Introducing Chaos

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This is an accessible introduction to an astonishing and controversial theory. Read more Read less. Review 'A beautifully succinct primer No customer reviews.

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Most helpful customer reviews on Amazon. May 14, - Published on Amazon. Verified Purchase. I was looking for an easy-to-understand book on Chaos Theory for some non-English speakers say, some Japanese students to read, and I personally like "Introducing Fractal Geometry", so I got my hand on this book It was a mistake. I would not say much about this. The author did introduce Chaos, not really Chaos theory, to the readers. He tried his best, I believe, to make things easy to understand by simplifying things However, in doing so, he had just created Chaos.

Hence, this book is probably one of the best examples of "How Simplicity creates Complexity and Chaos" One thing, while a lot of names technical terms were introduced, almost all of them are left unexplained. It is a constantly changing, complex system.

It is commonly supposed that some fluctuations created the galaxies - fluctuations that happened near the beginning of the formation of the universe. Chaos may have played a part in this. To understand this idea, we should look briefly at the theory of quantum physics. Since the 1 s, we have known that the classical physics of Newton is only an approximation of the physics that describes the sub- atomic world.

For an imaginary body, known as a black body, the graph of radiation intensity versus frequency has a very well-known curve. The peak would be in different places for different temperatures.

No one knew what was going on until Max Planck , a German professor at the University of Berlin, realized that classical physics was not working. I assumed the existence of a new constant, calling it h. Spectral lines appear when the light from heated hydrogen is passed through a spectroscope. The theory predicted the position of all the lines. However, Bohr was disappointed when he applied the new ideas to the more complicated helium atom - the theory fell apart. Something had not been understood. He wondered if particles had waves associated with them. The type of wave he envisaged was a stationary one.

Erwin Schrodinger realized that there was a need for a wave equation.

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In , Max Born suggested that the wave function did not represent the wave itself, but only a probability. This is where quantum theory now stands: probability waves in stationary humps. The lowest level is the ground level in which the system usu- ally exists. They leave these levels when a light is shone on them or in par- ticle terms, when they are hit by photons , jumping to higher energy levels or excited states.

Introducing CHAOS - A graphic guide

The question was investigated in the 1 s. And it produced a surprising result. This suppression is a subtle and delicate wave-interference effect. At low levels, the electron is attracted to the nucle- us, and there is no chaos. At strong levels, the electron is so weakly attracted to the nucleus that the magnetic field overcomes it, and the electron moves around the magnet- ic field lines.

There is no chaos. However, in between these two states, the electron does not know where to go, and becomes chaotic. In a weak magnetic field the electron remains in orbit round the nucleus. In a strong magnetic field the electron orbits the field lines. As it moves through the molecules, its trajectory is chaotic.

Small varia- tions in its entry direction or energy make large differences to its path and where it exits. The path can only be worked out using quantum mechan- ics, and since it depends on initial conditions, it has chaotic characteris- tics. But the field of quantum chaos is in its embryonic stage and there is much that we need to learn. The world has been linked into a single global market ruled by instantaneous transfer of capital by electronic sig- nals. Small changes can quickly multiply in the global electronic market and lead to serious perturbations.

Modern, high technology firms are rad- ically different from traditional old-fashioned businesses. Technological innovations proliferate rapidly, making nonsense of conventional ideas of a solid lead over competition.

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Value is generated in cyberspace, while jobs, pensions and welfare dis- solve and become weightless. Turbulence seems to be the order of the day. Indeed, chaos and complexity turn standard econom- ics theories upside down - and also open up optimistic perspectives on wealth creation. This chal- lenge comes from the concept of feedback. Negative feedback in economic terms is analogous to diminishing returns', positive feedback to increasing returns.

This way of viewing things is actually not new. In England, in the 18th century, entrepreneurs operated under conditions of diminishing returns. France, on the other hand, during ' the same period, operated under the conditions of increasing returns, gambling on long-term profits. Conditions in the markets today resemble those in France in the 1 8th cen- tury and not those found in most economics textbooks.

There is no inducement to vary the quantities of input or to change the level of output, because to move things around may affect the equilibrium point and lead to a loss of stability. But chaos tells us there are, in fact, several equilibrium positions in this market. But does it? There are never simply two countries trading, but a whole collection of connected nations and individuals. This dynamical system may not pro- duce equilibrium, but chaos.

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Contrary to popular belief, the best laid plans of governments to design better equilibrium could in fact lead to the oppo- site scenario - one of total chaos. Chaos challenges this law, and therefore strikes at the heart of a belief in a stable economic system under competition. But stubbornness cannot prevail against stark reality. Computers, software, optical fibres and telecommunications equipment, medical electronics and phar- maceuticals are all subject to increasing returns.

This is because, from the outset, they necessitate enormous outlays on research and development, designing and redesigning, developing a prototype, and setting up tools and automated plants for manufacture. However, once the products start rolling off the production line, the cost of making additional units drops very sharply in relation to the initial invest- ment. Brian Arthur of Stanford University and the Santa Fe Institute has developed new insights into the crucial role of positive feedback in the economy.

He realized that positive feedback makes the economy function as a nonlinear system. Positive feedback drives up sales once a threshold in economy has been reached and the market has been driven to a threshold of education and promotion. Software, once written, tested, debugged and enhanced, costs peanuts to duplicate. It can thus become a massive source of continuous, ever- increasing returns - until the producers decide that the time has come to bring out a better version. The best example of this is the VCR story.