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Nonlinear Dynamics, Psychology, and Life Sciences, 9, 505-538p. (2005)
The Bios Data Analyzer (BDA) is a set of computer programs (CD-ROM, in Sabelli et al., Bios. A Study of Creation, 2005) for new time series analyses that detects and measures creative phenomena, namely diversification, novelty, complexes, nonrandom complexity. We define a process as creative when its time series displays these properties. They are found in heartbeat interval series, the exemplar of bios .just as turbulence is the exemplar of chaos, in many other empirical series (galactic distributions, meteorological, economic and physiological series), in biotic series generated mathematically by the bipolar feedback, and in stochastic noise, but not in chaotic attractors. Differencing, consecutive recurrence and partial autocorrelation indicate nonrandom causation, thereby distinguishing chaos and bios from random and random walk. Embedding plots distinguish causal creative processes (e.g. bios) that include both simple and complex components of variation from stochastic processes (e.g. Brownian noise) that include only complex components, and from chaotic processes that decay from order to randomness as the number of dimensions is increased. Varying bin and dimensionality show that entropy measures symmetry and variety, and that complexity is associated with asymmetry. Trigonometric transformations measure coexisting opposites in time series and demonstrate bipolar, partial, and uncorrelated opposites in empirical processes and bios, supporting the hypothesis that bios is generated by bipolar feedback, a concept which is at variance with standard concepts of polar and complementary opposites.
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