In a famous episode in the "I Love Lucy" television series—"Job Switching," better known as the chocolate factory episode—Lucy and her best-friend coworker Ethel are tasked to wrap chocolates flowing by on a conveyor belt in front of them. Each time they get better at the task, the conveyor belt speeds up. Eventually they cannot keep up and the whole scene collapses into chaos.
The threshold between order and chaos seems thin. A small perturbation—such as a slight increase in the speed of Lucy's conveyor belt—can either do nothing or it can trigger an avalanche of disorder. The speed of events within an avalanche overwhelms us, sweeps away structures that preserve order, and robs our ability to function. Quite a number of disasters, natural or human-made, have an avalanche character—earthquakes, snow cascades, infrastructure collapse during a hurricane, or building collapse in a terror attack. Disaster-recovery planners would dearly love to predict the onset of these events so that people can safely flee and first responders can restore order with recovery resources standing in reserve.
I find this article fascinating. Thanks.
Linking Complexity Theory with uncertainty laws of chaotic events is quite a bit of food for thoughts.
The nature of uncertainty itself is a slippery concept. In computation processes, statistical complexity analysis measures the frequency of cases ranging from worst-case to best-case on actual data.
Even what the concept that this is intended to estimate actually means (probabilities of events) is not always so clear. This note that I translated recently from French (that I found on a bright young math wizard's site) explores why it is so in unpretentious, but interesting arguments.
Be that as it may, I enjoyed your article.
[[The following comment/response was submitted by Peter J. Denning on November 25, 2019.
We appreciate the kind words. Our main claim is that, regardless of how
you define probabilities, some random processes are too irregular to
allow confidence intervals to be calculated for predictions of the future.
Complexity theory, which studies these irregular processes, tells us these
processes obey power laws that have no mean or variance for powers
less than two. Complexity theory can help us explain what has happened
in those processes but cannot predict their futures.
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