How much of the world is chaotic?

The attractive name "Chaos", like many things these days, has been greatly exaggerated. Most natural systems are not chaotic, but there are enough reasons to make this theme attractive; The most interesting question is, regarding the division of chaotic and non-chaotic behaviors, which one is here and which one is there? Let's discuss what a chaotic system is and under what circumstances it is unpredictable. Imagine an experiment and throw some small pieces of wood into the river.

If the river is deep and the water flows smoothly, small pieces of wood that are close to each other will still be very close downstream; If the distance between the thrown small pieces of wood is doubled, it will be twice as long when it reaches the downstream. This is an example of a linear predictable system. Now imagine throwing a small piece of wood into a bubbling turbulence instead of into a deep-water river. Two small pieces of wood are close when they enter the water in the upstream, but always far when they reach the downstream; There is no simple linear relationship between the distance when they enter the water and the last distance. This is a chaotic system. Small changes in the initial state will produce great changes in the results.

We're about to reach the predictable place. If you can know the position of sawdust when it enters turbulence with absolute mathematical accuracy, you can accurately predict where they will eventually appear. However, if there is any uncertainty in the initial state, the final downstream position of the chip will be far from the predicted position. Because there is always some uncertainty in determining the initial position of small debris in the real world, it is practically impossible to predict where the debris will appear downstream.

If some systems in nature are chaotic, it is impossible to predict their future in practice (even if it is always possible in principle, it must be based on complete accuracy to measure their original state). In fact, in a chaotic system, the systems that start at the same time will develop into different systems, and the differences between them will inevitably increase exponentially with the passage of time.

There is an obvious but true fact: the analysis of turbulence and other chaotic systems has had a great philosophical impact on our thinking about the nature of the physical world. Since Newton, people have assumed that if the mathematical equation describing a system can be written down, then the future of the system can be predicted. In other words, we think that the ability to describe means the ability to predict. The discovery of chaos shows that this conclusion is not necessarily true? Some systems can be described by equations, but they are still unpredictable.

Since the discovery of chaotic system, scientists have been discussing another problem. Which systems in nature are chaotic systems? Some answers are obvious? Surging water, the stock market and the weather are almost certainly chaotic. But the other answers will be amazing,

For example, some scientists recently called the solar system? What is the most typical representative of Newton's predictability? There are many characteristics that can be confused. The complex computer brain model that tracks the orbits of planets and all the gravitational forces between them shows that within several hundred million years, the orbits of planets are likely to be chaotic Q. This conclusion comes from some studies. First, the orbits of distant future planets are predicted from a starting position, then the positions of the planets are assumed to be moved by several inches, and then re-predicted. The results seem to show the divergence phenomenon of small wood blocks in turbulence. There is no doubt that the computer simulation results of the solar system are chaotic. But I doubt whether these simulations really represent the world we live in.

But I don't want you to think that the existence of chaos has a completely negative impact on science. New discoveries are always the same: people are already thinking about how to take advantage of this phenomenon. For example, chaotic systems are very suitable for password generation. If two people know the equation describing a chaotic system, they can use it as the basis of the password.

They can use this equation to send out a series of random information, while others think that these information are only information they can understand. Similarly, some scientists may leave their academic jobs in the future, because they believe that they can use their expertise in chaos research to understand the stock market (I won't believe this is a wise move until I see these people continue to make a fortune in the stock market in Rolls Royce cars).