ABSTRACT

THE ONSET OF COMPLEXITY AND SCALE INVARIANCE
IN HUMAN LANDSCAPES


John McKim Malville
Department of Astrophysical, Planetary, and Atmospheric Sciences
University of Colorado at Boulder
Armik Mirzayan
Department of Physics
University of Colorado at Boulder

( ) Complex systems lie between perfect order and total randomness. In information theory the algorithmic information content (AIC) of a system refers to the size of a computer program necessary to represent its inherent information. The AIC ranges from zero for a state of perfect order to a high value in a random system. Pilgrimages have intermediate AIC, neither too orderly nor too random. Their high "effective complexity" may develop quickly through the formation of a new schema or slowly from the accumulation of individualistic events and "frozen accidents". Pilgrimage may involve multiple time scales as a build-up of stress and metastability is released through ecstatic vision in the initiation of a tradition and in the movement of people in established systems. Amplification of small fluctuations by non-linear processes and positive feedback speed the rate of transformation of both individuals and populations.

( ) Examples of other complex systems that exhibit slow and rapid time scales are the slow build-up to criticality of sand piles followed by sudden avalanches; the gradual twisting of magnetic fields in the sun and sudden energy release in flares; and the slow build-up of stress along fault lines and rapid release in earthquakes. In each of these cases and in many pilgrimage systems a critical level of complexity is reached such that the system develops scale invariance, system-wide cooperative behavior, tim e invariance, and fractal-like characteristics. Transformations of human landscapes such as Harappa in the Indus valley, the Chaco regional system of the American southwest, and scientific paradigms, such as the great revolutions of relativity and quantum mechanics, involved similar degrees of metastability and multiplicity of time scales.





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