Immunology: The Making of a Modern Science. New Science. Introducing Chaos, New Edition Introducing. A Wizard In Chaos. A Splendid Chaos. A Wizard in Chaos. Chaos in a Miniature.
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He is best known as the founder of modern chaos theory, the mathematics of complex dynamical systems that are highly sensitive to initial conditions. Lorenz was born in in West Hartford, Connecticut. He acquired an early love of science from both sides of his family. As a boy, Edward's mother got him hooked on chess. Edward then received a bachelor's degree in mathematics in from Dartmouth College and in a master's degree in mathematics from Harvard.
His doctoral dissertation, titled "A Method of Applying the Hydrodynamic and Thermodynamic Equations to Atmospheric Models" described an application of fluid dynamical equations to the real problem of predicting the motion of storms. Lorenz spent the entirety of his scientific career at MIT, in , he joined the Department of Meteorology as a research scientist.
In , he became an assistant professor in the department and was promoted to professor in From to , Lorenz served as head of that Department until the Department of Meteorology and Physical Oceanography merged with the Department of Geology in to become the current MIT Department of Earth, Atmospheric and Planetary Sciences, where Lorenz remained a professor before becoming an emeritus professor in On April 16, , Lorenz died at his home in Cambridge, MA, from cancer at the age of 90, after a decade of vigorous hiking around New England.
In , Lorenz took over leadership of a project at MIT that ran complex simulations of weather models that he used to evaluate statistical forecasting techniques.
By the late s, Lorenz was skeptical of the appropriateness of the linear statistical models in meteorology, as most atmospheric relationships like between pressure and wind speed in weather forecasting are non-linear. There was a lot of intuitive guesswork in creating these equations, so Lorenz used his own set of 12 equations that were reasonably good for short-range a few days forecast.
In , Lorenz has a lucky break but he was paying attention, when he restarted his computer during a long calculation using a number already printed out earlier.
The first part of his continuation run should have just exactly duplicated the first group of remaining numbers from before but they were increasingly different.
It took Lorenz a while to identify the problem: his computers were using six digit numbers like 0. That day, he decided that long-range weather forecasting was doomed; it was OK for a few days but the errors got larger as the forecast duration became extended. Everyone else just assumed that 'better' equations would solve the problem - they did not; it was the accuracy of the starting numbers that was critical.
This Sensitive Dependency on Initial Conditions was amusingly called the Butterfly Effect on the whimsical idea that whether a butterfly flapped its wings somewhere would later change the weather. Just reducing the number of equations to three that involved three inter-connected variables always produced this sensitivity also called Chaos.
In other words, this is a bigger problem with all of physics than weather, it had been hiding in plain sight for years. This was his solution to linking arithmetic or Algebra to Geometry. This ties back to the fact that Geometry is an Imaginary 'Science' that relates to perfectly defined objects in our imaginations that do NOT exist in reality: they are perfectly smooth and perfectly thin.
Lorenz did not see this deeper connection but saw it in terms of 'Order Masquerading as Randomness'. In fact, we shall see that non-linearity can manifest itself even in simple one-dimensional equations when they require finite recursion instead of Newton's Continuous Calculus [see my Infinitesimal essay]. Indeed, Lorenz plotted his three-value equations in a 3D space one direction for each variable and generated his famous interwoven pathway, now known as the Lorenz Attractor that resembles an owl's face; this shows that the system NEVER repeats itself, it loops around and around forever: a beautiful metaphor for the uniqueness of the Universe or even our individual lives.
Lorenz documented his realization 'discovery' in his best cited scientific paper in volume 20 in the Journal of Atmospheric Sciences with the title: "Deterministic Nonperiodic Flow". It was created by several clever intellectuals in classical Greece, who were inspired by the practical architects of ancient Egypt but the Greek pioneers only wished to construct a perfect scheme. This scheme used perfect idealizations, like the point of no size, lines of no thickness either connecting between two points to define 'the' line.
If every point on the line is exactly of the same distance from a special point the 'center' then the perfect circle can be defined. The fact that there were no real examples of these ideal shapes to be found in nature was not to held against them. Mind trumps body. Mandelbrot was a Polish-born French-American mathematician, who was attracted to the 'Art of Roughness'. He invented the concept of the fractal and the associated fractal-geometry, that explored the ideas of self-similarity.
Mandelbrot was born in a Lithuanian Jewish family, in Warsaw while Poland was a free republic. His father was a clothing wholesaler and his mother was a dental surgeon. When he was eleven, his family sensitive to political realities moved to Paris to live with his father's brother Szolem, a mathematician, who privately tutored him.
As the Nazis invaded France, the family moved again to Tulle, in central France. After D-Day in , the Germans retreated from France so that Mandelbrot could return to Paris, where he attended the Polytechnique, France's top school for science.
He studied at the California Institute of Technology CalTech from to , earning a Master's degree in aeronautics. He had to leave in when IBM closed their Pure Research Division, so he joined the mathematics department at Yale University, becoming a tenured professor at age He died from pancreatic cancer in Cambridge, MA at age One of his first projects was to see if there were any patterns in the prices of cotton that seemed to reflect both the economy and a random variation.
He was surprised to find there were too many large jumps while the ratio of the many small price changes to large was not as high as he expected: it certainly did not fit the Normal or Gaussian distribution and did not fall off quickly enough - it had a long tail. Mandelbrot then realized that the sequences of change were independent of scale: curves for daily price changes exactly matched those for monthly price changes; just across a smaller range.
He found that the degree of variation had remained constant over sixty years: through two World Wars and a global depression. He decided to explore the phenomenon of scaling. Increasingly, he came to question Euclidean Geometry with its perfect shapes: he would often remark that "clouds are not spheres, mountains are not cones". He was impressed when he found an old paper about nature written by Lewis F. Richardson, who asked the simple but provocative question: How long is the coast of Britain?
As Mandelbrot realized, the answer depended on the length of one's measuring stick. Sometimes referred to as "success magic" or "results-based magic", chaos magic claims to emphasize the attainment of specific results over the symbolic, ritualistic, theological or. Many of the essays presented here were first brewed up in gtbabowling. Some of which, previously unavailable, comprise the secret rituals of. However this is. Call Sign Chaos is a memoir of a life of war-fighting and lifelong learning, following along as Mattis rises from Marine recruit to four-star general.
It is a journey about learning to lead and a story about how he, through constant study and action, developed a unique leadership philosophy, one relevant to us all.
Search the world's most comprehensive index of full-text books. My library. The so-called butterfly effect has become one of the most popular images of chaos. Assistant Secretary of Defense. His next book is Author: Derek Chollet. Any info on release date of book 8 of Chaos Seeds. Saw a post from Aleron about it coming out in early a few months back.
Is there a more concrete release date or any info about it being pushed back. Last edited by Gozuru. Share this book. Eight Hundred Leagues on the Amazon. The birds of Killingworth.
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