What is Chaos? And how we found out about it...

As he looked at numbers e noticed that the oscillations of his model did not repeat.

In fact he entered the numbers again, and again, and again but his model would refuse to behave the same way twice.

During our long education we were taught that given the initial state of a system (the present parameters that define the state of the system) plus the equations that fully describe the system, you will be able to plot the future behavior of the system forever.

And we have plenty of evidence that this approach works. For one, we are able to predict when Comet Halley will next visit our corner of the galaxy. And many astronomers were able to predict that last visit thousands of years ago!

So, why was his model stubbornly behaving differently every time he punched the numbers in? After all he knew the system perfectly - he had designed it!

The best way he had to describe this "unpredictable" behavior was with the word "chaotic", a never ending sequence of never repeating patters. Nothing was the same even if the initial state was the same and he was the one defining the equations for this toy-weather model. I mean he had defined ALL the equations...

It took a few days, but he figured it out. He had entered the parameters with a precision of 1/1000, but during processing the computer executing the model would use numbers with a precision of 1/1000000. On initial consideration this did not seem a relevant difference, after all a difference of 1/1000 was equivalent to having a butterfly flap its wings in China and having that create a storm in North America.

Systems that would never repeat in behavior even if they ran for ever

Later, this and other experiments would be repeated all over the world, in many different domains but the results would be similar. All over the world scientists were discovering other systems that were "sensitive dependence to initial condition" (aka suffered from the Butterfly effect), the scientific definition for "chaos" which later became the popular term to describe systems that would never repeat in behavior even if they ran for ever. These systems exhibited infinite variety of behavior when certain conditions were met. What were those conditions? That we will explore in a later post

Photo credit: John Hammink, follow him on twitter