Chaotic versus random

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:

Random is as random does

2 thoughts on “Chaotic versus random

  1. 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.

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