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other systems are chaotic.
    The point about complex chaotic systems is that you can never measure the initial conditions of a system accurately enough to allow you to predict its behavior for all future time. Although your predictions and the real system may be close to each other for a while, eventually they will diverge. The inevitable errors inherent in any measurement, coupled with the extreme sensitivity of chaotic systems to initial conditions, means that for all practical purposes they are unpredictable (although they are perfectly predictable if the initial conditions are specified with mathematical precision).
    The weather provides the most familiar example of a chaotic system. Meteorologists make thousands upon thousands of measurements of wind speed, air temperature, and barometric pressure in their efforts to predict the weather. They do pretty well with 24-and 48-hour forecasts, and sometimes they even get the seven-day predictions right. But no matter how fancy the measurements and the computer simulations, there is no way to predict what the weather will be a year from now. The chaotic nature of atmospheric motion is sometimes dramatized as the “butterfly effect,” which says that in a chaotic system an effect as small as a butterfly’s flapping its wings in Singapore may eventually make it rain in Texas.
    Today the existence of chaotic systems is accepted by scientists, who now ask which systems are chaotic, how they behave, and how our newly won knowledge of that behavior can be utilized. Can we, for example, produce accurate monthly forecasts of the weather or the stock market?

CHAPTER TWO
Energy
    A FICIONADOS THINK THE OLD wooden roller coasters are still the best. If you’ve ever ridden one, you’re not likely to forget the experience. The adventure begins calmly enough, as you lean back in your cushioned seat enjoying the gradual climb to the ride’s highest point. The steady clack-clack-clack of straining gears belies the wildness to follow. In the best of roller coaster tradition the car comes almost to a stop, poised at the brink, before gravity takes over. Then comes the plunge.
    Faster and faster you go, 100 feet of free fall before the car hits bottom and zooms to the next height, only slightly shorter than the first. For a second time you almost come to a stop, and then another precipitous drop. Now the speeding ride takes off for a series of twists and turns, flinging you around tight loops and over violent bumps leading to one last mighty hill. The journey lasts only a couple of minutes, but you emerge, wobbly-legged, with a high that can last for hours.
    Roller coasters are a microcosm of the universe. You were probably a bit too preoccupied to think about it the last time yourode one, but as you climbed and zoomed down those hills, hitting all the fancy loops and bumps, you demonstrated the basic laws of how energy behaves. Everything you do or see requires energy, and that energy always follows two basic rules:
    Energy is conserved.
    and
    Energy always goes from more useful
to less useful forms.
    These two laws suggest good news and bad news. The first rule says that energy, the ability to perform useful work, comes in many different forms, and these forms are interchangeable. You can shift energy from one form to another the way you shift money between bank accounts. But just as transferring money neither adds to nor detracts from your wealth, changing energy from one form to another does not change the total amount of energy available. Energy cannot be created or destroyed, so the total energy of an isolated system stays the same. This powerful scientific statement is known as the first law of thermodynamics. It’s the good news.
    The bad news about energy is that its conversion always leads from more concentrated (i.e., more useful) to less concentrated (less useful) forms. When you burn coal or gas, the laws of nature require that some of the high-grade energy in the fuel must be