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What is chaos theory? What are its applications?

Chaos theory is a method that combines qualitative thinking and quantitative analysis. It is used to explore the necessary changes in dynamic systems (such as population movement, chemical reactions, meteorological changes, social behavior, etc.) Behavior that can be explained and predicted using holistic, continuous rather than single data relationships. Chaos theory is a method that combines qualitative thinking and quantitative analysis. It is used to explore behaviors in dynamic systems that cannot be explained and predicted by a single data relationship, but must use overall, continuous data relationships. "The original state of everything is a bunch of seemingly unrelated fragments, but after this chaotic state ends, these inorganic fragments will organically gather into a whole." The word chaos originally refers to the chaos before the universe was formed. The ancient Greek philosophers held the theory of chaos regarding the origin of the universe, arguing that the universe gradually formed the orderly world from the beginning of chaos. In the orderly universe, after long-term discussions, Western natural scientists have discovered many laws in nature one by one, such as the well-known gravity, the lever principle, the theory of relativity, etc. These natural laws can be described by a single mathematical formula, and the behavior of objects can be accurately predicted based on this formula. Over the past half century, scientists have discovered that even though many natural phenomena can be reduced to simple mathematical formulas, their behavior cannot be predicted. For example, meteorologist Edward Lorenz discovered that simple thermal convection phenomena can actually cause unimaginable meteorological changes, producing the so-called "butterfly effect." In the 1960s, American mathematician Stephen Smale discovered that the behavior of certain objects follows certain regularities. After the change, the subsequent development has no certain trajectory to follow and presents a chaotic state of disorder.