Chaos Theory
Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part. There were still many facets of the universe that were an enigma to physicists. Mathematicians could indeed illustrate patterns in nature but there were many aspects of Mother Nature that remained a mystery to Physicists and Mathematicians alike. Mathematics is an integral part of physics. It provides an order and a guide to thinking; it shows the relationship between many physical phenomenons. The error in mathematics until that point was linearity. “Clouds are not spheres, mountains are not cones, bark is not smooth, nor does lightning travel in a straight line.” - Benoit Mandlebrot. Was it not beyond reason that a process, which is dictated by that regularity, could master a world that shows almost no predictability whatsoever? A new science and a new kind of mathematics were developed that could show the universe’s idiosyncrasies. This new amalgam of mathematics and physics takes the order of linearity and shows how it relates to the unpredictability of the world around us. It is called Chaos Theory.
The secular definition of chaos can be misleading when the word is used in a scientific context. As defined by Webster’s dictionary chaos is total disorder. That may lead one to believe that chaos theory is indeed the study of total disorder, which it truly is not. In 1986 at a prestigious conference on Chaos another definition for chaos was introduced. It is stochastic behavior occurring in a deterministic set. This definition of chaos was hesitantly brought forth. The scientists, mathematicians and intellectuals present were hesitant to define a concept they did not truly understand yet. They left the scientific community with a rather cryptic and oxymoronic definition of chaos. Deterministic sets behave by precise unbreakable law. Stochastic behavior is the opposite of deterministic it has no finite laws, it is totally dependant upon ch...
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...are self-similar; in that case at higher and higher magnification the fractal image resembles the original.
The stock market is indeed chaotic and also self similar. It is truly random, but shows an orderly trend. It is highly dependant upon initial conditions, but because it is nearly impossible to describe those initial conditions it is impossible to predict the action of the market. Short term trading is random and futile. Long term trading however is not random at all. (Gleick 85) A deterministic order comes from chaos over time.
Chaos Theory has made quite an impact on the modern world. Even in its infancy it has been a powerful tool in shaping popular thought of the natural world. Once dismissed as a theoretical science with no practical application, chaos theory has blossomed into an intricate and beautiful pattern, much like the fractals it deals with. Chaos theory is a complex combination of math and physics, but with its mastery comes a new era in the human understanding of the world around us.
A. A violent order is disorder: and
B. A great disorder is an order.
These two things are one
Wallace Stevens
“Connoisseur of Chaos”
A complex adaptive system is entity of networks and connections. It can “learn and adapt to change over time” which can change the “structure of the system” (Clancy, Effken, Pesut, 2008). It contains twelve elements: autopoesis or self-regenerization, open exchange, participation in networks, fractals, phase transition between order and chaos, search for fitness peaks, nonlinear dynamics, sensitive dependence, attractors that limit growth, strange attractors of emergence...
Indirectly through out his novel, Camus compares people who rely too much on their logic and rationality, versus those who accept that our world is confusing and unpredictable. Similar to his thinking, in “Crickets, Bats, Cats and Chaos” Lewis Thomas suggests that chaos stimulates the brain and actually suggests that even crickets or cats have thoughts during chaotic or unpredictable situations. Even though I have always seen chaos as a total lack of order, a desperate situation in which an individual loses control, Thomas gave me a new concept for chaos. He says that it emerges when a system is altered by a small change or small uncertainty in its interior; chaos is then the
... in order to affect the world. Chaos becomes, by the end of the novel, nearly
Unpredictability cannot be measured, nor can the unpredictability be removed, as that would violate Heisenberg’s uncertainty principle. Humans generally fall under this principle, for although humans might seem to violate Heisenberg’s principle, there is a general unpredictability to the causality of intentional human action. The same goes for divine action, and science cannot forbid either of these
The development of the Chaos began with a computer and mathematic problems of random data that can calculate and predict patterns that repeat themselves. For example, it picks up the pattern of a person’s heart beat and the pattern of snowflakes hitting the ground. Researchers have found that the patterns may be viewed as “unstable”, “random” and “disorderly” they tend to mimic zig-zags, lightning bolts or electrical currents. This theory has not only been used by physicist, but has also been used by astronomers, mathematicians, biologists, and computer scientists. The Chaos Theory can be applied to predict air turbulence, weather and other underlying parts of nature that is not easily understood (Fiero, p.
System [14] etc.display chaotic behavior. A hyper chaos system is considered as a chaotic attractor having more than one positive Lyapunov exponents which gives the randomness and higher unpredictability of the corresponding system so the hyper chaos may be more useful in some fields such as communication, encryption etc. On the other hand the area which attracted much attention is chaos synchronization since the seminal work of Pecora and Carroll [12] recently synchronization of fractional-order chaotic systems starts to attract increasing attention due to its potential applications in secure communication and control processing. There are many types of synchronization for the fractional-order chaotic systems which are investigated, such as Cs [17], Gs [15], PHs [16], As [18], Ps [19, 20, 22] etc. Amongst all projective synchronization, which was first reported by Mainieri and Rehacek [19], is one of the most noticeable one because it can obtain faster communication with its proportional feature [21, 23]. In PS, the responses of the two systems synchronized up to a constant scaling factor. Recently, on account of linear separation Wang and He [26] introduced projective synchronization of the fractional-order chaotic systems Then GPS of the fractional-order chaotic systems was studied in [20, 24]. However, in the above studies, all the states of the drive and response systems synchronize up to an identical constant scaling factor. In [25], Chen et al. proposed a new hyper chaotic system through adding a nonlinear controller of the three- dimensional autonomous chaotic system. More recently, by stability theory of fractional- order systems and tracking control technique the function projective synchronization between fractional-or...
"entropy •n." The Concise Oxford Dictionary. Ed. Judy Pearsall. Oxford University Press, 2001. Oxford Reference Online. Oxford University Press. McGill University (Nylink). 25 Apr 2004.
I believe that the world is orderly and I base my assumption off of what I know from bible, astronomy, biology, and physics. I do not think the universe is chaotic, I think the world functions uniformly starting from an atomic level.
Scientists used to, before the chaos theory, believe in the theory of reductionism, many still do. Reductionism imagines nature as equally capable of being assembled
Looking at the world where we live everything in someway is connected. Our world is not simple and in fact consists of multiple complex systems. Some everyday examples of complex systems are the brain, immune system, insect colonies, and even social networks such as Facebook and twitter. So what exactly do all these have in common in order to be a complex system? First is the fact that each one has a large amount of simple components that work together by communication through signals without being under leadership. But not all systems are exactly the same so we can break it down further into chaotic systems, complex adaptive systems, and nonlinear systems. Chaotic systems differ in that they are non-linear and are sensitive to initial conditions. Therefore any uncertainty in the system will not produce an outcome that can be predicted later on. A good example of a chaotic system would be the stock market because the prediction of its outcome is unknown due to its sensitivity to initial conditions. Complex adaptive systems are just like they sound. They are capable of adapting to the environment such as the immune system. It’s white blood cells work together to recognize foreign bodies and create antibodies for future encounters.
“Chaos theory proves that unpredictability is built into our daily lives.”(Crichton 313). Ian Malcolm’s words resolve the book, Jurassic Park, in a very absolute way. Throughout the book, Malcolm, spoke about chaos theory and his self proclaimed “Malcolm Effect” to explain his reasoning in his predictions. Ian Malcolm had predicted the demise of Jurassic Park even before its opening, as well as its multiple problems and difficulties. Malcolm’s theory is evidenced countless times throughout the story of Jurassic Park; dinosaurs are breeding, dinosaurs are escaping, and systems fail.
The term “entropy” describes a “measure of disorder or randomness in an isolated system” (Dictionary.com). According to the Second Law of Thermodynamics, the entropy of an isolated system will always increase over time. Therefore, disorder and randomness are constantly increasing. Amis drew from both this law and the work of the physicist A.S. Eddington in writing T...
Howard, T , Rifkin, J. Entropy: A New world View. 1980. New York: Bantam Books. Print.
Newton presented that all vicissitudes in the natural world were elucidated by the doctrines of universal gravitation and the motion of bodies. Everything was thus administered by the same unbreakable laws, or mechanisms. Therefore, it is possible to compute every natural change with mathematical precision. A creation of Newtonian physics and advocate of newton’s previously mentioned, mechanistic world view, the "billiard ball" hypothesis, claims that once the preliminary conditions of the universe have been recognized, the rest of the history of the universe follows inexorably. The “billiard ball” hypothesis argues that the elementary particles of the universe function in the same manner as the rolling balls on a billiard table: moving and hitting each other in expectable ways to create anticipated outcomes. For example, if a man meets a woman and they fall in love, then according to the “billiard ball” hypothesis, their lives together will be predictable and prearranged; i.e. they will move in together, get married, and have kids, everything is already predetermined. In relation to the source, the “billiard ball” hypothesis provides a reason for the choosing of one path over the other: that, with knowledge of all the laws governing physical matter, it would be possible to calculate the time and place of the choosing of the
However, the long-term future cannot be predicted due to the same reasons as weather can only be predicted only three weeks into the future. The stock market is a nonlinear dynamical system as it contains positive and negative feedback. Positive feedback such as when you make a profit after investing in the stock market causes people to again invest money into the stock market leading to more buying which raises price. Highly complex systems are not always chaotic instead they will behave predictably for a certain period and then seemingly randomly ill shift into chaotic behaviour. These types of systems can be mapped using simple chaotic systems which often exhibit patterns called strange attractors which demonstrate the system jumping into different modes of behaviour. The chaos in stock markets are caused due to the human psychology of trading which is never completely rational due to many outside factors. By analysing the statistical data, it is possible to find fractal which are infinitely complex patterns that are self-similar across different scales. These fractals are created by repeating straightforward process over and over in an ongoing loop and due to the simplicity of the fractals they can be used to predict the short-term future. The long-term prediction is practically impossible just like weather due to similar reasons as well. The butterfly effect means that variables that seemingly have a very minute effect on the overall outcome of the stock market slowly have an increased amount of effect in the outcome. Therefore, the short-term future of the stock market can be predicted using the Lorenz attractors and fractals however the lack of information causes long term predictions to be practically