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The astonishing thing about technical analysis is not only how far out its predictive power goes, but also how, even with a future full of unknowns, it still seems able to see its way clear to make a meaningful prediction. A staggering number of great forces can wreak havoc with nancial markets scandals, war, governmental chaos, interest rates, terrorist attacks, earnings surprises, the social climate, and so forth. Through it all, the knowledgeable chartist can see what others cannot see and know what seems unknowable. Let s take a real-life example with a very long timespan: the Dow Jones Industrial Average over a period of more than 100 years. Figure 1.1 has two Fibonacci fans drawn on it (don t worry if you are not familiar with that term; it will be explained in 13). These fans are drawn from an extreme low to an extreme high. The rst is drawn from the low in 1903 (the Rich Man s Panic, it was called) to the peak of the roaring twenties bull market in 1929. The second is drawn from the

It is an empirical rule that the brightness of a star is proportional to its color (i.e., predominant wavelength emitted). The proportionality constant is roughly the same for all stars. Thus if we make a plot of brightness against color, we obtain what is known as the Hertzprung-Russell diagram, in which most stars fall within a linear strip called the main sequence, as shown in Fig. 11.4. There are, however, stars that are exceptions to this rule. There are the red giant stars, huge stars which are abnormally bright for their red color; and there are the white dwarf stars, small stars which are abnormally faint for their white color. The white

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dwarf star makes an interesting subject for our study, because to a good approximation it is a degenerate Fermi gas. A detailed study of the constitution of white dwarf stars leads to the conclusion that they lack brightness because the hydrogen supply, which is the main energy source of stars, has been used up, and they are composed mainly of helium. What little brightness they have is derived from the gravitational energy released through a slow contraction of the star. Probably these stars have reached the end point of stellar evolution. One of the nearest stars to the solar system, the companion of Sirius, 8 light years from us, is a white dwarf. So faint that it escapes the naked eye, it was first predicted by the calculations of Bessel, who tried to explain why Sirius apparently moves about a point in empty space. An idealized model of a white dwarf may be constructed from some typical data for such a star: Content: mostly helium Density"" 10 7 g/crrr "" 10 7 Mass"" 10

Central temperature"" 10 7 K "" To where the subscript 0 denotes quantities referring to the sun. Thus a white dwarf star is a mass of helium at an extremely high temperature and under extreme compression. The temperature 10 7 K corresponds to a thermal energy of 1000 eV. Hence the helium atoms are expected to be completely ionized, and the star may be regarded as a gas composed of helium nuclei and electrons. We regard the gas of electrons as an ideal Fermi gas, with a density of approximately 10 30 electrons/cm3. This corresponds to a Fermi energy of

Since the Fermi temperature is much greater than the temperature of the star, the electron gas is a highly degenerate Fermi gas, which behaves no differently from an electron gas at absolute zero. In fact we regard the electron gas to be an ideal Fermi gas in its ground state. The enormous zero-point pressure exerted by the electron gas is counteracted by the gravitational attraction that binds the star. This gravitational binding is due almost entirely to the helium nuclei in the star. The pressure due to kinetic motion of the helium nuclei, and to any radiation that may be present, will be neglected. Thus we arrive at the following idealized model: A white dwarf is taken to be a system of N electrons in its ground state, at such a density that the electrons must be treated by relativistic dynamics. The electrons move in a background of N /2 motionless helium nuclei which provide the gravitational attraction to hold

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