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April 29, 2011 by Actaphysica
Filed under Physics Book Reviews
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[...] Chaos: Making a New Science | Acta Physica [...]
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Another excellent book for non-experts,
I am not a hard scientist, but I like to have some idea of what is going on in those fields. Books like this one are ideal for people such as me. This book tackles the fascinating field of Chaos Theory. It turns out that certain patterns recur over and over in many diverse areas of the universe, whether it is the patterning of galaxies in clusters or the price of cotton.
Specialists working in many fields independently discovered curious patterns, and eventually, starting mainly in the 1970′s, they became aware of each others’ work. This book takes physics as the field on which it focuses, but it mentions many others. Since some of these fields involve conscious human decision making (especially economics), I have begun to wonder whether I can find comparable patterns in languages, my own specialty.
There are many reviews of a previous printing of this book: Chaos: Making a New Science, so you can go there to check them out. Other books useful to non-specialists interested in the history of and current research in the hard sciences are The Fabric of the Cosmos: Space, Time, and the Texture of Reality, A Briefer History of Time and Electric Universe: How Electricity Switched on the Modern World.
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An historical introduction to chaos theory,
This book is the first of its kind, which introduces a new branch of science, the chaos or chaos theory from the historical point of view. This theory is widely applied in the transdisciplinary field of meteorology, mathematics, physics, population biology, cell biology, philosophy, astrophysics, information theory, economics, finance, robotics, and other diverse fields. The author has done a tremendous job of putting this book together with very little mathematics. I found this book highly engaging.
A brief summary of the book is as follows: Chaos physics along with classical and quantum physics are required to fully describe physical reality. Physical laws described by differential equations correspond to deterministic systems. In quantum physics, the Schrödinger equation which describes the continuous time evolution of a system’s wave function is deterministic. However, the relationship between a system’s wave function and the observable properties of the system is non-deterministic (quantum physical phenomenon). The systems studied in chaos theory are deterministic. In general for a deterministic system, if the initial state of a system were known exactly, then the future state of such a system could be predicted. However, there are many dynamical systems such as weather forecasting that are highly sensitive to initial conditions. This sensitivity referred to as the butterfly effect which suggests that small differences in initial conditions (for example, rounding errors caused by limiting the number of decimals in numerical computation), yield different results, rendering long-term prediction impossible, hence they are called chaotic systems. In short these systems are deterministic; their future behavior is fully determined by their initial conditions, with no random elements involved. But that does not make it predictable, this behavior is known as deterministic chaos or chaos.
It is difficult to determine if a physical system is random or chaotic, because in practice no time series consists of pure ‘signal.’ There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness. Methods that distinguishes deterministic and stochastic (a process having infinite progression with random variables) processes rely on the fact that a deterministic system always evolves in the same way from a given starting point. Thus, given a time series to test for determinism, one can: Pick a test state; search the time series for a similar or ‘nearby’ state; and compare their respective time evolutions. Define the error as the difference between the time evolution of the ‘test’ state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error. Thus one can see that chaos is neither purely deterministic nor is it stochastic. Application of chaos into cosmology and quantum physical phenomenon illustrates that chaos theory is indeed an important feature of physical reality which requires further development of this field.
1. Does God Play Dice? The New Mathematics of Chaos
2. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers
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Chaos is one of Physics Foibles. As Godel revealed – maybe we can’t prove everything!! Weather prediction is trumped by Chaos Theory.
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