Bipolar feedback and biotic patterns in physical, biological and mathematical processes

1. The birth of Venus, the Spirit of Love, from the chaotic turbulence of water offers an interesting metaphor for the creation of complexity from simplicity. Boticelli’s choice of this pagan story contrasts with the traditional view of the Spirit as the Creator of matter.

2. The interaction of opposites generates Thom’s catastrophes. The fold represents the simplest co-creation. The sum of opposites is the energy of the process (Thom’s bifurcating parameter), and the difference between them (Thom’s asymmetric parameter), provides the information that determines the outcome.

3. Bipolar feedback and biotic patterns in physical, biological and mathematical processes Hector Sabelli and Lazar Kovacevic Chicago Center for Creative Development

4. A Study of Creation • Goal: modeling and analyzing creative processes • Purpose: to develop strategies for creative social and psychological behavior • Strategy: Study creative processes such as behavior and language, which never repeat. Heartbeat intervals (which are determined by emotions and behavior) are paradigmatic of bios, as turbulence is paradigmatic of chaos. • Hypothesis: Novelty, diversity and complexityare created by causal, generic processes that operate at multiple levels of organization.(Alternative: Causal processes are deterministic, not creative. Complexity is created by the selection of random events --Darwinian model).

5. BIPOLAR FEEDBACK: a feedback that is at times positive and at times negative --synergy and antagonism. Bipolar feedback is extremely common: Mathematical: recursion of trigonometric functions. Physiological: sympathetic versus parasympathetic innervation of heart, gastrointestinal tract, etc. Economic: supply and demand. BIOS: a creative form of chaos generated by bipolar feedback. Features of bios absent in chaotic attractors: Novelty, diversification, non-random complexity. Asymmetric statistical distribution. Global sensitivity to initial conditions. Irreversibility and contiguity.

6. Chaos: uniform bounded pattern; successive terms often cross the midline Bios: non-stationary non-uniform pattern; successive terms are contiguous

7. Pattern Uniform Complexes Aleatory Random Brownian Causal Chaos Bios BIOTIC PATTERNS IN NATURE: Heartbeats; respiration; air and sea temperature; galaxy distances; bases in DNA; many economic series; some literary texts.

8. Bios Chaos, process Random Chaos, logistic

9. BIOTIC FEEDBACK Hypothesis:Biotic feedback is a fundamental generator of complexity at multiple levels of organization. Hypothesis:Biotic feedback (both cooperation and conflict) is a major mechanism for biological evolution, economic development and social change –in contrast to Darwinian, economic and Marxian theories that focus on competition and struggle. The interaction of opposites (bipolar feedback) causally generates steady action (nonequilibrium), periods (harmony), chaos (conflict), and life-like (biotic) patterns.

10. Biotic feedback: action, bipolar feedback, and conservation Example: Diversifying equation

12. CONSERVATION IN THE GENERATION OF COMPLEXITY The generation of BIOS requires a conserve term, without which trigonometric functions generate only chaos and periodicity

13. As natural processes, BIOS is irreversible. CHAOS is reversible.

14. Biotic Hypothesis: Creative processes involve growth. Examples: expansion of intergalactic space, ecological spreading of species, growth of young organisms, extension of social systems (tribe, nation, federation, empire) and the expansion of chaos into bios.

15. EMPIRICAL ANALYSIS OF CAUSAL CREATION • Diversification (beyond diffusion) versus attraction • Episodic forms (complexes) versus stable uniform pattern • Novelty (greater change than random) versus recurrence • Non-random complexity (arrangement) defined empirically by observing creative processes versus algorithmic complexity (maximal for random, not applicable to empirical data). • Causation versus chance: Causal complex processes may be expected to contain the simpler processes that generate them. Time series are examined at low and high embedding dimensions.

16. BIOS DATA ANALYSIS* • Measures changes in statistical parameters • Quantifies isometry recurrences • Detects causation by partial autocorrelation and consecutive recurrence • Examines simple and complex components of variation by embedding the time series 1, 2, 3… N times. • *Sugerman et al, CD ROM in Sabelli, Bios, A Study of Creation. 2005 • A wide range of embeddings is necessary to demonstrate periodic order.

17. Bios but not chaos shows diversification Local diversification Local diversification: increase in S.D. with embedding Global diversification: increase in S.D. with N.

18. Diversification has practical significance Global diversification: S.D. grows with time RRI: heartbeat intervals Local diversification: S.D. grows with embedding (N) Less diversification in patients with Coronary Artery Disease.

19. PARTIAL AUTOCORRELATION: evidence for CAUSATION

20. CAUSATION DISTINGUISHES CARDIAC BIOS FROM 1/F NOISE CONSECUTIVE ISOMETRY PARTIAL AUTO-CORRELATION

21. RECURRENCE PLOTS: mathematical or natural biotic series show episodic patterns as clusters of isometries (complexes). Periodic and chaotic series show uniform patterns with numerous densely packed isometries. Complexes are the hallmark of complexity. time Complex

22. RRI Novelty: less isometry recurrence than shuffled copies Bios and noise are novel Shuffed Chaotic and periodic series are recurrent

23. Arrangement = % consecutive isometry / % total isometry Empirical observations suggest that arrangement measures non-random complexity. Arrangement is the product of causation (consecutive isometry) and novelty (1/isometry). (heartbeats)

24. Bios in empirical processes: less isometry than shuffled (novelty), more consecutive isometry than shuffled at low and high embeddings (simple and complex causation), significant arrangement (non-random complexity)

25. Periodic periodic recurrence, small arrangement DNA series Chaotic: recurrence, low dimension consecutive recurrence & arrangement Biotic: novelty, low and high dimension consecutive recurrence & arrangement Bios

26. Time-dependent Schroedinger equation Wavepacket representing an electron of average energy E(eV) confined to a region from x=0 to x=L(1E-10m). Time is stepped in units of dt(1E-16s).Time series are made on the peak of Gaussian pocket. E = 0 E = 5 E = 0 E = 0 E = 5

27. Time-dependent Schroedinger equation for a wavepacket representing an electron of average energy E(eV) confined to a region from x=0 to x=L(1E-10m). Time is stepped in units of dt(1E-16s). Program adapted from S. E. Koonin, Computational Physics, Addison-Wesley Publishing Company Inc, (1986) Energy = 0 Energy = 5

28. Cosmic Background Radiation: novelty without consecutive recurrence

29. The distribution of galaxies along the Z (time and space) axis shows partial autocorrelation, indicating non-random causation (bios) rather than random walk (Brownian). LCRS: Las Campanas Redshift survey 2dFGRS: 2-degree Field Galaxy Redshift Survey

30. Isometry analysis of the distribution of galaxies along the Z (time and space) axis. Non-random causation Novelty Complexity Recurrence plot: few recurrences clustered in separate complexes Shuffled copy: uniform distribution and more recurrence (novelty).

31. Isometry analysis of the distribution of galaxies along the X axis shows bios at some intermediate distances. Non-random causation Complexity Novelty

32. Creation Theory: Natural processes are creative - not conservative or decaying towards entropic disorder. Creative processes are largely causal –not aleatory. Mechanical movement, decay, and aleatory changes occur within the larger context of creative evolution.

33. WHAT ARE THE SIMPLE GENERATORS OF COMPLEXITY? 1. ASYMMETRY Pasteur’s discovery of biochemical asymmetry and his cosmic asymmetry hypothesis Unidirectional time in action (physical quanta, mathematical iteration, thought) Lattice order < as fundamental mathematical structure Empirical illustrations of asymmetry: thermodynamicirreversibility,weak force,optical rotation of atoms, non-equilibrium states in open processes, preponderance of matter over anti-matter, symmetry-breaking in cosmology, violation of gauge symmetry by superfluids, greater polarization of cosmic microwaves from one direction of space, ionic asymmetry across plasma membranes, brain asymmetry, social asymmetries. Biotic asymmetry: (1)statistical distribution of biotic series is asymmetric (2) Bios is generated at lower value of the parameter when the recursion is made asymmetric by adding a biasing factor q.

34. WHAT ARE THE SIMPLE GENERATORS OF COMPLEXITY? 2. OPPOSITION Sexual reproduction Greek Physiology, Chinese Taoism, German Dialectics Economic competition, Biological competition Generational, Sex, Class and National struggles Group theory (inverse = opposition) Sympathetic versus parasympathetic innervation of organs Psychodynamics and conditioning theory Quantum complementarity Thom’s catastrophe theory Logistic generator: A(t) versus 1-A(t) = unipolar opposition Biotic generators: bipolar feedback via trigonometric function

35. Heartbeat intervals (RRI) create extremely complex patterns because they are determined by ongoing behavior and emotions Decomposing a time series into opposites reveals that complex, apparently random processes contain relatively simple, highly ordered processes that presumably generate them (causation).

36. Complement plots

37. Bourbaki: Lattice (asymmetry), Group (inverse), Topology (continuity) are the mother structures of all mathematics Piaget: Same structures in mental development Creation theory: Same forms generate physical action, information and matter, and reoccur fractally generating higher levels of organization GENERIC GENERATORS

38. Fundamental mathematical structures Physical embodiment Biotic feedback recursions Bios Lattice asymmetry Action = energy * time Iteration Asymmetric distribution and irreversibility Group opposition and other symmetries Information; physical symmetries, biological symmetries, logical truth values Bipolar feedback Bipolar time series Topological continuity Spatial structures (matter) and higher dimensional organization Conservation term Contiguity

39. The generation of organic forms by the interaction of two process equations. X axis: Xt+1 = Xt + 0.1*Yt*sin(Yt). Y axis: Yt+1 = Yt + 0.01*Xt*cos(Xt) Note how each larger pattern contains and repeats at a larger scale the previous ones (fractality).

40. GENERATION OF SPATIAL COMPLEXITY BY BIOTIC PROCESSES: Tridimensional scatter plots of multiple computations of the process equation At+1 = At + g * (q + sin(At) (x-axis) at multiple values of gain g (y-axis) and asymmetry parameter q (z-axis). Each point represents the 2000th iteration. Gain g Gain g q Action A Information q

41. HYPOTHESES • Biotic feedback is a fundamental generator of complexity at multiple levels of organization: • Biotic patterns in physical, biological, and social processes • Coexistence of opposites (male/female, supply/demand, sympathetic/parasympathetic) in all processes • Biotic feedback is a necessary consequence of the universality of action (energy flow in asymmetric time), opposition (group symmetry) and conservation (topological continuity) • Biotic feedback (both cooperation and conflict) is a major mechanism for biological evolution, economic development and social change –in contrast to Darwinian, economic and Marxian theories that focus on competition and struggle.

42. Bios: a newly identified pattern that is widespread in nature. Biotic hypothesis: Expansion and diversification beyond diffusion (rather than convergence to an attractor) is essential for creation. Bios Data Analyzer:new measures of diversification, novelty and non-random complexity; these features are present in natural processes and in mathematical bios --not in chaotic attractors. Generic generators:Fundamental creative processes originate from fundamental mathematical structures (cause) rather than from maximally complex random change (chance). Biotic feedback: Action, Bipolar feedback, and Conservation generate steady action, periods, chaos, and biotic (life-like) processes with creative features, including irreversibility. SUMMARY