A butterfly flapping its wings can cause a hurricane in China!
You don't need to see an Optometrist, and you did not drink an excessive amount of alcohol, at least I did not, however, I am not sure about you..!
There is nothing wrong with you if you see
BABA
,
PDD
,
JD
,
BIDU
creates the exact same pattern..!
This could be explained in mathematics!
What is Chaos Theory?
Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit complex, chaotic behavior. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. For example, by understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to a desired location. By understanding that our ecosystems, our social systems, and our economic systems are interconnected, we can hope to avoid actions which may end up being detrimental to our long-term well-being.
Chaos Theory
Chaos theory is concerned with unpredictable courses of events. The irregular and unpredictable time evolution of many nonlinear and complex linear systems has been named chaos. Chaos is best illustrated by Lorentz’s famous butterfly effect: the notion that a butterfly stirring the air in Hong Kong today can transform storm systems in New York next month. The definition of deterministic chaos implies that our prediction in the form of a model, for instance, is very sensitive to the initial conditions. The difference between predictions with slightly different initial conditions grows exponentially:
d(t)=d(0)eat*
where d(t) is the difference between the two predictions at time t and d(0) at time zero, t is the time, and a is a positive number.
*at: is the power of e, I do not know how to type power in TradingView..!
Chaos theory, more technically nonlinear dynamical systems (NLDS) theory, is an exciting, rapidly developing area of mathematics with increasing application in the physical, biological, and social sciences. Along with the great metaphorical appeal, nonlinear dynamical systems can also add rigor and realism to human sciences; they may help illuminate creativity, an elusive, sometimes near-magical phenomenon that has defied simple explanations. Chaotic or near-chaotic systems can demonstrate surprising flexibility and adaptability. Despite connotations of ‘chaos,’ they also demonstrate order, complexity, and self-organization. Some relatively simple, mechanistic, completely deterministic systems are capable of surprising, discontinuous, and seemingly unpredictable change.
Challenged by Instability and Complexity
Challenged by Instability and Complexity…
Jan C. Schmidt, in Philosophy of Complex Systems, 2011
1 Introduction: the Stability Assumption Is Unstable …
Nonlinear Dynamics — including Complex Systems Theory, Chaos Theory, Synergetics, Dissipative Structures, Fractal Geometry, and Catastrophe Theory — is a young and fascinating field of scientific inquiry that spans many established disciplines (cf. ). However, it poses challenging problems for both scientific methodology and the philosophy of science. Methodological prerequisites as well as metaphysical assumptions are questioned, e.g., predictability, reproducibility, testability, explainability as well as lawlikeness (determinism/causation). The common denominator of all of these challenges is instability — that is the main thesis of this paper.
Since the advent of Nonlinear Dynamics and its advancement in the realm of physics in the 1960s — interlaced with methodological developments in computer technology and the computer's ability to numerically handle nonlinearity — further evidence for the existence and prevalence of unstable and complex phenomena in the physical world has emerged. Nonlinear systems, even those with just a few degrees of freedom, can exhibit static, dynamical and structural instabilities. Although instabilities call implicit metaphysical-methodological convictions and well-established underlying prerequisites of mathematical science into question, today they are not viewed in just a negative way. On the contrary, instabilities are highly valued — we find a positivization of instabilities: instabilities constitute the nomological nucleus of self-organization, pattern formation, growth processes, phase transitions and, also, the arrow of time (cf. ). Without instability, there is no complexity and no change. The phenomena generated by underlying instabilities in nature, technology and society are manifest; we can observe these phenomena with our unaided senses. In fact, instability is the root of many homely phenomena in our day-to-day experience — for example, the onset of dripping from a tap or water freezing to ice in a refrigerator. Instability has to be regarded as an empirical fact of our life-world and beyond — not just as a contingent convention.
A reconsideration of the traditional methodological-metaphysical stability assumptions therefore seems to be indispensable. (a) In the past, stability was taken for granted as an implicit a priori condition to qualify a mathematical model as physically relevant or adequate. Stability seemed to be a key element underlying any kind of physical methodology: it was regarded as the sole possibility to guarantee the application of methods of approximation and, also, to deal with empirical and experimental uncertainties. (b) In addition to methodology, an underlying metaphysical conviction was pervasive throughout the history of physics, guiding the focus of interest and selecting the objects that were considered worth researching. Framing and conceptualizing nature as “nature” insofar as it is stable, time-invariant and symmetrical (metaphysics), was indeed a successful strategy to advance a specific physical knowledge (methodology). It is interesting to see that metaphysical convictions and methodological considerations are interlaced; there is no clear line between metaphysics and methodology, as will be shown in this paper.
Throughout history, stability metaphysics has always played a major role in science, beginning in ancient times with Plato's stability concept of the cosmos. In modern times, stability metaphysics can be found in the works of outstanding physicists such as Newton and Einstein. For instance, in his Opticks Newton did not trust his own nonlinear equations for three- and n-body systems which can potentially exhibit unstable solutions . He required God's frequent supernatural intervention in order to stabilize the solar system. In the same vein, Einstein introduced ad hoc — without any empirical evidence or physical justification — the cosmological constant in the framework of General Relativity in order to guarantee a static and stable cosmos, “Einstein's cosmos” . Both examples, from Newton and Einstein, illustrate that metaphysical convictions — what nature is! — can be incredibly strong, even if they are in conflict with what is known about nature at the time.
Today, however, ex post and thanks to the advancement of Nonlinear Dynamics, we can identify a “dogma of stability” that has determined the selection (or construction) of both the objects and the models/theories in physics. “We shall question the conventional wisdom that stability is an essential property for models of physical systems. The logic which supports the stability dogma is faulty.” : the stability assumption is itself unstable! Although the discovery history of instabilities traces back to physicists such as Newton, Laplace, Stokes, Maxwell, Poincaré and Duhem, physical objects were (and often still are) perceived and framed from the perspective of stability — even by the pioneers of instabilities. Throughout the history of exact sciences, instabilities were not acknowledged by the scientific community. This has been changing since the 1960s when physics began widening its methodological horizon — including getting rid of the restriction of methodology to stability requirements. The need to advance physical methodology emerged because instabilities have turned out to be so very fundamental in nature, technology, and even in social processes. In order to deal with instabilities, physicists have over the last 30 years successfully replaced the traditional quantitative, metrically oriented stability dogma by weaker, more qualitative topological characteristics. Many models (theories, laws) in Nonlinear Dynamics are unstable, “and we are confident that these are realistic models of corresponding physical systems” .
Nonlinear Dynamics shows that instability is not an epiphenomenon of minor relevance: instabilities are broadly present in our entire world. Discovering and acknowledging instabilities impels both a reconsideration of the metaphysical views that undergird the stability dogma and a revision of the methodological presuppositions. The outline of this paper is as follows: In section 2, I characterize instabilities and distinguish between three kinds of instability. In section 3, I focus on methodological problems and challenges caused by instabilities; the limitations of classical-modern sciences will be discussed. In section 4, I show how present-day physics manages, at least to some degree, to cope with instabilities.
Instabilities cannot be considered as exceptions within a stable world. Rather, it is the other way around: instabilities are the source of complexity, pattern formation and self-organization. This is why instabilities do not only appear in a negative light; a positive understanding emerges and shows challenging future prospects and perspectives for the rapidly progressing field of Nonlinear Dynamics — and beyond: for all mathematical sciences.
My Soul is painted like the wings of a butterfly..!
Moshkelgosha
References :
https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/chaos-theory
https://fractalfoundation.org/resources/what-is-chaos-theory/
There is nothing wrong with you if you see
BABA
,
PDD
,
JD
,
BIDU
creates the exact same pattern..! This could be explained in mathematics!
What is Chaos Theory?
Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit complex, chaotic behavior. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. For example, by understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to a desired location. By understanding that our ecosystems, our social systems, and our economic systems are interconnected, we can hope to avoid actions which may end up being detrimental to our long-term well-being.
Chaos Theory
Chaos theory is concerned with unpredictable courses of events. The irregular and unpredictable time evolution of many nonlinear and complex linear systems has been named chaos. Chaos is best illustrated by Lorentz’s famous butterfly effect: the notion that a butterfly stirring the air in Hong Kong today can transform storm systems in New York next month. The definition of deterministic chaos implies that our prediction in the form of a model, for instance, is very sensitive to the initial conditions. The difference between predictions with slightly different initial conditions grows exponentially:
d(t)=d(0)eat*
where d(t) is the difference between the two predictions at time t and d(0) at time zero, t is the time, and a is a positive number.
*at: is the power of e, I do not know how to type power in TradingView..!
Chaos theory, more technically nonlinear dynamical systems (NLDS) theory, is an exciting, rapidly developing area of mathematics with increasing application in the physical, biological, and social sciences. Along with the great metaphorical appeal, nonlinear dynamical systems can also add rigor and realism to human sciences; they may help illuminate creativity, an elusive, sometimes near-magical phenomenon that has defied simple explanations. Chaotic or near-chaotic systems can demonstrate surprising flexibility and adaptability. Despite connotations of ‘chaos,’ they also demonstrate order, complexity, and self-organization. Some relatively simple, mechanistic, completely deterministic systems are capable of surprising, discontinuous, and seemingly unpredictable change.
Challenged by Instability and Complexity
Challenged by Instability and Complexity…
Jan C. Schmidt, in Philosophy of Complex Systems, 2011
1 Introduction: the Stability Assumption Is Unstable …
Nonlinear Dynamics — including Complex Systems Theory, Chaos Theory, Synergetics, Dissipative Structures, Fractal Geometry, and Catastrophe Theory — is a young and fascinating field of scientific inquiry that spans many established disciplines (cf. ). However, it poses challenging problems for both scientific methodology and the philosophy of science. Methodological prerequisites as well as metaphysical assumptions are questioned, e.g., predictability, reproducibility, testability, explainability as well as lawlikeness (determinism/causation). The common denominator of all of these challenges is instability — that is the main thesis of this paper.
Since the advent of Nonlinear Dynamics and its advancement in the realm of physics in the 1960s — interlaced with methodological developments in computer technology and the computer's ability to numerically handle nonlinearity — further evidence for the existence and prevalence of unstable and complex phenomena in the physical world has emerged. Nonlinear systems, even those with just a few degrees of freedom, can exhibit static, dynamical and structural instabilities. Although instabilities call implicit metaphysical-methodological convictions and well-established underlying prerequisites of mathematical science into question, today they are not viewed in just a negative way. On the contrary, instabilities are highly valued — we find a positivization of instabilities: instabilities constitute the nomological nucleus of self-organization, pattern formation, growth processes, phase transitions and, also, the arrow of time (cf. ). Without instability, there is no complexity and no change. The phenomena generated by underlying instabilities in nature, technology and society are manifest; we can observe these phenomena with our unaided senses. In fact, instability is the root of many homely phenomena in our day-to-day experience — for example, the onset of dripping from a tap or water freezing to ice in a refrigerator. Instability has to be regarded as an empirical fact of our life-world and beyond — not just as a contingent convention.
A reconsideration of the traditional methodological-metaphysical stability assumptions therefore seems to be indispensable. (a) In the past, stability was taken for granted as an implicit a priori condition to qualify a mathematical model as physically relevant or adequate. Stability seemed to be a key element underlying any kind of physical methodology: it was regarded as the sole possibility to guarantee the application of methods of approximation and, also, to deal with empirical and experimental uncertainties. (b) In addition to methodology, an underlying metaphysical conviction was pervasive throughout the history of physics, guiding the focus of interest and selecting the objects that were considered worth researching. Framing and conceptualizing nature as “nature” insofar as it is stable, time-invariant and symmetrical (metaphysics), was indeed a successful strategy to advance a specific physical knowledge (methodology). It is interesting to see that metaphysical convictions and methodological considerations are interlaced; there is no clear line between metaphysics and methodology, as will be shown in this paper.
Throughout history, stability metaphysics has always played a major role in science, beginning in ancient times with Plato's stability concept of the cosmos. In modern times, stability metaphysics can be found in the works of outstanding physicists such as Newton and Einstein. For instance, in his Opticks Newton did not trust his own nonlinear equations for three- and n-body systems which can potentially exhibit unstable solutions . He required God's frequent supernatural intervention in order to stabilize the solar system. In the same vein, Einstein introduced ad hoc — without any empirical evidence or physical justification — the cosmological constant in the framework of General Relativity in order to guarantee a static and stable cosmos, “Einstein's cosmos” . Both examples, from Newton and Einstein, illustrate that metaphysical convictions — what nature is! — can be incredibly strong, even if they are in conflict with what is known about nature at the time.
Today, however, ex post and thanks to the advancement of Nonlinear Dynamics, we can identify a “dogma of stability” that has determined the selection (or construction) of both the objects and the models/theories in physics. “We shall question the conventional wisdom that stability is an essential property for models of physical systems. The logic which supports the stability dogma is faulty.” : the stability assumption is itself unstable! Although the discovery history of instabilities traces back to physicists such as Newton, Laplace, Stokes, Maxwell, Poincaré and Duhem, physical objects were (and often still are) perceived and framed from the perspective of stability — even by the pioneers of instabilities. Throughout the history of exact sciences, instabilities were not acknowledged by the scientific community. This has been changing since the 1960s when physics began widening its methodological horizon — including getting rid of the restriction of methodology to stability requirements. The need to advance physical methodology emerged because instabilities have turned out to be so very fundamental in nature, technology, and even in social processes. In order to deal with instabilities, physicists have over the last 30 years successfully replaced the traditional quantitative, metrically oriented stability dogma by weaker, more qualitative topological characteristics. Many models (theories, laws) in Nonlinear Dynamics are unstable, “and we are confident that these are realistic models of corresponding physical systems” .
Nonlinear Dynamics shows that instability is not an epiphenomenon of minor relevance: instabilities are broadly present in our entire world. Discovering and acknowledging instabilities impels both a reconsideration of the metaphysical views that undergird the stability dogma and a revision of the methodological presuppositions. The outline of this paper is as follows: In section 2, I characterize instabilities and distinguish between three kinds of instability. In section 3, I focus on methodological problems and challenges caused by instabilities; the limitations of classical-modern sciences will be discussed. In section 4, I show how present-day physics manages, at least to some degree, to cope with instabilities.
Instabilities cannot be considered as exceptions within a stable world. Rather, it is the other way around: instabilities are the source of complexity, pattern formation and self-organization. This is why instabilities do not only appear in a negative light; a positive understanding emerges and shows challenging future prospects and perspectives for the rapidly progressing field of Nonlinear Dynamics — and beyond: for all mathematical sciences.
My Soul is painted like the wings of a butterfly..!
Moshkelgosha
References :
https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/chaos-theory
https://fractalfoundation.org/resources/what-is-chaos-theory/