The Artful Chaotic Magic Trilogy

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Sensitivity to initial conditions is popularly known as the " butterfly effect", so-called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C., entitled Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?. [28] The flapping wing represents a small change in the initial condition of the system, which causes a chain of events that prevents the predictability of large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the overall system could have been vastly different. Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism--the idea that to understand the world we only need to study its pieces--and it is how most social scientists approach their work. Safety-I is defined as the freedom from unacceptable harm. The purpose of traditional safety management is therefore to find ways to ensure this 'freedom'. But as socio-technical systems steadily have become larger and less tractable, this has become harder to do. Resilience engineering pointed out from the very beginning that resilient performance - an organisation's ability to function as required under expected and unexpected conditions alike - required more than the prevention of incidents and accidents. This developed into a new interpretation of safety (Safety-II) and consequently a new form of safety management. Sensitivity to initial conditions means that each point in a chaotic system is arbitrarily closely approximated by other points that have significantly different future paths or trajectories. Thus, an arbitrarily small change or perturbation of the current trajectory may lead to significantly different future behavior. [2]

Thanks to this revolutionary perspective, we can finally transcend the limits of reductionism and discover crucial new ideas. Scientifically founded and beautifully written, A Crude Look at the Whole is a powerful exploration of the challenges that we face as a society. As it reveals, taking the crude look might be the only way to truly see. In Overcomplicated, complexity scientist Samuel Arbesman argues that we've reached a new era: a time when our technological systems have become too complex and interconnected for us to fully understand or predict.In addition, this book highlights certain group phenomena that have been given only cursory attention in many group textbooks, including women in authority, group metaphors, regressive groups, and the transpersonal potential of small groups. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. A consequence of sensitivity to initial conditions is that if we start with a limited amount of information about the system (as is usually the case in practice), then beyond a certain time, the system would no longer be predictable. This is most prevalent in the case of weather, which is generally predictable only about a week ahead. [30] This does not mean that one cannot assert anything about events far in the future—only that some restrictions on the system are present. For example, we know that the temperature of the surface of the earth will not naturally reach 100°C (212°F) or fall below −130°C (−202°F) on earth (during the current geologic era), but we cannot predict exactly which day will have the hottest temperature of the year.

The original text, published 1990, was the first quantitative introduction to chaos for science undergraduates. This has now been revised and skilfully extended … Suitable as a source text for lecture courses.’ Chaotic academia books fall under 2 categories: banned literature, and books that weren't banned but are still chaotic (in a good way) in their own right. For instance, Ella Minnow Pea wasn't widely banned, but as the book goes along, the author stops using certain letters of the alphabet. Chaotic Dynamics is refreshingly down-to-earth … I recommend it to anyone who wishes to penetrate beneath the flashy surface of the popular image of chaos to the hardcore science beneath. The book makes an excellent text for physics or mathematics students, and its reliance on concrete examples offers a welcome antidote to the esotericism of many undergraduate science courses.’ For other uses, see Chaos theory (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.

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Chaotic dynamics [ edit ] The map defined by x → 4 x (1 – x) and y → ( x + y) mod 1 displays sensitivity to initial x positions. Here, two series of x and y values diverge markedly over time from a tiny initial difference. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. [7] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution [8] and is fully determined by their initial conditions, with no random elements involved. [9] In other words, the deterministic nature of these systems does not make them predictable. [10] [11] This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as: [12]Written by one of our wisest scientists, The Emergence of Everything offers a fascinating new way to look at the universe and the natural world, and it makes an important contribution to the dialogue between science and religion.