Chaos is defined as the science of surprises, of the nonlinear and the unpredictable. It teaches people to expect the unexpected.
While most of the traditional science deals with supposedly predictable phenomena, such as gravity, electricity, or some chemical reactions, the Chaos Theory deals with nonlinear things which are effectively impossible to predict or control, such as turbulence, weather, the stock market, our brain states, and a lot more.
These phenomena are usually described by fractal mathematics, which captures the infinite complexity of nature. A lot of natural objects exhibit fractal properties, which include landscapes, clouds, trees, organs, rivers and so on, and a lot of the systems in which we live exhibit complex, chaotic behavior.
Recognizing the chaotic, as well as the fractal nature of our world can actually give us new insight, power, and wisdom. For instance, with understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to the desired location. With the understanding that our ecosystems, as well as our social and economic systems, are connected with one another, we can hope to avoid actions that may actually end up being harmful to our long-term well-being.
The principles of the chaos.
1. The Butterfly Effect
This is an effect which grants the power to cause a hurricane in China to a butterfly flapping the wings in New Mexico. It is probably going to take a very long time, but the connection is actually a real one. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened.
Another more rigorous way of expressing this is that small changes in the initial conditions lead to some drastic changes in the final results. Our lives are simply an ongoing demonstration of this first principle. Who can know what those long-term effects of teaching millions of kids about chaos, as well as about fractals are going to be?
2. Unpredictability
As we can never know all the initial conditions of a complex system in sufficient detail, we cannot hope to predict the latest fate of a complex system. Even some slight errors in measuring the state of a system are going to be amplified dramatically, rendering any prediction useless. As it is impossible to measure the effects of all the butterflies in the world, the accurate long-range weather prediction is always going to remain impossible.
3. Order / Disorder
Chaos is not simply a disorder. Chaos also explores the transitions between order and chaos or disorder, which usually happens in surprising ways.
4. Mixing
Turbulence ensures that two adjacent points in one complex system are probably going to end up in very different positions after some time has elapsed. For example, two neighboring water molecules may end up in different parts of the ocean or even in different oceans. One group of helium balloons which launch together are probably going to land in drastically different places; mixing is actually thorough as turbulence happens at all scales. It is also nonlinear: fluids cannot be mixed.
5. Feedback
Systems can usually become chaotic when there is feedback present. One good instance is the behavior of the stock market. As the value of a stock rises or falls, people are often inclined to buy or sell that stock. This, in turn, will further affect the price of the stock, causing it to rise or fall chaotically.
6. Fractals
Fractals are never-ending patterns. They are infinitely complex patterns which are self-similar across different scales. They are created by repeating one simple process over and over again in an ongoing feedback loop.
Fractals, driven by recursion, are actually images of dynamic systems – the pictures of Chaos. Geometrically, they exist between our familiar dimensions. Fractal patterns are extremely familiar, as nature is full of fractals. For example trees, coastlines, rivers, clouds, mountains, hurricanes, seashells, and so on.
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