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The power of water, and reflections on critical thinking


A plot of the Q-function, the tail probability...
Image via Wikipedia

A testimony to the power of water, in recent Australian floods.

www.youtube.com/swf/l.swf?video_id=kYUpkPTcqPY

Water level in rivers follows the Log-Pearson 3 probability distribution(see attached picture)

Tightly clustered around the mean, with little variation, and a limit on how far the left hand tail can go (ie “dry”)

The right hand tail though is much fatter than the standard normal distribution. Even though it remains a very low probability event, the consequences keep going; they don’t trail off to insignificance like in the standard normal

In forecasting and then living the future, we see something like the Log-Pearson 3 distribution in practice. We get accustomed to extrapolating from previous “normalish” experience which works so often that it becomes a reasonable technique and standard practice. Our monkey brain is poorly adapted for remembering the lessons of fat tails and properly estimating their effect on our plans

When the underlying process though is NOT a generator of standard normal, but rather has elements of chaos and uncertainty in it, we can get to experience the surprise of consequences which conform to power laws: unpredictable as to frequency of occurrence or seasonality, and unpredictable in terms of magnitude of consequence.

Our monkey brain will tend to discount the early indications of potential disaster as a combination of a number of well-known biases and fallacies. Remember that cognitive biases get turned into fallacies when you start experiencing the consequences. Ask the guy holding the camera in the video clip.

We often can’t know the degree of chaos in the underlying process until we discover results that suddenly and stubbornly refuse to conform to standard normal expectations.

In digiworld you get do overs.

In realworld, you get the opportunity to learn from other peoples’ catastrophes; you don’t get to learn from your own catastrophes.

This is the basis for Nassim Taleb‘s (“Black Swan”) discussion of 4th Quadrant problems: when our statistically based insights can actually expose us to far more risk than standard models can/will describe.

http://www.edge.org/3rd_culture/taleb08/taleb08_index.html

Taleb’s advice on living in the 4th Quadrant: What Is Wise To Do (Or Not Do) In The Fourth Quadrant

1) Avoid Optimization, Learn to Love Redundancy

2) Avoid prediction of remote payoffs—though not necessarily ordinary ones

3) Beware the “atypicality” of remote events.

4) Time. It takes much, much longer for a times series in the Fourth Quadrant to reveal its property.

5) Beware Moral Hazard.

6) Metrics. Conventional metrics based on type 1 randomness don’t work in the Fourth Quadrant.

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  1. February 5, 2011 at 2:28 pm

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