Comments about Wikipedia: Chaos Theory

Following is a discussion From Wikipedia, the free encyclopedia
In the last paragraph I explain my own opinion.


Chaos theory

In mathematics, chaos theory describes the behavior of certain dynamical systems that is, systems whose state evolves with time that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect)
As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos. Chaotic behaviour is also observed in natural systems, such as the weather. This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural system.

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Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder.


Reflection

There are two mayor problems with the above text
  1. First the text is not clear. The main reason is a mathematical explanation versus a physical explanation. Many text books high light the mathematical approach, that means there main points are around the differential equations involved, and they minimize the physical difficulties.
  2. The second reason is what clearly is the chaos theory. Is this only the fact that certain differential equations are highly sensitive to initial conditions ? This is true in mathematical sense but much more difficult to demonstrate in physical sense i.e. related to the real world.
  3. A third reason is the usage of the word deterministic. Deterministic systems imply order. That means are predictable. Non Deterministic implies less order, less predictable or more unpredictable. In that sense is the word deterministic chaos very misleading.
  4. Pierre Simon Laplace (See the book "Pierre Simon Laplace 1749 - 1827 A life In exact Science" by Charles Coulston Gillispie) and others, used two concepts in relation to deterministic, namely order and cause and effect. With the first he expressed that there is stability in the solar system. With the second change in time, the relation between past versus future expressed in mathematical laws.
    The question is how exact can we describe the physical world in mathematical laws.

The following link also discusses "deterministic chaos" Here we read:
A system is chaotic if its trajectory through state space is sensitively dependent on the initial conditions, that is, if unobservably small causes can produce large effects

In the last few decades, physicists have become aware that even the systems studied by classical mechanics can behave in an intrinsically unpredictable manner. Although such a system may be perfectly deterministic in principle, its behavior is completely unpredictable in practice. This phenomenon was called deterministic chaos.


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Created: 5 june 2008

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