Chaos is the science of surprises - it is learning to expect the unexpected. While most traditional
science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions,
Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather,
the stock market, our brain states, and so on. These phenomena are often described by fractal mathematics,
which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds,
trees, organs, rivers etc, and many of the systems in which we live exhibit complex, chaotic behavior. Recognizing
the chaotic, fractal nature of our world can give us new insight, power, and wisdom.
For example, by understanding the chaotic dynamics of the atmosphere, a balloon pilot can "steer" a balloon
to a desired location. By understanding that our ecosystems are unpredictably interconnected, we can hope to
avoid actions which may end up being detrimental to our long-term well-being.
- The Butterfly Effect:
This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. It may take a very long
time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened.
A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results.
Our lives are an ongoing demonstration of this principle. Who knows what the long-term effects of teaching millions of kids about
chaos and fractals will be?
Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot
hope to predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be
amplified dramatically, rendering any prediction useless. Since it is impossible to measure the
effects of all the butterflies (etc) in the World, accurate long-range weather prediction will always remain impossible.
Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed.
Examples: Two neighboring water molecules may end up in different parts of the ocean or even in different oceans.
A group of helium balloons that launch together will eventually land in drastically different places.
Mixing is thorough because turbulence occurs at all scales. It is also nonlinear: fluids cannot be unmixed.
Systems often become chaotic when there is feedback present. A good example is the behavior of the stock market.
As the value of a stock rises or falls, people are inclined to buy or sell that stock.
This in turn further affects the price of the stock, causing it to rise or fall chaotically.
Fractals are infinitely complex patterns that are that are self-similar across different scales.
They are created by repeating a simple process over and over in an ongoing feedback loop.
Fractals can be thought of as the images of chaos. Geometrically, they exist in between our familiar dimensions.
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain,
they do not refer to reality."