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 International Conference on Complex Systems (ICCS2007)

The Biotic Pattern of Prime Numbers Supports the Bios Theory of Creative Evolution from Radiation to Complexity

Hector Sabelli
Chicago Center for Creative Development

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     Last modified: December 10, 2007

Mathematical experiments reveal biotic novelty and harmonic features in prime number series. All processes are physical actions (energy change in time), and may thus be expected to exhibit regularities homologous to radiation. The sine wave pattern of radiation embodies transformation among multiple bipolar opposites. Recursions of trigonometric functions generate bios (Kauffman, Sabelli, Cybernetics and Systems, 1998), a pattern characterized by causal novelty (measurable as reduction in recurrence by randomization). Bios is demonstrated in quantum, cosmological, meteorological, cardiac, population, and economic series (Sabelli et al, J. Mind Behavior, 1997; Sabelli, Bios, World Scientific, 2005; Sabelli, Kovacevic, Complexity, 2006). As radiation embodies harmonic opposites, recursions of harmonic functions generate biotic novelty, diversity and complexity, and bios is ubiquitous in nature, we conjecture that homologous processes of harmonic feedback causally generate complexity at all levels of organization. This supports a method: (1) analyze time series; (2) sine and cosine transforms as complementary opposites; (3) recurrence quantification. Biotic features of novelty, causation and episodic patterning are observed in the distribution of primes, the difference between consecutive primes, and other detrended transformations. Plots of the sine versus cosine transforms of the primes (as heartbeats and Schrodinger equation) show the circular symmetry of radiation. As number series abstract fundamental properties of action, and the primes epitomizes causal novelty, these results support the hypothesis that bipolar (synergic and conflictual) and mutually transforming (not mutually excluding) opposites is a major mechanism in physical and biological evolution (Sabelli, 2007. In Richardson, Cilliers. Explorations in Complexity Thinking. ISCE Publishing).

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