Chaos theory can be described as “the science of surprises”.
It revolves around non-linear and unpredictable systems, and teaches us to expect the unexpected. Most fields of science focus on solving predictable patterns, such as gravity, chemical reactions, and electricity. Chaos theory focuses on addressing patterns that are completely unpredictable or controllable, such as disturbances, weather, and the stock market. These phenomena are often described by fractal mathematics, which revolves around the infinite complexity of nature. Many objects in nature have fractal properties, including landscapes, clouds, trees, internal organs, rivers, etc.; Many of the systems in which we live have complex, chaotic behavior. Before we delve further into the principles of chaos theory, let’s briefly review the history of chaos theory.
Edward Lorenz.
In 1961, a meteorologist named Edward Lorenz made a remarkable discovery. Lorenz used the latest computer of the time to forecast the weather. He was extremely excited about the idea of creating a mathematical model to solve unpredictable patterns. In this mathematical model, he loaded in a set of numbers that accurately represented the current weather; This set of numbers will predict the future weather a few minutes from the present time. After the successful implementation of the program, Lorenz focused on improving long-term predictability. This can be done by feeding back into the computer the predictive responses of previous forecast data. As a result, Lorenz’s model can accurately forecast month by month, even year by year, not just minute by minute as before.
One day, Lorenz decided to run the weather forecast again. Because he wanted to save time, he did not choose to start from scratch, instead taking a value that was half-run in a computer program and using it as the starting point to restart the program. After going for coffee, he turned around and discovered something completely unexpected. Although the new computer’s predictions are initially the same as before, there are two sets of significantly different forecast results. Is there something wrong in the calculation?
Lorenz quickly realized that the computer gave the prediction as 3 decimal places, but the numbers entered into the original processing were 6 decimal places. That is, while Lorenz started the second run of the program with the number 0.506, the first run actually used the number 0.506127. One part difference in thousands of other parts led to a remarkable result. It’s like the flap of a butterfly’s wings can create a strong gust of wind in your face. The initial weather conditions were mostly the same, but the two subsequent forecasts were not. Lorenz found the seeds of chaos.
There are many other theories that fall within the chaos theory. The most famous and important theory is the “Butterfly Effect” – a butterfly flapping its wings in New Mexico can cause a hurricane in China. From the flapping of its wings to the formation of a major storm can take a very long time, but there is a real connection between them. If the butterfly doesn’t flap its wings at a specific point in space/time, the storm won’t happen. A more understandable and philosophical example to describe this effect is, even the smallest actions we take will lead to a significant impact in our lives in the long run. long.
Butterfly effect
The next branch of chaos theory is “Unpredictability” . It is a fact that we can never know all the initial conditions/conditions of a complex system in detail, which means that we cannot hope to predict the final outcome. that a complex system would produce. Even the smallest errors in monitoring the health of a system will be greatly amplified, rendering any prediction inaccurate. Since it is not possible to assess the effects of every butterfly and disturbances similar to the flapping of a butterfly’s wings in the world, it will always be important to accurately forecast the weather over a long period of time. impossible.
The third theory is “Mixing” and “Feedback” . “Mix” or “Shuffle” refers to the fact that two adjacent points in a complex system will eventually end up in very different locations after a certain amount of time. An example of this theory is two water molecules that are located close to each other, but then will “each in their own way”, wandering somewhere in different parts of the ocean, or even in different oceans. . A group of balloons that are released into the sky together will also end up in very different locations. Regarding “Feedback”, systems often become chaotic in the presence of feedback. An illustrative example of this behavior is the behavior of the stock market. When the value of a stock goes up or down, people tend to buy or sell that stock. This in turn contributes to the impact on the price of the stock, causing its value to continue to rise or fall further.
Mandelbrot Fractal.
One of the last things to talk about when discussing chaos theory is “Fractal” . A fractal is a geometric pattern with no end point. They are infinitely complex textures that when you zoom in or out by a certain ratio, the result is still the same original texture. They are created by repeating a simple process over and over in an ongoing feedback loop. With its core recursive, fractal is the picture of dynamic systems – the picture of chaos. Geometrically, they exist in our familiar dimensions. Fractional patterns are extremely familiar, because in nature there are many such patterns, including components of trees, rivers, coastlines, mountains, clouds, seashells, storms, etc. Many other subjects are related to chaos theory, but the ones mentioned above are the most interesting and important ones.