The Co-Creation Principle,
by H. Sabelli:
The interaction of opposites creates complexity. Systems are processes, i.e. transformations of energy (action). Oppositions between positive and negative actions encode information, and their synergic and antagonistic interplay creates tridimensional structure, and higher dimensional organization. This hypothesis is modeled by the process equation At+1 = At + k * t * sinAt, in which the bipolar (positive and negative) feedback generates a sequence of patterns: convergence, bifurcation cascade, periodicity, chaos, and bios. This principle formulates Heraclitus' interlocking concepts of diversifying unity, union of opposites, and creative becoming in terms of physical action, complementary information, and organization by creative feedback. These concepts guide the ongoing development of methods to study creative processes, and that made possible to recognize bios, a pattern that appears to be common in natural processes hereto suspected to be random or chaotic.
1. Action (energy): Physical action, the conjoint change of energy and time, is the universal constituent of reality at every level of organization. There is nothing simpler than action, because the Plank's quantum, the smallest unit of existence, has the dimensions of action (both energy and time), not of energy alone. Likewise macroscopic processes are made of actions; e.g. cardiac action is the product of the force, duration and frequency of contraction. Energy is conserved as a quantity, but it is continually transforming in quality. Everywhere there is movement, nowhere rest or equilibrium. The uni-verse literally is, as its etymology indicates, an unidirectional flow.
This hypothesis has rich corollaries: (1) Change and conservation: Action implies both change and transitivity. (2) Monism: One and the same stuff underlies the diversity of the universe. This is possible because the “stuff” that makes the universe is action rather than static substance. At the simplest physical level, all forms of energy convert into each other (first law of thermodynamics) and into matter (Einstein's law). Ideas exist only as embodied in energetic and material processes, and are therefore capable of modifying other physiological processes. (3) Spontaneity: Action determines itself; it requires no external cause. (4) Quantity: Action is made up of discrete units at every level of organization -e.g. Planck quanta, action potentials, atoms. Action is a quantity. (5) Pasteur's universal asymmetry: Beginning with time, natural processes are asymmetric, in one dimension –action–, in two dimensions –information–, in three dimensions -structure–, and in multiple dimensions of organization, statistical distribution and systems? hierarchy. Thus systems are lattices (sets ordered by asymmetric and transitive relations), one of the mother structures of mathematics (Bourbaki, Piaget, MacLane?).
2. Opposition (information): Opposition is a universal pattern of action, that carries information, and is embodied in complementary structures.
Opposition is universal, in space, in time, and in quality. There are opposites in every respect: action and reaction, positive protons and negative electrons, electromagnetic polarities, complementary DNA strands, anabolism and catabolism, feminine and masculine, cooperation and competition, certainty and uncertainty. As processes differentiate (bifurcate), the number and diversity of opposites multiply. Sharing a common origin, opposites are fundamentally similar; diverging from each other, they are fundamentally different and, in some respect, antagonistic.
Opposites are distinct but united. Every physical entity is both a particle and a wave (Bohr's quantum complementarity). Every person is both feminine and masculine, albeit to different degrees. Evolution and decay coexist in cosmology and history (enantiodromia), contrary to one-sided views of progress and of entropic decay. Opposites are complementary, not mutually exclusive. Opposites are separated in space, time or quality (local formulation of the logical principle of no-contradiction), but coexist as components of every process (global principle of dialectic contradiction).
Opposites can be synergic (e.g. opposition of the thumb and the other fingers, opposite sides of a square), antagonistic, or both (nonlinear opposites, e.g. complementarity). Linear antagonists are inversely related: as one waxes, the other wanes. Naturally occurring opposites can both grow or diminish at the same time, albeit rarely if ever independently.
Harmony and conflict always coexist. There is harmony in the tension of opposites, as in the bow and the lyre (Heraclitus). Even homeostatic systems contain mutually antagonistic components; conflict is not the sole motor of change, and it often destroys more than it creates – at variance with Darwin, Marx, and Freud.
Opposites are co-dominant, each prevailing in a different way, and/or at different time or place. Parents control their young children, but eventually power shifts to the younger generation. Male supremacy is widespread, but in modern society women outlive men, and everywhere mothers are the first universe, the first love, and the first identification figure (female priority). Even in authoritarian regimes, government depends on the governed. There never is absolute primacy. Each hierarchy generates its dual (a theorem of lattice theory). This principle applies not only to relations between classes at a given level of organization, but also to the relation between different levels of organization, illustrating Y.P. Rhee?s complementarity of vertical and horizontal dimensions of systems. In the vertical dimension, the priority of the simple leads to the supremacy of the complex. The priority of the objective is followed by the supremacy of the subjective. These concepts enter into Fran�ois? notion of priority of the simple and supremacy of the complex in the upbuilding of systems regulations and controls, and also relate to Salthe?s notion that in order to capture the complexity of a system, minimally three scalar levels must be explicitly represented in the model.
Every entity contain its opposite in a diminished form: opposite qualities result from quantitative difference, not from different composition. Yet opposites are not polar extremes of a linear continuum, because they are in part similar and in part different, in part synergic and in part antagonistic, at times dominant and at times dominated. They must be conceived as located in any relation within a two dimensional plane. Synergic opposites may be almost parallel, antagonism may approach linear polarity. Paradigmatic opposites are fully complementary, exactly orthogonal to each other (a relation usually interpreted as statistical independence). The simplest model for complementary opposition is the complementarity of the sine and cosine functions. Validating the model, fundamental processes, such as light waves, a carrier of energy and information, are constituted by orthogonal, bipolar and continuous electrical and magnetic fields.
Information is the news of a difference (Bateson). Asymmetric opposition, the difference between two values, is the unit of information. Communication is an interaction. Action carries information. Information is an action, not a separate substance. The quantum is the smallest unit of information. Uncertainty applies to subquantic fluctuations. According to quantum mechanics, the apparently empty space consists of small fluctuations of energy, so fast that space appears symmetric and uniform, formless and informationless. Void and action , as other opposites, differ in quantity, not in substance. Macroscopic processes include quantum uncertainty; quantum flux contains action quanta. Certainty and uncertainty are not mutually exclusive, but coexisting opposites, as highlighted by the principles presented by G. Klir. There also is a third complementary: misinformation -error, myth, deception.
Although opposites can be asymmetric (e.g. massive protons and small electrons make up atoms), opposition is a fundamental symmetry of nature, and a heuristic principle in physics. Physical entities are postulated, and subsequently discovered, by reasons of symmetry. Fundamental physical processes can be described as a group (a set in which every member has an opposite, its inverse), the second mother structure of mathematics. Just as inverses are necessary but not exclusive members of a group, natural opposites are embedded into larger systems of complementarity. Triads are common (e.g. tridimensional space, three primary colors), and fundamental (period 3 implies an infinite sequence of periodicities and infinitations –Sarkovskii's theorem).
3. Non-uniform, relatively stable structure (matter) is a universal component of systems. Tridimensional interactions generate non-uniform stabilities, i.e. structure, rather than formless, uniform, disordered equilibrium. Matter is the tridimensional structuration of mass. Mass exists everywhere, condensed as in matter or sparse as in the energy that fills the void. Matter is energy concentrated in a tridimensional structure, i.e. a relatively stable tridimensional asymmetry. Energy and matter are interconvertible E = m * c2. As the speed of light c represents a maximum in energetic interactions, and communication involves two simultaneous actions, c2 represents the maximum rate of communication. Interpreting c2 as information in Einstein?s law, energy E equals matter M times information I. In cosmological evolution, there is a net conversion from energy into matter and information I, so the symmetric relation ?=? in Einstein?s law represents two opposite but unequal actions:
E M I Although components may play only one function in the system, action, information and structure are three inseparable aspects of each entity: energy is particulate; waves are associated with matter; information can only be carried by an energetic or material messenger; structure conserves, and action carries, information. A nerve impulse is an electrical current, a signal, and a displacement of ions. Behavioral actions are inseparable from subjective emotions and ideas, and from macroscopic brain structures and molecular neurohormone structures. These are practical, rather than speculative, notions: we decrease marital conflict with blockers of acetylcholine (a molecular trigger for rage), and one can treat depression with medications or by replacing PEA (the mediator of psychological energy). Causation includes energetic, informational, and material factors, an Aristotelian concept newly developed by I. Balsamo.
Creative organization: Material structure represents only a particular case of the formation of complex forms from simpler ones, and even at the physical level it coexists with higher dimensional organization. A distinction between tridimensional material structure (e.g. a building), and higher dimensional organization (e.g. the institution housed in the building) is cogent. Material particulate structure is universal, and more stable. Interrupting the flow of energy causes death, i.e. terminates living organization, but leaves temporarily unchanged the physical body; in contrast, organization such as Prigogine?s dissipative structures, ceases when the throughput of energy is interrupted. Using a different terminology, P. Bunnell points to an important coincidence of opposites: when a structure is organized, it becomes an organizer.
Einstein's law and cosmological evolution establish that in fact action creates matter; biological evolution and human history indicate that evolution creates life and mind. Systems are in continual and continuous transformation, as described by topology, the third mother structure of mathematics. A system is a lattice of actions (energy change in time), a group of relations (i.e. of repetitive interactions generating mutual and bipolar feedback, i.e. information), and a continuous topological transformation of tridimensional matter. This hypothesis exemplifies the notion of natural systems as embodiments of mathematical form, that runs from Pythagoras to Kauffman's principle.
Creation involves the formation and transformation of patterns of limited duration (e.g. life), diversification, symmetry-breaking, novelty, and complexification, features that can be measured in empirical data using process methods, and that do not obtain in deterministic processes.
Bios, the pattern of creative processes: Bios is a newly found type of organization composed of transient and novel patterns. Most of these patterns are aperiodic, and of greater amplitude, morphological diversity, and sensitivity to initial conditions than chaos. Bios also includes transient periodicities and linear transitions, features that, together with sensitivity to initial conditions, differentiate deterministic bios from 1/f patterns generated by statistical processes. Bios shows novelty (less recurrence than its randomized copy), diversification (increase variance with increased duration), non-random complexity, and 1/f power spectrum (implying change and conservation). Diversity, novelty, complexity, and episodic patterning are found in natural processes, but are absent in chaos.
Biotic patterns are found in empirical time series portraying meteorological, biological, and economic processes. This widespread occurrence of biotic patterns suggests that bios may be the canonical form of natural processes. It is thus cogent that bios can be generated by mathematical models of bipolar feedback.
Co-creation (self-organization): The interaction of different processes spontaneously creates organization. Interactions co-create form, ranging from transient patterns to stable particles, and higher dimensional organization. The balance between opposites creates stability of structure. In this manner, opposites co-create systems. Systems are organized by relations, as T. Mandel describes. Every system is autodynamic because it contains opposites, and it relates to opposite processes in the environment. Only through these interactions systems ?self?-organize. There are many forms of co-creation, as illustrated by two sexes procreating a new individual, oppositely charged particles combining to form atoms, and subsystems engaging in mutual feedback.
In the interaction between processes, the sum of opposite is the energy of the system. Conversely, increasing the energy of a system increases both opposites; e.g. high energy binds and split atoms, energetic persons make stronger bonds and trigger stormier conflicts. The energy of the system determines the occurrence of bifurcations, and thereby the pattern of the process (equilibrium, periodicity, chaos, bios). The difference between opposites is the information that determines the direction of change. This is suggested by empirical experiments and catastrophe models. Creation is fostered by a moderate intensity and a near symmetry of opposites. This is suggested by experiments with models for creative feedback.
Creative feedback: A fundamental form of co-creation is feedback. Systems continually interact with their environment, and thereby receive ceaseless feedback. The inputs received by a system are at least in part reactions to its previous action; in turn, each input contributes to determine the following action. As such interaction is repetitive, it provides feedback, and more specifically, mutual feedback. Through its repetitive interactions with others, each subsystem becomes both self-referential and co-creative. Positive feedback generates growth. Negative feedback maintains stability. Resistance to growth (logistic equation) generates periodicities and chaos, homologous to eddies and turbulence. Bipolar feedback (process equation) also generates bios.
In natural systems, feedback usually is bipolar, i.e. positive and negative. Natural environments are enormously diverse, so the output of any system is synergic to some processes in the environment, and opposed to others, and in turn systems continually receive synergic and antagonistic inputs. Bipolar feedback is creative. This is illustrated by the process equation At+1 = At + k * t * sinAt, in which At models action, that is additive and changes in time, the trigonometric function, ranging from 1 to -1, models bipolar feedback, and the feedback gain increases with time as determined by the constant k. As the intensity of the feedback increases, this recursion generates convergence to a steady state, bifurcation, periodicity, chaos and bios. This represents a progression in complexity. Steady state, periodic and chaotic patterns remain uniform in time. Bios is constituted by sequences of episodic patterns that expand in amplitude and diversity with time, rather than converging to a stable state; they also are more variable than their randomized copies, demonstrating novelty. Diversity, novelty, complexity, and episodic patterning are hallmarks of creativity.
As noted, the biotic pattern is similar to those observed in time series of natural processes known to continually generate novelty, such as heartbeat intervals or language. Organic forms can be generated by models of bipolar and mutual feedback, such as At+1 = At + g * Bt * sin(Bt) and Bt+1 = Bt + k * At * cos(At), or At+1 = At + g * sin At + k * cos(Bt), and Bt+1 = Bt + j * sin(Bt) + h cos(At), where g, h, j, and k are constants. In a system, feedback necessarily is reciprocal.
Creative development: These observations support the hypothesis that the interaction between synergic and antagonistic complementary opposites in natural processes may be a major factor for creative evolution. As action and bipolar feedback are universal, the sequence of patterns generated by the process equation may portray a fundamental pattern of development at all levels of organization: from one origin through bifurcation into pairs of opposites, multiple oppositions (2n periods), chaos, and triads (period 3, that implies all others) to bios. Cosmological and embryological development include these transformations, along with many more concrete features. A development that is both determined and creative offers an alternative to the emergence of complexity by chance, or by supernatural intervention, in a universe that is determined, and/or bound to entropic decay. If creation is the spontaneous result of interaction, the universe is a process that, far from tending towards entropic disorder, generates an infinitely complex attractor:
Creation implies the diversification of systems, a fundamental fact highlighted by H. Bhola, at variance with equilibrium models of health and economics, and with homeostatic models of family and social systems. Co-creation provides guidelines for social and personal growth, and indicates the inadequacy of purely conflictual models of biological and social evolution. Co-creation also represents a systemic manner of thinking, which this article, with its cross-disciplinary perspective and its multiple authorship, exemplifies.
