Carlos Gershenson's blog... scattered ideas, random notes, and a bit of science...
Gottfried Mayer died last January 25th, after more than a year of fighting with cancer. I've taken his position as editor of Complexity Digest. I will try to keep up the standards that Gottfried set. We will miss him.
Education at all levels is facing several challenges in most countries [1-4], such as low quality, high costs, lack of educators, and unsatisfied student demand. Traditional approaches are becoming unable to deliver the required education. Several causes for this inefficiency can be identified. I argue that beyond specific causes, the lack of effective education is related to complexity [5, 6]. However, information technology is helping us overcome this complexity.
Complexity can be measured with information theory and can be seen as the balance between stability and variability [7-10]: phenomena without change or with constant change cannot exhibit complex behavior. It has been noted that to actively control a complex system, the controller has to be at least as complex as the controlled [11, 12]. For example, a successful healthcare provider has to match the complexity of the patients she attends. Treatment is highly specific for different patients, so a general practitioner must ha…
Many people assumed that if a system is deterministic, it should be predictable. Chaos and complexity each show different situations where this fails to hold.
In deterministic chaos, even when you know precisely the "laws" of a system, its extreme sensitivity to initial conditions (formally described with positive Lyapunov exponents) implies that sooner or later, very similar initial states will tend to very different states, since trajectories diverge exponentially. OK, some people may argue that if we had infinite precision, then we could predict precisely the future, so it is just a practical nuisance that in theory should work (I have no idea how, but anyway... people are stubborn (not me! I am just self-confident!)).
But you cannot get away with lack of predictability that is inherent of complexity. Within a complex system, yes even with deterministic rules, interactions between components generate novel information that determines the future of the system. This informa…