Chaos theorem?

Chaos theory is a scientific revolution in recent 30 years. Together with relativity and quantum mechanics, it is listed as the greatest discovery and scientific masterpiece in the 20th century. Quantum mechanics questions the physical causal law of the micro-world, while chaos theory immediately denies the deterministic causal law including the Laplace type of the macro-world.

When Lorenz, an American meteorologist, studied the atmospheric flow in weather forecast in the early 1960s, he revealed two basic characteristics of chaos: unpredictability and extremely sensitive dependence on initial conditions. At the same time, he also found that the seemingly chaotic chaos still has a certain order. Its extremely sensitive dependence on initial conditions is reflected in the butterfly effect: a butterfly flying in Beijing today will disturb the air and may lead to a big storm in new york next month.

The discovery of chaos reveals a basic misunderstanding of the relationship between law and result behavior, that is, the relationship between cause and result. We used to think that deterministic causes would produce regular results, but now we know that they can produce extremely irregular results, which is easily misunderstood as randomness. We used to think that a simple cause must produce a simple result (that is, a complicated result must have a complicated cause), but now we know that a simple cause can also produce a complicated result. We realize that knowing these laws does not mean that we can predict future behavior.

This idea has been turned into a very useful practical technology by a group of mathematicians and physicists, including William Tito, Allen garfinkel and Jim York, who call it chaos control. Essentially, the idea is to make the butterfly effect work for you. Small changes in initial conditions lead to great changes in subsequent behaviors, which may be an advantage; All you have to do is make sure you get the big change you want. Understanding how chaotic dynamics works makes it possible for us to design a control scheme that can fully realize this requirement. This method has achieved some success. One of the earliest achievements of chaos control was that a "dead" satellite changed its orbit and collided with an asteroid, leaving only a very small amount of hydrazine. The National Aeronautics and Space Administration (NASA) maneuvered the satellite to revolve around the moon five times, nudging the satellite with a little hydrazine each time, and finally collided.