social control, emergence, communication, efficiency, efficacy, and connectivity. Norbert Wiener defined cybernetics in 1948 as "the scientific study of control and communication in the animal and the machine Definitions[edit] Other notable definitions include: Etymology[edit] W.
Mitchell Feigenbaum Mitchell Jay Feigenbaum (born December 19, 1944) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants. Biography[edit] Feigenbaum was born in New York City,[1] to Polish and Ukrainian Jewish immigrants. He attended Samuel J. After short positions at Cornell University and the Virginia Polytechnic Institute and State University, he was offered a longer-term post at the Los Alamos National Laboratory in New Mexico to study turbulence in fluids. In 1983, he was awarded a MacArthur Fellowship, and in 1986, he was awarded the Wolf Prize in Physics "for his pioneering theoretical studies demonstrating the universal character of non-linear systems, which has made possible the systematic study of chaos". Bifurcation diagram of the logistic map. Work[edit] The logistic map is a prominent example of the mappings that Feigenbaum studied in his noted 1978 article: Quantitative Universality for a Class of Nonlinear Transformations.[3]
Geodesy The science of the geometric shape, orientation in space, and gravitational field of Earth Definition[edit] The word "geodesy" comes from the Ancient Greek word γεωδαισία geodaisia (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying gravity field. Geodesy in the German-speaking world is divided into "higher geodesy" ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on the global scale, and "practical geodesy" or "engineering geodesy" ("Ingenieurgeodäsie"), which is concerned with measuring specific parts or regions of Earth, and which includes surveying. To a large extent, the shape of Earth is the result of rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates and of volcanism, resisted by Earth's gravity field. History[edit] Geoid and reference ellipsoid[edit] Coordinate systems in space[edit] Coordinate systems in the plane[edit] Heights[edit]
Alex Faickney Osborn Alex Faickney Osborn (May 24, 1888 – May 5, 1966) was an advertising executive and the author of the creativity technique named brainstorming. Founding of BBDO[edit] In 1919, Osborn joined with Bruce Fairchild Barton and Roy Sarles Durstine to form the BDO advertising agency. Osborn acted as manager of BDO's Buffalo branch. Creativity theorist[edit] Osborn became increasingly active as an author, and published several books on creative thinking. In 1954, Osborn set up the Creative Education Foundation, sustained by the royalties earned from his books. Notable advertising work[edit] Books[edit] A Short Course in Advertising, London, New York: Sir I. Osborn also contributed frequently to trade publications such as Printer's Ink. Family life[edit] On September 15, 1916, he married Helen Coatsworth, the daughter of a wealthy Buffalo lawyer. Sources[edit] Bruce Fairchild Barton, Roy Sarles Durstine, and Alex Faickney Osborn, Joan Vidal, João Lins. References[edit] 3.
String theory String theory was first studied in the late 1960s[3] as a theory of the strong nuclear force before being abandoned in favor of the theory of quantum chromodynamics. Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. Five consistent versions of string theory were developed until it was realized in the mid-1990s that they were different limits of a conjectured single 11-dimensional theory now known as M-theory.[4] Many theoretical physicists, including Stephen Hawking, Edward Witten and Juan Maldacena, believe that string theory is a step towards the correct fundamental description of nature: it accommodates a consistent combination of quantum field theory and general relativity, agrees with insights in quantum gravity (such as the holographic principle and black hole thermodynamics) and has passed many non-trivial checks of its internal consistency.