From John D. Barrow’s chapter in Design and Disorder:

The standard folklore about chaotic systems is that they are unpredictable. They lead to out-of-control dinosaur parks and out-of-work meteorologists. …

Classical … chaotic systems are not in any sense intrinsically random or unpredictable. They merely possess

extreme sensitivity to ignorance. Any initial uncertainty in our knowledge of a chaotic system’s state is rapidly amplified in time.… although they become unpredictable when you try to determine the future from a particular uncertain starting value, there may be a particular stable statistical spread of outcomes after a long time, regardless of how you started out.

Emphasis added.

**Related post**:

This property seems to be heuristic. Suppose that I am at the initial state of a chaotic system, and I am partially ignorant about this state in the following way: I know the position of the system to relative error 10% at 1000 steps in the future, but I don’t know the exact value of the current state of the system.

In this case, my initial ignorance of the system state becomes *diminished* as time increases.

I searched the blog for ‘prigogine’ and the search came up empty.

I read his ‘popular’ book “Order out of Chaos” first and later discovered his Nobel address speech, but you can do it the other way round:

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1977/prigogine-lecture.html

I think that the algorithmic randomness provides the easiest way to understand the difference between the chaos and randomness:

http://www.scholarpedia.org/article/Algorithmic_randomness