: What is the butterfly effect?
In: Mathematics
There are certain mathematical systems where tiny changes in the initial state of the system result in big differences later on. One of the simplest examples is the “full logistic map”. Take a number between 0 and 1, let’s call it “x”, then calculate 4*x*(1-x), where “*” means multiplication. Then treat this number you get as your new x and plug it back into the equation. Do this over and over again and you’ll get a sequence of numbers. If you do this whole process all over again starting with a very slightly different initial number between 0 and 1, instead of getting roughly the same list of numbers like you might expect, your list will eventually diverge from the original list and you’ll start seeing completely different numbers.
The main reason why this is so important is because quite a lot of mathematical systems turn out to behave this way, including many that model real-world behaviour such as turbulence in fluids. The full logistic map itself is actually a special case of a simplified model of how a population of animals changes over time. And if small changes to the initial state of a system can result in big differences later on, that means it’s very difficult to predict what the system will do, since in practice we can only measure the current state of a system to a certain level of accuracy.
Edward Lorenz discovered chaos while using computers to try and develop models of the weather. He liked to use a metaphor to describe the phenomenon in which a butterfly flapping its wings in one part of the world could eventually cause a tornado somewhere else.
Also chaotic systems turn out to have all kinds of interesting and complicated mathematical properties (google “strange attractor” for some pretty pictures of weird stuff they do), so they have remained a major area of study.
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