Strategies and Rubrics for Teaching Chaos and Complex Systems Theories as

Elaborating, Self-Organizing, and Fractionating Evolutionary Systems

Fichter, Lynn S., Pyle, E.J., and Whitmeyer, S.J., 2010, Journal of Geoscience Education (in press)

SOCSelf-

Organized Criticality

Self Organized CriticalityEvolution Via Self

Organization

Self Organized CriticalityEvolution Via Self

Organization

“Complex behavior in nature reflects the tendency of large systems with many components to evolve into a poised, "critical" state, way out of balance, where minor disturbances may lead to events, called avalanches, of all sizes. Most of the changes take place through catastrophic events rather than by following a smooth gradual path. The evolution to this very delicate state occurs without design from any outside agent. The state is established solely because of the dynamical interactions among individual elements of the system: the critical state is self-organized. Self-organized criticality is so far the only known general mechanism to generate complexity.”

Self-Organized CriticalityPer Bak

1948-2002

The sand pile builds . . . grain . . . by grain . . . by grain . . . by grain . . . by grain . . . by grain . . . by grain . . . by grain . . . Building toward the critical state . . .

Where it avalanches

building

avalanche

building

avalanche

building

avalanche

Avalanche Behavior

Avalanche- a large mass of snow, ice, etc., detached from a mountain slope and sliding or falling suddenly downward.Avalanche- anything like an avalanche in suddenness and overwhelming quantity: an avalanche of misfortunes; an avalanche of fan mail.

Now, imagine the sand supply follows a power law (or is fractal), with different numbers of grains falling at different times.

Power Law Sand Supply

Avalanches will follow a power law distribution.

http://atlas.gc.ca/maptexts/topic_texts/english/images/TemperatureCO2.jpg

Earth Temp. curve over the past 400,000 years

Examples of Extreme Avalanches

1929 stock market crash

1987 stock market crash

Cascading Power Grids Failures – when a hub is required to carry more than it is capable of carrying, and so crashes, leading to the next hub to crash, etc.North America blackout 1965 North America blackout 2003

Examples of Extreme Avalanches

Note that most genera have a life span of 10 million years or less, and that very few genera survive over 100 million years. This is a power law relationship.

0 50 100 150Life Span (millions of years)

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2000

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Distribution of Geologic Life Spansof Fossil Genera

Note that the number of large extinctions are very infrequent. The largest, the Permian, is the only one of its size. Smaller extinctions— <10 %—on the other hand, occurred in over 50 separate geological stages.

0 20 40 60 80 100Percent Extinction

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50 Extinction Intensity ForPhanerozoic Genera

In 106 Time Intervals (stages)

Devo

nian

K-T an

d Tria

ssic

Ordovic

ian

Permian

Are mass extinctions differentfrom background?

Life is a Self Organized Criticalphenomena

Examples of Extreme AvalanchesExtinctions

Stuart Kauffman“The critical point is not, as Stuart Kauffman once described it, “a nice place to be.” So “survival of the fittest” does not imply evolution to a state where everybody is well off. On the contrary, individual species are barely able to hang on - like the grains of sand in the critical sand pile.” Systems are always at the critical point, or if they are not at the critical point they are evolving toward the critical point.

That is, the common idea that systems evolve toward equilibrium is a misperception of reality.