Science and development of chaos theory
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The document discusses the evolution of chaos theory, which challenges the deterministic view of nature by revealing the unpredictable behavior in complex systems. Key figures like Henri Poincaré and Edward Lorenz contributed significant insights, with Lorenz demonstrating how small initial changes can lead to vastly different outcomes, encapsulated in the 'butterfly effect.' Overall, the theory has broad implications across various fields, including economics and climate science, highlighting the importance of understanding chaos and complexity in predicting system behaviors.
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SCIENCE AND DEVELOPMENT OF CHAOS THEORY
Fernando Alcoforado *
Supported in the Newtonian laws of Physics described by differential equations,
scientists have long believed that nature was determinist knowing that on that basis, it
was possible to predict all phenomena. Around the turn of the nineteenth to the
twentieth century, advances in the natural sciences and mathematics put serious doubts
on the validity of Newtonian mechanistic view. Quantum Mechanics has questioned the
determinist worldview introducing the uncertainty principle. In the traditional
deterministic approach, the uncertainty was seen as a result of ignorance of the different
causes involved in holding an event, and the complexity of it.
Chaos Theory or the new Science of Complexity suggests that the world should not
strictly follow the deterministic Newtonian model, predictable and certain, because it
has chaotic aspects. The observer is not who creates instability or unpredictability due
to their ignorance because these phenomena exist in nature. A typical example is the
weather. The processes of reality depend on a huge set of uncertain circumstances that
determine, for example, that any small change in one part of the planet, there will be in
the coming days or weeks a considerable effect on the other side of the Earth. Chaos
Theory or Science of Complexity represented one of the great advances in scientific
research of the twentieth century ending with the dichotomy that existed in the
traditional deterministic approach between determinism and randomness [MURPHY,
Robert. La teoria del Caos (Chaos Theory). Madrid: Union Editorial, 2012 and BORN,
Max, AUGER, Pierre, SCHRÖDINGER Erwin e HEISENBERG, Werner. Problemas
da Física Modern (Modern Physics Problems). São Paulo: Editora Perspectiva, 2011].
In 1908, the French mathematician Henri Poincaré (1854-1912), who had studied the
nonlinear mathematical systems reached conclusions that, over time, would be
important to conceptualize Chaos Theory. Poincaré stated that if we know exactly the
natural laws that govern the evolution of the Universe, we can accurately predict your
situation at any later point in time, but as we never know exactly the initial state of
Universe always would be making a mistake to define it. In other words, the Universe
of the initial state can only be known with some approximation. Even assuming that we
could determine the laws governing its evolution, our forecast of any subsequent state
would be also approximate (POINCARÉ, Henri. Science et method. Paris: Flammarion,
1918).
The "three body problem" was one of the problems studied by the great French
mathematician Henri Poincare in the nineteenth century. Poincaré, to escape into the
complexity of the considered problem has become, without being aware of it, the father
of modern Chaos Theory [DE RERUM NATURA. O problema dos três corpos e o caos
(The three-body problem and chaos). Available on the website <http://
dererummundi.blogspot.com.br/2011/03/o-problema-dos-tres-corpos-eo-caos.html>].
Until then, approximate forecasts would not be attributable to the existence of chaos in
reality, but a limitation in our knowledge of the initial conditions. Henri Poincaré
realized in his pioneering studies in this field that are not required complex systems to
produce randomness. Poincaré studies are updated in the 1960s thanks to American
mathematician and meteorologist Edward Lorenz. His perplexity had much to do with
the inability to predict weather events beyond a certain number of days. In the early
1960s, Lorenz began to develop a mathematical model to predict atmospheric
phenomena, and by chance found that the same mathematical tool used produced](https://image.slidesharecdn.com/scienceanddevelopmentofchaostheory-160516221558/85/Science-and-development-of-chaos-theory-1-320.jpg)
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unexpected and unpredictable differences in the results by simulating small changes in
initial conditions.
In the twentieth century, scientific determinism created by the Classical Science was in
crisis because the unpredictability became object of a serious scientific study when the
American meteorologist Edward Lorenz discovered in 1960 that seemingly simple
phenomena have a chaotic behavior. He came to this conclusion when testing a
computer program that simulated the movement of air masses. One day, Lorenz dialed
one of the numbers that fed the machine calculations with a few decimals less, hoping
that the outcome would change little. But the change insignificant completely
transformed the pattern of air masses. It was founded Chaos Theory. Over time,
scientists have concluded that the same unpredictability appeared in almost everything,
from the rhythm of heartbeats to the prices Stock Exchange. From the 1960s, Chaos
Theory eliminated the Laplacian fantasy of deterministic predictability. The central idea
of Chaos Theory is that a tiny change in the start of an event can bring any huge
consequences and absolutely unknown in the future. Therefore, such events would be
virtually unpredictable - chaotic, so. Science found that systems that obey immutable
and precise laws do not always act in a predictable and regular basis. simple laws cannot
produce simple behaviors and vice versa [MURPHY, Robert. La teoria del Caos
(Chaos Theory). Madrid: Union Editorial, 2012].
The Poincaré and Lorenz efforts joined the contributions of Benoit Mandelbrot
(communications engineer), Edward Feigenbaum (mathematical) Libchaber (physical),
Winfree (biologist), Mandell (psychiatrist) and others. According to Chaos Theory or
the Science of Complexity, chaos is a "mixture" of disorder and order born of new
structures, structures called "dissipative" [PRIGOGINE, Ilya. As leis do caos (Laws of
chaos). São Paulo: Editora UNESP, 2002]. Chaos Theory suggests that the Universe has
an cycle of order, disorder, order, and so on. So that one leads to the other and so on,
perhaps indefinitely. One of the main implications of Chaos Theory has to do with the
return generated in chaotic situations, ie, the negative and positive feedback. The
negative feedback tends to correct a deviation, causing the system to its original state.
Such processes are opposed to change, as always look back to return to a previous state.
On the other hand, the feedback positive promotes change, the formation of new
structures, more sophisticated, more adaptive, and more subtle. Whereas involves the
creation of a new structure, the processes are irreversible, unlike the feedback negative,
that tending to the original state, is reversible..
Exemplifying the feedback negative: if we walk in the desert toward a distant goal, we
must, from time to time, correct our course, correcting our target deviation through
regular updates on our way. But if we make a mistake of a millimeter of the target, with
the time error will be expanded and eventually come to a place away from the goal. The
negative feedback seeks to correct the deviations to return to the original path. In the
positive feedback, small changes can lead to big changes that lead to new unknown
targets, perhaps better, although we cannot predict exactly where we will are going.
While Classical Science centered on stability, on determinism, emphasizes the process
of negative feedback that tends to reduce the change, returning the system to its
equilibrium position, the positive feedback promotes change.
Example of positive feedback: technological innovation creates a new business and the
presence of this, in turn, stimulates the generation of further innovation. This explains
how small change creates great final change (butterfly effect). Progress to exist requires](https://image.slidesharecdn.com/scienceanddevelopmentofchaostheory-160516221558/85/Science-and-development-of-chaos-theory-2-320.jpg)
![3
Progress to exist requires instability, irreversibility and the ability to make sense of
small events for a structural change occurs. The irreversibility (fluctuations) makes
possible things that would be impossible in a state of balance and provides an important
constructive law, the origin of a new state and its highly complex and sophisticated
structures derived. Once the process results in the creation of a complex structure, the
dissipation structure, a new imbalance cycle occurs and chaos starts where new
instabilities or fluctuations occur (Figure 1).
Figure 1 - Dynamic Systems and the Positive "Feedback"
Fonte: Ervin Laszlo. O Ponto do Caos (The Chaos Point). São Paulo: Editora Cultrix, 2006.
Figure 1 shows what happens to a dynamic system with an old structure when it is
subjected to instability or "fluctuations" that leads to a bifurcation point from which the
system reaches a new dynamic stability (revolutionary advancement) with a new
structure or collapses, according to Ervin Laszlo (LASZLO, Ervin. O Ponto do Caos.
(Chaos Point). São Paulo: Editora Cultrix, 2006). Figure 2 shows that in the bifurcation
point the system has to be restructured or collapse. Chaos refers mainly to something
that evolves over time. ChaosTheory explains the functioning of complex and dynamic
systems such as, for example, economic systems and climate system. In these systems,
several elements are interacting in a manner unpredictable and random. It should be
noted that Ilya Prigogine, commenting on bifurcation points in chemical reactions,
states that "they demonstrate that even in macroscopic level our prediction of the future
mixture determinism and probability. In the bifurcation point, the prediction is
probabilistic, while between the bifurcation points, we can speak of deterministic laws
[PRIGOGINE, I. As leis do caos (The laws of chaos). São Paulo: Editora UNESP,
2002].
It is worth noting that chaos is present in a wide variety of science disciplines. Research
about chaos began in the 1970s. Physiologists began investigating why the chaos of
normal heartbeat produced a sudden cardiac arrest, ecologists analyzed how certain
Beginning of
fluctuations
State of
the system
Time
Collapse
3
2
1
Fluctuations
Instability
(Crisis)
Revolutionary
advancement
Dynamic stability
Old structure
Bifurcation
point or
Change
Irreversible
New Dynamic stability
New structure](https://image.slidesharecdn.com/scienceanddevelopmentofchaostheory-160516221558/85/Science-and-development-of-chaos-theory-3-320.jpg)
Science and development of chaos theory
- 1. 1 SCIENCE AND DEVELOPMENT OF CHAOS THEORY Fernando Alcoforado * Supported in the Newtonian laws of Physics described by differential equations, scientists have long believed that nature was determinist knowing that on that basis, it was possible to predict all phenomena. Around the turn of the nineteenth to the twentieth century, advances in the natural sciences and mathematics put serious doubts on the validity of Newtonian mechanistic view. Quantum Mechanics has questioned the determinist worldview introducing the uncertainty principle. In the traditional deterministic approach, the uncertainty was seen as a result of ignorance of the different causes involved in holding an event, and the complexity of it. Chaos Theory or the new Science of Complexity suggests that the world should not strictly follow the deterministic Newtonian model, predictable and certain, because it has chaotic aspects. The observer is not who creates instability or unpredictability due to their ignorance because these phenomena exist in nature. A typical example is the weather. The processes of reality depend on a huge set of uncertain circumstances that determine, for example, that any small change in one part of the planet, there will be in the coming days or weeks a considerable effect on the other side of the Earth. Chaos Theory or Science of Complexity represented one of the great advances in scientific research of the twentieth century ending with the dichotomy that existed in the traditional deterministic approach between determinism and randomness [MURPHY, Robert. La teoria del Caos (Chaos Theory). Madrid: Union Editorial, 2012 and BORN, Max, AUGER, Pierre, SCHRÖDINGER Erwin e HEISENBERG, Werner. Problemas da Física Modern (Modern Physics Problems). São Paulo: Editora Perspectiva, 2011]. In 1908, the French mathematician Henri Poincaré (1854-1912), who had studied the nonlinear mathematical systems reached conclusions that, over time, would be important to conceptualize Chaos Theory. Poincaré stated that if we know exactly the natural laws that govern the evolution of the Universe, we can accurately predict your situation at any later point in time, but as we never know exactly the initial state of Universe always would be making a mistake to define it. In other words, the Universe of the initial state can only be known with some approximation. Even assuming that we could determine the laws governing its evolution, our forecast of any subsequent state would be also approximate (POINCARÉ, Henri. Science et method. Paris: Flammarion, 1918). The "three body problem" was one of the problems studied by the great French mathematician Henri Poincare in the nineteenth century. Poincaré, to escape into the complexity of the considered problem has become, without being aware of it, the father of modern Chaos Theory [DE RERUM NATURA. O problema dos três corpos e o caos (The three-body problem and chaos). Available on the website <http:// dererummundi.blogspot.com.br/2011/03/o-problema-dos-tres-corpos-eo-caos.html>]. Until then, approximate forecasts would not be attributable to the existence of chaos in reality, but a limitation in our knowledge of the initial conditions. Henri Poincaré realized in his pioneering studies in this field that are not required complex systems to produce randomness. Poincaré studies are updated in the 1960s thanks to American mathematician and meteorologist Edward Lorenz. His perplexity had much to do with the inability to predict weather events beyond a certain number of days. In the early 1960s, Lorenz began to develop a mathematical model to predict atmospheric phenomena, and by chance found that the same mathematical tool used produced
- 2. 2 unexpected and unpredictable differences in the results by simulating small changes in initial conditions. In the twentieth century, scientific determinism created by the Classical Science was in crisis because the unpredictability became object of a serious scientific study when the American meteorologist Edward Lorenz discovered in 1960 that seemingly simple phenomena have a chaotic behavior. He came to this conclusion when testing a computer program that simulated the movement of air masses. One day, Lorenz dialed one of the numbers that fed the machine calculations with a few decimals less, hoping that the outcome would change little. But the change insignificant completely transformed the pattern of air masses. It was founded Chaos Theory. Over time, scientists have concluded that the same unpredictability appeared in almost everything, from the rhythm of heartbeats to the prices Stock Exchange. From the 1960s, Chaos Theory eliminated the Laplacian fantasy of deterministic predictability. The central idea of Chaos Theory is that a tiny change in the start of an event can bring any huge consequences and absolutely unknown in the future. Therefore, such events would be virtually unpredictable - chaotic, so. Science found that systems that obey immutable and precise laws do not always act in a predictable and regular basis. simple laws cannot produce simple behaviors and vice versa [MURPHY, Robert. La teoria del Caos (Chaos Theory). Madrid: Union Editorial, 2012]. The Poincaré and Lorenz efforts joined the contributions of Benoit Mandelbrot (communications engineer), Edward Feigenbaum (mathematical) Libchaber (physical), Winfree (biologist), Mandell (psychiatrist) and others. According to Chaos Theory or the Science of Complexity, chaos is a "mixture" of disorder and order born of new structures, structures called "dissipative" [PRIGOGINE, Ilya. As leis do caos (Laws of chaos). São Paulo: Editora UNESP, 2002]. Chaos Theory suggests that the Universe has an cycle of order, disorder, order, and so on. So that one leads to the other and so on, perhaps indefinitely. One of the main implications of Chaos Theory has to do with the return generated in chaotic situations, ie, the negative and positive feedback. The negative feedback tends to correct a deviation, causing the system to its original state. Such processes are opposed to change, as always look back to return to a previous state. On the other hand, the feedback positive promotes change, the formation of new structures, more sophisticated, more adaptive, and more subtle. Whereas involves the creation of a new structure, the processes are irreversible, unlike the feedback negative, that tending to the original state, is reversible.. Exemplifying the feedback negative: if we walk in the desert toward a distant goal, we must, from time to time, correct our course, correcting our target deviation through regular updates on our way. But if we make a mistake of a millimeter of the target, with the time error will be expanded and eventually come to a place away from the goal. The negative feedback seeks to correct the deviations to return to the original path. In the positive feedback, small changes can lead to big changes that lead to new unknown targets, perhaps better, although we cannot predict exactly where we will are going. While Classical Science centered on stability, on determinism, emphasizes the process of negative feedback that tends to reduce the change, returning the system to its equilibrium position, the positive feedback promotes change. Example of positive feedback: technological innovation creates a new business and the presence of this, in turn, stimulates the generation of further innovation. This explains how small change creates great final change (butterfly effect). Progress to exist requires
- 3. 3 Progress to exist requires instability, irreversibility and the ability to make sense of small events for a structural change occurs. The irreversibility (fluctuations) makes possible things that would be impossible in a state of balance and provides an important constructive law, the origin of a new state and its highly complex and sophisticated structures derived. Once the process results in the creation of a complex structure, the dissipation structure, a new imbalance cycle occurs and chaos starts where new instabilities or fluctuations occur (Figure 1). Figure 1 - Dynamic Systems and the Positive "Feedback" Fonte: Ervin Laszlo. O Ponto do Caos (The Chaos Point). São Paulo: Editora Cultrix, 2006. Figure 1 shows what happens to a dynamic system with an old structure when it is subjected to instability or "fluctuations" that leads to a bifurcation point from which the system reaches a new dynamic stability (revolutionary advancement) with a new structure or collapses, according to Ervin Laszlo (LASZLO, Ervin. O Ponto do Caos. (Chaos Point). São Paulo: Editora Cultrix, 2006). Figure 2 shows that in the bifurcation point the system has to be restructured or collapse. Chaos refers mainly to something that evolves over time. ChaosTheory explains the functioning of complex and dynamic systems such as, for example, economic systems and climate system. In these systems, several elements are interacting in a manner unpredictable and random. It should be noted that Ilya Prigogine, commenting on bifurcation points in chemical reactions, states that "they demonstrate that even in macroscopic level our prediction of the future mixture determinism and probability. In the bifurcation point, the prediction is probabilistic, while between the bifurcation points, we can speak of deterministic laws [PRIGOGINE, I. As leis do caos (The laws of chaos). São Paulo: Editora UNESP, 2002]. It is worth noting that chaos is present in a wide variety of science disciplines. Research about chaos began in the 1970s. Physiologists began investigating why the chaos of normal heartbeat produced a sudden cardiac arrest, ecologists analyzed how certain Beginning of fluctuations State of the system Time Collapse 3 2 1 Fluctuations Instability (Crisis) Revolutionary advancement Dynamic stability Old structure Bifurcation point or Change Irreversible New Dynamic stability New structure
- 4. 4 places on the planet have undergone random changes in nature, engineers sought to find the causes of behavior to sometimes erratic oscillators, chemists analyzed the causes of unexpected fluctuations in the reactions of chemicals and economists tried to detect some kind of order in unexpected price changes, etc. In classical science, chance was an intruder, but Chaos Theory has become a partner of uncertainty. Chaos Theory or the Science of Complexity presents an interesting perspective from the point of view of its application to the economy mainly in the phenomena of explanation that seems to have a disruptive behavior. Behind the apparent disorder in the economy, there is a dynamic that can be explained by mathematical techniques and appropriate statistics, typical of this theory. In dynamic systems, such as the economy, which constantly change over time, small changes at a given time may be the cause of great importance in the future. The global crisis that erupted in 2008 in the United States has produced several consequences that manifest themselves today. Whereas the capitalist economy is a dynamic system, nonlinear and complex, the difficult to plan and anticipate problems requires consideration of long-term development prospects. Means that it´s necessary to plan the economy recognizing that chaos and complexity are present and that must deal with this situation in the best possible way. Ervin Laszlo defends the thesis that the systems enter into a state of chaos when fluctuations that were until then corrected by negative feedbacks self stabilizing get out of control. The development trajectory becomes nonlinear: prevailing trends collapse and in its place comes a range of complex developments. Rarely chaos is an extended condition. In most cases, only a transient time from more stable states. When the fluctuations in the system reach irreversibility levels, the system reaches a critical point where it collapses into its stable individual components or undergoes a rapid evolution toward a strong state to fluctuations that destabilized it (revolutionary advancement or positive feedback). If the path of the positive feedback or revolutionary advancement is selected, the system evolves to a state in which it has information processing capability intensified and more efficient use of free energy as well as more flexibility, greater structural complexity and additional levels of organization. The opinion of Ervin Laszlo is that "a dynamic system, whether it occurs in nature, in society or in a computer simulation, is governed by attractors. These define 'the phase portrait' of the system: how it behaves over time. Stable attractors pull the trajectory of system development into a recurring and recognizable pattern, taking it to converge at a given point (if the system is governed by point attractors) or describe cycles through different states (when it is under the command of periodic attractors). However, dynamic systems can also achieve a state in which the attractors that emerge are not stable, but 'strangers'. Are chaotic attractors". It should be noted that an attractor is the set of points in phase space for which a system tends to go as it evolves. The attractor may be a single point, a closed curve (cycle limit) which describes a system of periodic behavior, or a fractal (also called strange attractor) when the system has chaos. In chaotic system the movement never repeats, though often have to occur within certain limits. Thus, only an infinitely complex figure - a fractal - can handle to represent this path that never repeats itself in phase space. Change and time are the two fundamental aspects of Chaos. A field of study that has received attention recently in organizational studies is the area of Chaos Theory and Science of Complexity. Dynamic approaches to strategic management are being developed. Organizations are being considered as non-linear
- 5. 5 systems, complex, dynamic, that does not evolve in a predictable manner, stable. These ideas impact in the field of information systems. While the concepts of Chaos Theory can provide some help in explaining the information systems in organizations, it is difficult to identify their applicability in predicting or in providing principles generalizable given that the apparent unpredictability is part of the nature of Chaos Theory (THOMPSOM, J. M. T & STEWART, H. B. Nonlinear Dynamics and Chaos. Chichester: John Wiley & Sons, 1986). The concept of chaos suggests a lack of organization, a disorder in which uncertainty and unpredictability predominate. This would seem a strange field of study to unify with information systems that are predominantly concerned with the order. However, Chaos refers to what can be called an orderly disorder. The idea of Chaos is married to the complexity. Complex systems may exhibit chaotic behavior, which is not a lack of order, but the order of a complexity that is difficult or impossible to describe in simple terms that cannot be solved with simple equations, which requires complex narrative to describe it (PRIGOGINE, Ilya and STENGERS, Isabelle. Order Out of Chaos. Available on the website <http://www.mountainman.com.au/chaos_02.htm> 1984). The Classical Sciences in the past offered a number of methods to understand reality and build economic and organizational models that no longer meet the needs of the contemporary era. We live and work in a world that can no longer be analyzed based on the concepts of Newtonian mechanics, the rationalism of Descartes and the determinism of Laplace. * Fernando Alcoforado, member of the Bahia Academy of Education, engineer and doctor of Territorial Planning and Regional Development from the University of Barcelona, a university professor and consultant in strategic planning, business planning, regional planning and planning of energy systems, is the author of Globalização (Editora Nobel, São Paulo, 1997), De Collor a FHC- O Brasil e a Nova (Des)ordem Mundial (Editora Nobel, São Paulo, 1998), Um Projeto para o Brasil (Editora Nobel, São Paulo, 2000), Os condicionantes do desenvolvimento do Estado da Bahia (Tese de doutorado. Universidade de Barcelona, http://www.tesisenred.net/handle/10803/1944, 2003), Globalização e Desenvolvimento (Editora Nobel, São Paulo, 2006), Bahia- Desenvolvimento do Século XVI ao Século XX e Objetivos Estratégicos na Era Contemporânea (EGBA, Salvador, 2008), The Necessary Conditions of the Economic and Social Development-The Case of the State of Bahia (VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG, Saarbrücken, Germany, 2010), Aquecimento Global e Catástrofe Planetária (P&A Gráfica e Editora, Salvador, 2010), Amazônia Sustentável- Para o progresso do Brasil e combate ao aquecimento global (Viena- Editora e Gráfica, Santa Cruz do Rio Pardo, São Paulo, 2011), Os Fatores Condicionantes do Desenvolvimento Econômico e Social (Editora CRV, Curitiba, 2012) and Energia no Mundo e no Brasil- Energia e Mudança Climática Catastrófica no Século XXI (Editora CRV, Curitiba, 2015).