Bios: empirical studies

and mathematical theory of Creative Processes

H. Sabelli

Chicago Center for Creative Development

Louis Kauffman

University of Illinois at Chicago

Linnea Carlson-Sabelli,

Rush University

Valerie Busch-Zurlent, M.S.

Truman College, Chicago

Hector_Sabelli@rush.edu

Abstract: This article presents current advances in Bios research demonstrating that creative and causal patterns are widespread in mathematical, physical, biological and human processes, and to explore its theoretical implications regarding thermodynamics, complexity and human science.

The development of analytic methods to study nonlinear processes provided an opportunity to mathematically and empirically study psychobiological processes. We developed new time series analyses¹ to study heart beat intervals as a biological embodiment of emotional processes; heart rate also has medical significance in cardiology and neonatal pediatrics. These studies led us to identify a non-stationary fractal pattern which we labeled Bios^{2 3} that is causal and creative.

Subsequently we found Bios in the prime numbers⁴, the movement of electrons (Schrodinger’s equation),^{5 6} the pattern of dispersal of matter (galaxies, quasars) in three different surveys,^{5 6 7} the LIGO recordings presumably portraying gravitational waves,^{7 8} the Cosmic Background Radiation,^{3 7} planetary temperature,^{3 7} geographical forms (rivers, shores)³, DNA³, animal⁷ and human⁸ populations, respiration,³ cardiac patterns in healthy individuals and cardiac and psychiatric^{3 9} patients, economic processes economic (financial, employment) processes,^{3 10} and music ^{11 12}.

Bios is presumably chaotic insofar as it is erratic, causally-generated and when generated mathematically, highly sensitive to initial conditions (it is of course not possible to establish sensitivity to initial conditions in empirical data). Bios displays a wide power spectrum (“complexity”), changes in pattern with time (“temporal complexity”), increase in variance with duration of the time series and with increasing embeddings (“diversification”), and less recurrence than randomized copies of the data (“novelty”)¹³. Together, temporal complexity, diversification and novelty indicate creativity. These properties are not observed in chaotic attractors, but they are evident in random walks. Bios differs from random walks by the empirical demonstration of non-random causation.

Bios is generated mathematically by recursions of bipolar feedback (i.e. positive and negative feedback) such as the process equation¹⁴ and similar recursions involving groups (this paper), but not by unipolar feedback (e.g. logistic equation purportedly describing population dynamics in a Malthusian fashion).

These results contradict the widely accepted views that creative processes are either supernatural or random, and that complexity arises from selection in a Darwinian fashion. Instead, they indicate that evolution is a causal and creative process, and suggest that bipolar feedback (cooperation and conflict) is a generic mechanism for the creation of complexity, at variance with conflict models of opposition from Darwin and Marx and to contemporary sociobiological and economic models (e.g. Friedman).

The (empirically unsupported) Malthusian speculations embodied in the logistic model give credence to competition and aggression, while do not portray the actual pattern of animal or human populations.

A Mathematical Theory of Complexity

Based on these empirical studies that demonstrate the widespread occurrence of life-like patterns in physical processes, Bourbaki’s foundations of mathematics, and dialectic process philosophy, this article advances a theory of complexity: causal co-creation.

For many centuries mathematics has been recognized as a possible framework understanding the physical world. The well-accepted Bourbaki school has identified three basic structures of mathematics, lattice (sets organized by asymmetry and transitive relations among members), group (sets in which every member has an opposite), and topology (sets with space-like and plastic structure), which are irreducible to each other. These basic structures of mathematics are empirically found in mental processes that develop during early stages of development in children (Piaget). They are also evident in physical¹⁵ and biological¹⁶ processes and structures.

(I) Natural and human processes are creative, as demonstrated by diversification (increasing variance), novelty (less recurrence than randomized copies), temporal complexity (observable in recurrence and wavelet plots) and asymmetry. Bios, a pattern characterized by causality and creativity, is present in quantum, cosmological and climatic processes, in DNA sequences, physiological processes, population dynamics, economic processes, and musical and literary texts. (II) Bios is generated by recursions of bipolar feedback such as the trigonometric process equation and similar recursions using groups. The generation of Bios requires three generic causal factors identifiable with Bourbaki’s mother structures of mathematics, Piaget’s fundamental cognitive structures, and embodied in fundamental physical forces and biological, social and psychological processes: (1) physical unipolar action (flow of energy in asymmetric time); (2) bipolar opposition (e.g. electromagnetic force, sexuality, two values required to encode information); and (3) conservation and transformation of tripolar matter from simple to complex. (III) Bios-like patterns are generated by the addition of sine waves that also involve linear action, bipolar opposition, and conservation. But the simple addition of sine waves does not increase diversity in time. (IV) Simpler processes are global, originate earlier and contain large amounts of energy and matter, thus dominating overall (priority of the simple and global); complex processes are local, concentrate energy and information, and are thereby more powerful in limited and transient processes (supremacy of the complex).¹⁷

Asymmetry, symmetry and transformation are demonstrable at all levels, from physics to brain anatomy. Processes are sequences of actions (changes of energy in asymmetric time); the structures are transformed are material. Also the fundamental physical forces embody asymmetry in unipolar gravity, opposition in bipolar electromagnetic processes, and triadicity in the three colors of quarks engaged in the strong and weak nuclear forces. The human central nervous system embodies these three simplest fundamental forms: asymmetry in the dorsal-ventral dimension that corresponds to action, symmetry in the left-right axis, and levels of increasing complexity in the vertical axis, with priority of the simpler spinal cord and supremacy of the newer and complex brain structures. Process theory thus interprets Bourbaki’s mother structures as universal laws of natural and human processes (Sabelli, 1989) and as laws for dialectic logic. Everything that exists is an action, a flow of energy in asymmetric time, every action is paired with an opposite action, and the interaction of these two factors transforms simple structures into complex ones.

Biothermodynamics

The study of Bios is significant regarding thermodynamics. While it is claimed that entropy increases with disorder, and therefore the universe continuously decay, such view is at variance with the evolution of life. Schrödinger (1943) proposed that importing high-quality energy (low entropy) materials from outside their bodies may account for the success of biological organisms. Organisms feed on "negative entropy". Prigogine ( ) considered the same questions and came to a complementary solution of Schrödinger’s paradox: the excretion of high entropy materials. The entropy produced by biological organisms is exported to the external environment. For instance, organisms excrete entropy through the skin (heat), respiration (CO₂), urination (metabolites), and defecation (gastrointestinal secretions and unabsorbed food).

Contrary to many claims, ordered series (numbers in increasing order, sine waves) have greater entropy than random ones. It is simply wrong to say that entropy means disorder. Entropy increases with increasing complexity of pattern, from equilibrium to periodicity to chaos. In contrast, entropy is lower in the more complex biotic pattern. (It is thus also wrong to say that entropy means complexity.)

The reduced generation of entropy in creative biotic processes (such as the synthesis of low entropy biomolecules) is an additional mechanism for the lowering of entropy in living organisms, one that does not involve increasing entropy in the environment (Sabelli, 2005).

Human implications

After reviewing these principles, we shall explore how the concepts of causal creativity and bipolar feedback provide methods for integrated clinical care,¹⁸ psychotherapy,^{2 3 19}innovation²⁰ and progressive social action.^{8 21}