Transcript: Chaos Theory Intro to Chaos... Edward Lorenz Basics of Chaos... Butterfly Effect The idea that very small things, such as the flap of a butterfly's wings in South America can cause larger things, such as a hurricane that wipes out Asia. Unpredictability The factor of randomness and chaos that would make most things seem unpredictable. When Chaos Theory is uesd, howevr, those things become predictable. Unpredictabilty is the backbone of the Chaos Theory. Instability Determinism The idea that everything that happened could not have happened in a different way than it did. Conclusion The Butterfly Effect Unpredictability Instability Determinism Chaos Theory http://fineartamerica.com/featured/chaos-theory-kerry-krueger.html Let's review: Butterfly effect Unpredictability Determinism Instability An Mit meteorologist who first discovered Chaos Theory. http://bergeronperformance.com/2011/02/26/strength-despite-size/ Instability plays a major role in diferent parts of not only chaos, but everything that has ever happened. One small collapse that causes something bigger and more effective to happened. Dog breeds, other differences within a species. http://wednesday1993.files.wordpress.com/2011/01/clip_image002.jpg http://tarun-gupta.blogspot.com/2007/09/butterfly-effect-chaos-theory.html http://www.shutterpoint.com/Photos-ViewPhoto.cfm?id=159159 http://www.plexusinstitute.com/edgeware/archive/images/v_10.gif http://eprotocol.blogspot.com/2011/05/chaos-theory.html
Transcript: Thank you for your attention (and for giving me a wonderful mark) Subject 3 In 1961, Edward Lorenz started exploring Chaos Theory. He was primarily a meteorologist. At one time Lorenz was running computerised equations to theoretically model and predict weather conditions. Having run a particular sequence, he decided to replicate it. Lorenz reentered the number from his printout, taken half-way through the sequence, and left it to run. What he found upon his return was, contrary to his expectations, these results were radically different from his first outcomes. Lorenz had, in fact, entered not precisely the same number, .506127, but the rounded figure of .506. According to all scientific expectations at that time, the resulting sequence should have differed only very slightly from the original trial, because measurement to three decimal places was considered to be fairly precise. Because the two figures were considered to be almost the same, the results should have likewise been similar. Chaos Theory Conclusion Chaos Theory A Nice Story However, this sensible assumption based on the everyday use of the term is incorrect. Chaos theory is one of the most interesting fields of complex mathematics. It is the very essence of order, as you will come to understand. "It has been said that something as small as a flutter of a butterfly's wings can ultimately cause a typhoon half way around the world" Chaos Theory A common misconception about chaos and chaos theory is that it revloves around disorder... is here "Chaos was the law of nature; Order was the dream of man" Subject 3
Transcript: Chaos Theory Bifurcation Code Taken from Understanding Nonlinear Dynamics by Kaplan and Glass Our focus is Computer Projects 1 and 2. We were asked to examine two Nonlinear Difference Equations: Equation A: xt+1= 4 * lambda *xt*(1- xt) Equation B: xt+1= lambda * sin(xt*pi) We were then asked to see how changes in lambda would affect the system for lambda between 0 and 1. Nonlinear Finite-Difference Equation is: x_t+1 = R*x_t(1-x_t) where x_t is the state of the system at time t and R is parameter. We are interested in how the state changes in time depending on R: dynamics of the system. Bifurcation Diagram Our Problem In our calculus studies we have looked at many equations that are classified as Differential Equations. Not to be confused with Difference Equations in which the equations are defined recursively. This project focuses on Difference equations Behavior of the nonlinear equation • Steady state– solution creeps up on steady state from one side. The solution could also alternate sides so that it creeps up on the solution. • Periodic cycle– could alternate between values depending on the number of periods. • Aperiodic– irregular oscillation that is neither exponential growth nor decay. One of the requirements for a system to be chaotic. Difference vs Diffrential Chaos Theory Nonlinear Finite-Difference Equation
Transcript: "If you could stop every atom in its position and direction... then if you were really, really good at algebra you could write the formula for all the future.... the formula must exist just as if one could." - Thomasina Coverly The branch of mathematics that deals with complex systems whose behaviour is highly sensitive to slight changes in conditions, so that small alterations can give rise to strikingly great consequences "Fractal geometry will make you see everything quite differently. There is danger in reading further. you risk the loss of your childhood of clouds, forests, flowers, galaxies, leaves, feathers, rocks, and much else besides. Never again will your interpretation of these things be quite the same" - Michael Barnsley Chaos Theory Non-linear relationships that cause things to look random. The science of predicting seemingly random events Fractals Figures that have an infinite amount of detail, are self similar (such as lines and grids) Where did it begin? Henri Poincare, in the late 1800's Edward Lonrenz in the 1960's Application of Fractals
Transcript: Apocalypse Now Review Apocalypse Now is easily one of the most stunning, haunting and thrilling movies in cinematic history that has set standards that movies today still aspire to meet. Its fearlessness and blatancy, trademark methods of the legendary Francis Ford Coppola, plow its way into what is widely considered the most accurate depiction of the Vietnam War in a film ever. The both clever and haunting viewpoint of Willard, the troubled protagonist, holds the viewer captive in a perspective that will ultimately alter their outlook on war and the extent to which one would go to make it back to their home. This POV allows one to relate to Willard and sympathize with the toil he goes through, on a much lesser scale, of course, but it also allows for his confusion and the exposure of his personal haunts, further reeling the viewer in. While the beginnings of movies are often the most difficult part of entire project, Apocalypse Now does it flawlessly, although the ending does leave a little more to be wanted. All in all however, Apocalypse Now proves to be a force still to be reckoned with. Its visual beauty, fearless direction and evocative performances create an overwhelmingly powerful film as a whole ***1/2 Techniques Lap dissolve ECU Nonsynchronous Sound Establishing Shots POV Voiceover Low-key lighting What makes a movie great? Beauty Talent Defiance Relativity Mystery The Odyssey -the struggle for home -obstacles overcome -haunts endured -ambition
Transcript: Like crisis theory, chaos theory does not have a set intervention, rather it can be used to guide thinking in conjunction with other theories. Particularly with narrative theory. Questions pertaining to the nature of the chaos and what positives and creativity could stem from it should be asked. It is important to be aware of patterns (fractals) and realize the importance of small changes (the butterfly effect). This has been shown to work well with individuals, groups, and companies. Chaos theory is on the rise in the world of child welfare, because in these cases tension and chaos are rampant and entropy is more present than order, so this theory could have major implications for that area of practice. The theory is not completely developed; thus more information is needed before it can be used to its full potential. It will be difficult to evaluate the effectiveness of the theory as it expects people to remain in chaos and suggests that goals and objectives are not going to measure change. Creativity Works With: Systems Theory Person-in-Environment Crisis Theory Brief Treatment Narrative Weber's Organization of Offices Problems are a result of humans desire for structure in an unstructured world, the attempt to organize our lives into neat boxes, the desire for predictability, and the aspect of human nature that desires to view situations in black and white rather than in shades of grey. History of the Theory Chaos theory is a fairly new theory and it is still in the development process. It's creation was encouraged by: the computer age, finical crises, organizational restructuring, and the desire for knowledge. Prigogine and Stenger began the creation of the theory in 1984 by questioning the concepts of Thermodynamics and Weber's "organization of offices." The theory was added to by Lorenz (1963) and Mandelbrot (1983) at a later date. Chaos emerges from tension that stems from the evolving, erratic, and complex situations that we experience (i.e. life). On the bounds of this tension is the margin of chaos. Remember, from chaos comes creativity; therefore, tension breeds creativity, and is not inherently negative. Common Themes and Principles Creating Chaos Macro: has implications for management practice for organizations. How Problems Arise: Micro: can be used to empower clients; help them find strengths, creativity, and new beginnings in times of unpredictability or chaos. Theoretical Concepts: Surmises that creativity results from chaos; therefore, chaos is not inherently negative. A self organizing system will have an energy flow that allows for the existence of dualities. These dualities are the simultaneous existence of paradoxical states including: order and disorder and complexity and simplicity. Chaos Theory Fractals: expose the geometric nature of chaos; a mathematical concept that explains that things happen in patterns on all levels. It is important to be able to point out these fractals. The Butterfly Effect: can be described as a sensitive dependence on initial conditions; meaning that even a minor change can make a massive difference elsewhere. Non-linearity Numerous parts with no casual relationships A network of feedback (communication) loops Unpredictability Flow of energy towards self organization Dualities: open and closed systems, order and disorder, complexity and simplicity, etc. Implications: Humans: can be viewed as a complex system that exists in the realm of other complex systems (whole part theory) and we are in a constant feedback loop with these other systems. Change is a direct component of creativity that results from chaos. Works Against: Structural Structural Family Medical Model Bureaucracy A concept based in physics discovered by Isaac Newton in 1687. States that: (1) matter cannot be created or destroyed, (2) entropy in a system not in equilibrium will increase, and (3) the entropy of a system approaches a common value as the temperature approaches absolute zero. In layman's terms: entropy is the measure of disorganization in a system, so this theory suggests that nothing can be created or destroyed, disorder does not decrease, and the longer a system is not in equilibrium the system will become more disorderly. Chaos theory can be used on all levels of social work practice: Mezzo: use with interdisciplinary teams: frequent impromptu meetings should spur creativity and solutions. Chaos Theory Criticisms: Intervention: The Law of Thermodynamics Chaos theory suggests that creativity will allow people to come up with new answers. These answers do not necessarily have to be in a result to a problem, rather they can be a new way of looking at the world. In terms of problem solving creativity will allow for unique solutions to a person's specific problems. Creativity is enhanced through spontaneous meetings of the minds, the ability to adapt to and thrive under chaos, and the ability to work through tension. The two previous concepts share a few concepts believed to be
Transcript: By Maggie Molen Cause and Effect Identical initial conditions consistently create the same outcome Patterns of order emerge within chaos Dynamic equilibrium Meteorologist attempting to predict weather patterns "Butterfly Effect" Determinism A Sound of Thunder by Ray Bradbury The Butterfly Effect (movie) Butterfly Effect in Pop Culture Challenged determinism Studied motion of planets Found that small changes in initial conditions can have disproportionate effects on final outcome Chaotic systems = sensitive dependence on initial conditions Edward Lorenz The Chaos Theory Henri Poincare What is Chaos? Strange Attractors
Transcript: CHAOS - ORDER & Complexity Classical Science Newtonian Physics Can flap of a butterfly's wings in Brazil set off a Tornado in Texas?!! Butterfly effect Very small changes in initial conditions magnified over the time result in large changes in the state of the system after some time steps Mathematics of self-similarity Mandelbrot set (Thumbprint of GOD) Islands of order in the sea of chaos! BASE OF SCIENCE: All the mess around us Incomprehensible things Eventually: simple rules and laws to explaine the complicated things Newton's formula Enstine's E=mc2 ... How complicated things emerge from simple systems?! Cellular Automata Is there a single, simple cellular automation-like rule that is definite "ultimate model of the universe"??! - Source for everything that exists!! CHAOS More Information THANK YOU! http://mathworld.wolfram.com/ The Secret Of Chaos FEEDBACK! A[simple] initial condition: Time reversible Patterns Initial state is known 1924-2010 Complex - Unpredictable patterns 20th Century Wolfram: Highly sensitive to initial condition British physicist, software developer, mathematician, author and businessman Deterministic Results after some time steps: Complexity A set of simple rules: Edward Lorenz Fractal Math French American mathematician Self Organizing Systems Rules "I'm guessing it's really very short- in Mathematica, for example, perhaps three, four lines of code!" All subsequent & Preceeding States are predictable 18th Century Romanesco broccoli (1960's) Relativity Theory Benoit Mandelbrot Under Simple Completely known Where to start? Complex - Unpredictable patterns Any geometric structure that has detail on all scales of magnification; no matter how big you make it, you still see extra new details, you couldn't see before! Quantum Theory Geometric Equation of a snowflake! Stephen Wolfram American meteorologist Fractal:
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