Sabelli, H. , Kauffman, L. Patel, M.,  Sugerman, A.,. Carlson-Sabelli, L. , Afton, D. and J. Konecki. How is the universe, that it creates a human heart?  Part I. Primary Processes.  Systems thinking, globalization of knowledge, and communitarian ethics. edited by Y.P. Rhee and K.D. Bailey  Proc. International Systems Society, Seoul, Korea, 1997, pp 912-923.

 

                               How is the universe, that it creates a human heart?

                                                       I. Primary Processes

 

                                    H. Sabelli, L. Kauffman, M. Patel, A. Sugerman,

                                          L. Carlson-Sabelli, D. Afton, J. Konecki.

                                        Chicago Center for Creative Development,

                                Rush University, and University of Illinois at Chicago.

                              2400 Lake View Avenue, Chicago, Illinois 60614, U.S.A.

 

                                                                 Abstract

This is a bird's eye view of natural processes grounded in contemporary biological science. From Pythagoras' formulation of the first numerical law of science to Pasteur's discovery of cosmic asymmetry in biomolecules, living processes reveal the fundamental laws of nature, and their mathematical form. Returning to the original concept of physiology as the science of nature as a living process, we seek fundamental theory in primary processes, rather than elementary physical components. Empirical evidence suggest four patterns as universally present, from physical strings to psychological processes: 0. Bipolar energetic flux (such as quantum flux, biological variability, and heat): flux is random, bipolar, always above absolute zero, and contains and is contained in organized action. 1. Asymmetric action (action = energy x time, such as Planck's quanta): the unidirectionality of time is Pasteur's cosmic asymmetry, Einstein's fundamental order, and thermodynamic irreversibility. 2. Complementary opposites (such as physical symmetries, quantum complementarity, anabolism and catabolism, feminine and masculine, synergy and conflict): opposition encodes information. 3. Creative trifurcations: opposites co-create tridimensional structures such as matter itself, and higher dimensional organization. Triads of colored of quarks generate a diversity of subatomic particles, and three primary colors generate boundless hues. Mathematically, period three implies all other cycles [Sarkovskii's theorem) and chaos. Physically, chaotic processes generate dissipative structures [Prigogine].

Fractal homology: These four primary patterns repeat at every level of organization and in every respect, thereby creating fractal self-similarity. Their combination co-creates novelty, diversity and complexity. Semantic creativity: Alphabetical levels of organization consisting of a small number of classes of exchangeable modules (atoms, nucleotides, letters) create unlimited variety at higher levels (molecules, genes, language). Biological creation: The empirical measurement of novelty differentiates static order from creative organization, suggesting that they represent opposite departures from randomness. Conscious creativity: Validating human reasoning, mathematical calculations describe physical processes with wondrous exactness. The basic cosmic forms, (1) asymmetry, (2) opposition, and (3) trifurcation are abstracted by the three pillars of mathematics (lattices, groups and topology). Abstracting process and opposition, a simple equation [Kauffman and Sabelli, This volume] generates dynamic features specific to each of the primary processes described above. Continuing creation: Evolution cannot conceivably culminate with the human species. The creation of life and consciousness by physical processes suggests that processes spontaneously evolve toward an Attractor of infinite complexity, rather than toward disorder. We are active participants in this continuing co-creation.

 

Key words: asymmetry, action, biotic, co-creation, complementarity, information, opposition. How is the universe, that it creates a human heart?  Dramatic differences in cardiac rhythm are associated with emotional changes (figure 1). Thus "heart" names an organ essential to life, but also means soul, and symbolizes love. Physical and psychological processes together temper the heart, because both are physical actions. Calculating can produce greater oxygen deficit in cardiac muscle than exercise. Competitiveness, anger and rushing can be as important as lipid metabolism in the causation of cardiac illness; they depend on psychological make up, but are largely caused by personal interactions and social circumstances. Actions are interactions. Internal and external processes are not mutually exclusive categories, or polarities of a continuum, but the components of the interactions that occur at every moment and place, inseparable and complementary opposites. The rhythms of the heart belong to the rhythms of the universe, just as the heart itself is made of physical matter. Examining the heart we can learn about the world it inhabits. Nicholas of Cusa pointed out that, as we can learn more about man by examining his head rather than his hand, we can learn more about nature by studying man rather than rocks. Fundamental processes manifest in life, not only in subatomic particles.

 

Figure 1. Patterns of cardiac timing associated with various emotions. Recurrence plots from one 56 y/o male patient with coronary artery disease, associated with diary entries indicating anxiety (A), angina (B), sex (C) and sleep (D). A distinct pattern (B) accompanied chest pain associated with an emotional reaction to a movie, although it was not accompanied by a change in the ST segment. Note its similarity with a pattern observed when the subject reported anxiety (A), and the difference with (C) and (D). Each plot includes 480 data points, and was constructed with 50 embeddings, and a 1% radius. See Carlson-Sabelli et al [This Volume] for description of the method.

 

 

 

 

 

 

 

 

Figure 2. "Reflections", painted by numbers as discussed in Part II.

 

How is a tree, that man paints it?  Figure 2 may help us to understand how a tree is born, and the man who paints it. We see an oriental painting of trees; we see not only the object depicted, but also the style of its painter, the way in which a culture translates it. Alas, some persons see smoke, not trees, in the figure! Information is always a translation from the message emitted to the message received. Reality is one, but perception is multiple. There are at least two translations for every message.

 

Color would help us to know whether the painting represents trees or smoke, but figure 2 is in black and white. Black and white are sufficient to write words and to portray form. Two opposites are necessary, and sufficient, to code information: 0 and 1 encode any number, sound or image in a computer or a digital record. 

 

Figure 3. Color structure: The physical continuum of frequencies is divided by the retinal receptors into three primary colors, three secondary colors that are their inverses (e.g. blue + yellow = green = complementary of red), black, and its inverse white. Colors have the properties of a group (inverses) and of a lattice, two fundamental mathematical structures (presumably, psychological archetypes and cosmic forms).

 

What is color, that flowers offer it to birds and bees?  Light is our perception of electromagnetic waves. The eye creates color, three colors, to be exact, which in their multiple combinations generate the infinite gradations of the color wheel, and even beyond, the browns of earth, wood, and flesh. Color is the art of life. The physical world has no color. Dawn it did not know it was beautiful. Color is an invention of flowers and bees, and of human hands painting faces in canvas, and women's faces with cosmetics. Married to unreasonable reason, and dismissing appearance as a fickle lover, some philosophers have disregarded color as an illusion of the senses. Actually color is a call from plants to have their flowers visited. The trifurcation of light into color in the retina marks a transition from a physical to a biological process, thereby revealing the cosmic form of creation. Color-like categories are observed at every level of organization (homology). Classes and combinations of quarks can be described by analogy to the three primary colors (quantum chromodynamics). Likewise social, psychological and logical categories occur in triads, and colors are often used to portray moods in words as well as in canvas. Color vision arises from the three-way split of light frequencies by the retinal pigments. The combination of these three primary colors generates an almost unlimited range of hues. The brain's initial step is the combination of three primary colors to create complementary opposites, generating a structure that has properties of mathematical lattices and groups (figure 3), two of the three fundamental pillars of mathematics. As lattices, colors are organized by a uni-directional order. As group elements, each color has a complementary opposite. Each color is itself generated by two opposite processes, the emission of light by an energy source, and the selective absorption by a material pigment. We meet over and over oneness and asymmetry, twoness and opposition, threeness and structure.

 

What is man, who knows number?, asked physiologist Warren McCulloch. How is it possible that mathematics, a product of human thought, so admirably describes reality?, asked Einstein. We can calculate with surprising accuracy interplanetary travel, and we can demonstrate with certainty properties about numbers, suggesting that these products of our minds also exist objectively. Number is a paradigmatic example of the fit between physical reality and psychological processes. This is to us a mathematical proof of the competence of human perception and reasoning. The remarkable coincidence between the mathematics we imagine and the mathematics of the real world, indicates the commonality of form between reality and mind. When we are at our most subjective, "freely inventing" mathematics, we reach our most certain and objective knowledge of the world. It should not be surprising, as the human brain is the best organ (insofar as we know) developed by the evolutionary processes of adaptation and selection. Thus brain processes should be expected to provide us with a reasonably appropriate, albeit certainly not perfect, picture of the real world. In this light, our preconceived notions, such as number, space, and time, must have profoundly rational bases. As physical organisms, humans generate concepts shaped by physical reality. Attending to the subjective can reveal the forms of nature, because physical and psychological processes are homologous: thoughts are made of energy, brain is made of matter. The adequacy of thinking is further improved by adaptative evolution through the creation of complex structures and patterns. Yet complexity also breeds error. Intuition and neurological organization combine to generate appropriate portraits of reality, but imagination can further generate consistent structures that can be partially divorced from reality. A naturalist epistemology thus recognizes and highlights the supremacy of multiple perceptions, but insists on the priority and the finality of one physical reality. Science is not objective as a process, but in its goal. One should not take the objectivity of science for granted, but we can expect to approach objectivity through observation, reasoning, and critical re-evaluation of every assumption. Doubting the ability of perceptions and reason appears modest, but actually is a grandiose disrespect for the wisdom of nature that created eye and brain. As numbers, nature is complex, real and imaginary, where "imaginary" is real, only in a different dimension. Mathematics is the consciousness of natural forms. 

 

                                Physiology and the first numerical law of science

Pythagoras inaugurated natural science (physiology) with the empirical measurement and mathematical formulation of a psychobiological phenomenon, musical harmony. Thus science originated with a unified and process perspective in which the spontaneous creativity of biological matter was taken as evidence, and as a model, for spontaneous creativity in physical processes. Matter was regarded as alive and creative, pregnant with co-creative opposites. Yet, in a significant alternation of opposites, science developed through the separation of the physics from biology and psychology, and the adoption of static, mechanical, and idealized models. The evolutionary perspective was replaced by the ideal of permanence and invariance. With advent of mechanical materialism and of philosophical spiritualism, the physiology of living organisms became separate from the physics of inanimate matter, and psychological issues were relegated to the humanities.

 

Twenty-five centuries later, as the notion of evolution was regained, Pasteur discovered cosmic asymmetry in biomolecules. Having demonstrated that biomolecules deviate polarized light in one direction or its opposite, and that living organisms are made of predominantly, and most often exclusively, of one of these opposites, Pasteur concluded that it must be the product of an asymmetric physical process. Such asymmetry is not explainable by classic thermodynamics and hence has been attributed to chance, and, more recently, to extraterrestrial seeding of the earth. In contrast, Pasteur reasoned that biochemical asymmetry must be the result of asymmetry of physical elements, and that life itself was a consequence of the asymmetry of the universe. 

 

Biological patterns can reveal fundamental features of physical processes not evident in simpler phenomena. Pythagoras' discovery of harmony in music, and Pasteur's discovery of cosmic asymmetry in biomolecules, embody and epitomize the creativity of thinking that takes complex processes as magnified cases of physical processes. Through such expansion, essential features common to all processes are revealed, and inferences can be made from the complex to the simple. Such top down complex-based inference is a relatively underutilized method. Analyzing and accounting for complexity in terms of simpler processes has been the only operative scientific strategy throughout the centuries. Reduction and complex-based inferences complement each other. They examine processes from the double perspective of simpler and more complex levels of organization.

 

                                                             Cosmic forms

Mathematics and psychology offer complementary perspectives to consider form. Mathematics itself, as well as the learning of mathematics, indicates that asymmetry, opposition and reciprocal transformation are fundamental forms. Studying how children learn to count and to reason, Piaget concluded that there are three "mother structures", lattice, group and topology, irreducible to each other. Lattices describe order, such as temporal priority, which is characterized by asymmetry and transitivity. Groups describe inverses such as opposition, negation and rotation; groups are symmetric, as every element of the group has an opposite. Topology studies transformations, dealing with continuity, neighborhood and limits. Similarly, the group of mathematicians who, under the collective name of Bourbaki, were the cutting edge of mathematical research earlier in this century, considered lattice theory, group theory and topology as the necessary and sufficient foundations of all mathematics. As we shall see, physical and physiological data also support a fundamental role for asymmetry, opposition and transformation.

 

The unidirectionality of asymmetry, the duality of opposition, and the tridimensionality of topological bifurcations and of the simplest knot, the trefoil, support the Pythagorean conjecture that small numbers abstract cosmic forms. Oneness, twoness and threeness appear to be universal forms that manifest themselves in many different ways. Numerical constants such as pi, and physical constants such as Planck's, indicate that nature does not favor integers, but supports the speculation that the most basic forms of nature will eventually be represented by numbers. In fact the possibility of digitally coding information implies that this must indeed be the case. This hypothesis has the advantage of suggesting a way in which complex forms, measurable in terms of mathematical dimensions, may be understood in terms of simpler numerical forms. We do not mean ideal Platonic forms, immutable in time, and separated from matter, but patterns such as catastrophes and attractors, embodied in energy and matter, and interacting in time to create new and more complex forms. Thom called them logoi to honor Heraclitus. The mathematical level of form and the physical level of matter are coextensive. In the late nineteenth century, Lord Kelvin hypothesized that atoms could be described as vortices in the ether, a name then given to the substance constituting apparently empty space. While the concept of ether fell into disfavor, current physics regards the void as filled with energy and virtual particles, subatomic elements as strings. Bohm regards the difference between matter and the vacuum state as form. 

 

Modern mathematical dynamics demonstrates how forms are generated through iterative processes that combine opposites, as illustrated in a companion article in this volume [Kauffman and Sabelli, 1997]. The logistic equation x_t+1 = R x_t (1 - x_t) combines growth with opposition to growth, such as it may result from physical resistance, environmental depletion, or any other negative feedback. As opposition increases, iteration of simple equations generates convergence to an equilibrium state, bifurcation into two alternative outcomes that alternate, a cascade of bifurcations, chaos, periodicities (described by the Sarkovskii's series, including the spiral Fibonacci's series), and marches towards infinity. The process equation A_t+1 = A_t + g * sin(A_t), modeling  bipolar feedback, also generates biotic patterns characterized by novelty and organization, between chaos and infinitation.

 

                                                    Four Primary Processes

Empirical evidence indicates that asymmetry, opposition and topological form are universal components of all physical processes, and that in addition, we must also consider flux as a primary process. Energy in its simplest form is a bipolar flux that pervades matter and space, and generates uncertainty. Action (energy x time) is an asymmetry, namely energy flow, the common stuff of what all is made. Communication is opposition, i.e. binary difference or distinction. Tridimensional form is relatively stable pattern, such as matter, and generate a tridimensional alphabet of color.

 

0. Zero pattern: energy flux: A perfectly regular pulse predicts death within twenty-four hours, contradicting the traditional view of health as equilibrium and regularity. Life implies uninterrupted variation, and the production of heat at moderate temperature; psychological processes as we know them occur in a narrow range around 37^oC. Temperature is a measure of the degree of agitation of the molecules. Heat is flux. The Nernst theorem, considered as the third law of thermodynamics, determines that there is no absolute 0^o temperature. There is flux at every level of organization, from physical systems to psychobiological ones. By flux we mean constant, complex and apparently disorganized change, overtly without direction. Flux is an universal component of all processes. Everything seems to be in flux, at all levels of organization. There is no permanence, no zero, but everywhere there is heat and chaos, chance and uncertainty. At the subatomic level, there is a flux of energy everywhere, in matter and in space. Everything is made of fluctuating energy.

 

Zero is not an empty set. It is the concrete absence of unidimensional action, of tow-dimensional information, and of three dimensional structure. In the physical world there never is 0 in all dimensions. Further, disordered flux and uncertainty separates us from absolute zero in each dimension. There always is something, rather than nothing. Purported absences actually are diminished forms of something concrete, their putative positive opposites. Vacuum is not absolute: it contains energy (3^oK background radiation), and is in constant flux. Pairs of opposite virtual particles spontaneously appear and disappear within the limits of the Planck constant h. Thus flux is not simply random: it is symmetrically distributed about zero. A defining characteristic of flux is random bipolarity. As we shall see presently, bipolar random distributions have richer properties than random distributions with only positive numbers. Flux is the minimum of opposition. Zero is an even number between two ones. Flux has 0 dimensions of pattern, but it embodies also 1, 2, and 3 as forms: flux produces action, is bipolar, and spherical (as 0).

 

Certainty and uncertainty are not exclusive opposites. There is uncertainty for events smaller than h, but not absolute uncertainty because quantum flux has significant physical consequences, i.e. it can originate action. Conversely, there is greater certainty above h, but certainly no absolute certainty. Flux can promote action by acting upon a notched ratchet wheel that can rotate in only one direction. Ordered change creates disordered flux, as illustrated by the production of heat by friction, and of chaos by deterministic equations. Due to their extreme sensitivity to initial conditions, chaotic processes amplify microscopic flux, reproducing random-like patterns at a macroscopic level. This is another way in which microscopic flux has macroscopic consequences. Thus flux is continuous with action and organization. Flux contains and is contained in organized action. Higher temperature (flux) is associated with structure and order: stars are hot nuclei dispersed in cold space, organisms are as a rule warmer than their environment, cities are local hot spots that become warmer as population increases. Systems are fires. All is fire, said Heraclitus.

 

1. One substance: asymmetric action: Cardiac function consists of a sequence of contractions and relaxations. Action is organized in units separated by no action. Physical actions are multiples of Planck quanta; systems are made of atoms, molecules, organisms.

 

The amount of blood pumped in each contraction depends on both the force and the duration of contraction: in physics, action equals energy times time. This concept of action is applicable to all levels of organization: physical attr-action, chemical re-action, biological action potentials, psychological e-motions. A static perspective focuses on energy, and its conservation throughout its transformations. A process perspective focuses on action;  energy never exists separate from time, because the Planck constant has the dimensions of energy times time. Matter is interconvertible with energy, hence with action. Made of the same stuff, action, physical and psychological processes readily interact. Separating matter and soul as different substances, dualism offers no explanation as how the two interact in brain. As actions, natural entities can be expected to change and diversify; regarding matter or ideas as the fabric of nature does not explain variation and diversification.

 

Action flows in one direction, time. Parents procreate their children. Actions cause consequences. Time flows from past to future. Life evolves from birth to death --it is perhaps our human longing for immortality that promotes the search for permanence, and mechanician's denial time's arrow. We regard the asymmetry of time as a fundamental law of physics, a principle that finds no exceptions, and that cannot be inferred from others. In contrast, classic, relativistic, and quantum mechanics assumes that inertial movement continues unimpeded forever, and time is reversible. Numerous publications study putative reversals of time. In mechanics, time is viewed as a geometric dimension. All the laws of physics are time-symmetric. Time's arrow has to be explained as the result of the statistical collective properties of ensembles of molecules. But time reversibility excludes creation. The existence of creative processes refutes theoretical constructs that purport to explain irreversible processes as macroscopic results of microscopically reversible mechanics.

 

There is an immense amount of evidence supporting that time unidirectionality is a universal law of nature, and no facts that contradict it, only speculation. Although postulating a hypothetically symmetric initial state, cosmology describes a sequence of "symmetry breakings" --i.e. a time asymmetry. Prigogine has shown how symmetry is broken also at the microscopic level, thus accounting for thermodynamic irreversibility. In other words, there is a microscopic time arrow! A principle of asymmetric action fits mechanics to thermodynamics and to evolution, rather than belaboring to infer thermodynamics from mechanics, and attributing evolution and life to chance. Illustrating the collective wisdom embodied in language, "uni-verse" means unidirectional flow. 

 

Time leaves its mark in the structures it constructs: this is the cause of asymmetry in the shape and inner structure of material entities. Pasteur's concept of cosmic asymmetry is being supported by empirical data at all levels of organization: left vs right distinction in beta decay, optical rotation of atoms, preponderance of matter over anti-matter, violation of gauge symmetry by superfluids, fluctuations in the cosmic microwave radiation, greater polarization of radio waves from galaxies lying in one direction of space, ionic asymmetry across cellular membranes, anatomical asymmetries such as left-right brains, and power asymmetries of age, sex and class.  

 

From the perspective of processes, the unidirectionality of time is the most basic asymmetry of nature, i.e. Pasteur's cosmic asymmetry. Including time, structural asymmetry, and thermodynamic irreversibility, asymmetry itself may be the most fundamental law of nature. We regard Pasteur' asymmetry as the fundamental order that Einstein postulated must exist, beyond quantum probability. This view of asymmetry as a cosmic order is also based on the recognition of lattice theory (the mathematical study of the asymmetric order relation < ) is one of the three pillars of mathematics according to Bourbaki. Thom's catastrophe theory makes asymmetry one of the two fundamental parameters in determining bifurcations. This background accounts for the importance given by the process method to the measurement of asymmetry.

 

At a similar abstract level, action is connected to a numerical form, one, in the oneness of substance, its organization in units, and also in its flow in one direction, time. The same cosmic form makes itself evident in many different forms: physically as action, algebraically as asymmetry, and numerically as oneness. But action implies change, hence diversity and multiplicity. The world around us and within us is composed of many units sharing one composition, and differing in their many patterns of organization. "One is many, and many is one", said Heraclitus. There are many ones, in every direction, beginning with the complementary pair, 1 and i (the square root of -1).

 

2. Two complementary opposites: information: Cardiac action must be constantly adjusted to the needs of the organism. Brain informs the heart about present bodily needs, and upcoming ones, through the opposing actions of the sympathetic and parasympathetic nerves. Opposition is the manner in which the brain provides information to every organ of the body. Information translates into a pattern of acceleration and deceleration. We can thus measure the amount of information received by studying the differences between successive cardiac beats [Carlson-Sabelli et al, 1997]. A beat is a bit.

 

From computers to genetics, information, rather than energy, has become the focus of our civilization at the end of the twentieth century. Bateson defined information as news of a difference. Conversely, we add, in the context of variation, repetition is information. In either case, information is a communication between two entities, and the message itself is a pairing. Information is a double opposition, news and difference.

 

Everywhere there are two opposites: women and men, left and right, positive and negative, harmony and conflict. Matter is constituted by positive protons and negative electrons. Action itself consists of energy waves and potential differences, not only of unidirectional time. Action begets interaction, and triggers reaction, opposition, and change. Action communicates. Information, the stuff of brains, computers and heredity, is difference, contrast, opposition. Structures that appear to be stable are actually constantly being generated by the interaction of opposing forces: galaxies are made and maintained by the opposing forces of gravity and cosmic expansion; our bones are constantly constructed by osteoblasts and constantly destroyed by osteoclasts, two types of cells with complementary function. Numbers have a positive or negative sign. The most fundamental laws of mechanics discovered by Newton refer to the relation between action and reaction, while the creation and disappearance of oppositely charged particles within the boundaries of the Planck constant is the fundamental flux that permeates the void in which all matter and energy are immersed. Cooperation and conflict both are fundamental biological and social processes. Binary digital schemes are technically successful. Drawing a distinction is a useful step in logical reasoning, purportedly the most elementary one. Bifurcations occur at every step of development; oppositions are not necessarily pre-existing, and requiring resolution, but are created in the course of processes. Opposites are continuous, similar, and relative, their separation is fuzzy, and their existence sometimes undesirable, but none of the above denies their reality. Opposition is not reducible to quantity, nor an arbitrary creation of language. Opposites coexist, as illustrated by quantum complementarity (e.g., electron as wave and particle). This is the union of opposites.

 

Process theory regards the complementarity of opposites as a fundamental principle of nature. Opposition is a cosmic form. Process theory adopts this intuitively obvious fact as a hypothesis and as a method. The method centers on the study of every process as a function of the interaction between two opposite forces: this is the diamond of opposites. The hypothesis is that opposition is a fundamental and universal pattern of processes, communications and structures. Opposition is twoness. Information is encoded in opposition: 0 and 1 in digital coding, true and false value in logic, action or resting potential in muscle and nerve cells. As a cosmic form, opposition occurs in every dimension and in every respect. For instance in communication we consider the two values of information, the two entities communicating, the two roles of each as source and receiver, and the dual meaning of each message as generated by its source and as translated by its receiver. As asymmetry, also symmetry is a cosmic form. Supporting this thesis, symmetry arguments have been immensely productive in physics since they became to be recognized in the second part or the twentieth century. An opposition represents a symmetry created by two oppositely directed asymmetric actions. Our body is overtly symmetric, although there also is an essential asymmetry. Babies born with two right sides (or two left sides) have marked difficulties, often fatal.

 

The principle of the union of opposites includes two complementary but asymmetric parts: opposites coexist in processes (dialectic contradiction), but are separated in time, space, respect, or intensity (local principle of no-contradiction). Thus every normal person has feminine and masculine traits, at the same time, obviously in the same place, and sometimes in the same respect, but in different proportions. Opposites are in part synergic and in part antagonistic. They attract and repel each other. They are fundamentally similar, and fundamentally different. Opposites are extremes of a linear continuum in some respects, but  they have a complex relationship, not just reciprocity. They can increase or decrease together; attraction and repulsion coexist in various proportions, depending on the distance between particles or between persons. Distance thus determines two thresholds: the distance below which repulsion predominates over attraction, and the maximum distance beyond which attraction fails to sustain connection. Opposites are not poles of a continuum, but orthogonal dimensions in a plane. Conversely orthogonality does not imply independence, as usually interpreted, but complementarity. Linear opposition, as represented by positive and negative numbers, portrays only abstract categories. Concrete opposites, being both synergic and antagonistic, must be measured in the complex plane, defined in the real and imaginary axes [Carlson-Sabelli, This Volume].

 

The union of opposites is a process, not a static unity. Opposites alternate, in random, periodic, chaotic, or biotic manner. Electrical and magnetic components of light are paradigmatic of the complementary relation between opposites. Each component is a sinusoidal wave. They are orthogonal to each other, in the real and imaginary axes. They are opposed in phase. Light illustrates a simple alternation of opposites. The electrical and magnetic components of light waves are orthogonal to the direction in which light travels (action), and to each other. Likewise opposites are complementary, orthogonal to each other, not opposite poles of a unidimensional axis. Models that portray opposition in two dimensions allow to represent the synergic component of opposition, namely, their similarity. A universal similarity is that both opposites are actions, hence sharing the time dimension, and both providing energy to the system. But opposites are similar also in many other respects. Complementary opposites embody the same information, albeit in reversed form --as illustrated by the complementary form of enzyme and substrate, drug and receptor, feminine and masculine genitals. The simplest form of opposition as pattern is bipolar flux. A wave represents the next level, harmonic complementarity. Light waves are double oppositions; the electrical and the magnetic components provide a model for energy waves and alternating opposite information as coexisting variations in time. Opposition manifests itself in many different forms. For instance, biological oppositions include circulation and other asymmetric rotations, spontaneous cycles of acceleration and deceleration, and accelerating and decelerating reactions to external inputs.Biological and psychological oppositions, such as mating, conflict, and contradiction, are more complex than wave forms. In contrast, standard logic portrays opposition as mutual exclusion, a simpler pattern.

 

Opposition is a drive. Opposites create tension of opposites, as in the bow and the lyre, that propels the arrow and sings the music, not equilibrium. Coexisting in time, but out of phase, spontaneity and reactivity, autonomy and interaction, create complexity. Opposition is also a process, namely the creation (bifurcation) and the destruction (convergence) of opposites, and their combination to generate simpler or more complex patterns (from equilibrium to organic forms). The emergence of two opposites from one process is the fundamental process of creation. Opposite entities, like protons and electrons, or woman and man, co-create something new and complex. Cosmological evolution includes spontaneous symmetry-breakings. These are bifurcations, equivalent to Epicurus' swerving of the atoms a fundamental process missing in Democritus' atomism, the intellectual ancestry of mechanism. Spontaneous bifurcations generate novelty and dimensions. 

 

3. Structure formation, Co-Creation, and Threeness: We define co-creation as an interaction that generates a new and relatively stable pattern. Pairs complementary opposite actions generate tridimensional, diverse and relatively stable patterns, such as matter itself. The interaction of light beams creates interference patterns and, when polarized, holographic images. Fields of energy create material particles. The bonding of oppositely charged particles creates atoms. Two sexes procreates new individuals. The concept of co-creation stresses that organization is a process, a trans-formation, not a form, that generates novelty and complexity. Focusing on the generation of structure, it stresses that they are not permanent. Co-creation provides a model for "self"-organization as the result of interactions.

Oppositions generate bifurcations, such as Thom's elementary catastrophes, non-linear changes from one stability to another. A catastrophe is a simple structure, a more or less complex fold in one dimension governed by bifurcating and asymmetric parameters in two other dimensions. We meet here again these basic forms, asymmetry and twoness, as well as tridimensionality. Process theory interprets catastrophes as the result of interactions between opposing forces as discussed by Carlson-Sabelli et al [This Volume]. We envision co-creations as sort of mirror images of catastrophes. A catastrophe is a jump between complementary opposites as if they were poles of a linear continuum (asymmetric factor), while the trajectory between them is nonlinear, folded in a third dimension, when the energy of the bifurcating factor is high. A co-creation is a symmetrization of opposites that constructs a organization, and hence hierarchy. The diamond of opposites defines the control plane, as in a catastrophe, determining two control parameters as described above. Hierarchy, the third dimension of the outcome surface, raises along the energy factor, and from the opposing poles to the central axis, with 0 amplitude in the boundaries represented by the axes themselves. In a co-creation, novelty and complexity increase with the symmetry (informational parameter) and energy (asymmetric bifurcating factor) of opposites. For instance, in an open system, a small temperature difference between air masses produces a breeze, and larger differences produce winds and tornados. In spite of the example chosen, the terms catastrophe and co-creation may be appropriate rather than arbitrary. The polarization of opposites often leads to catastrophic consequences, whereas the union of opposites is highly creative. The formation of long lasting structures such as a cell requires both high energy and symmetric opposites, anabolism and catabolism. Creativity can be promoted by increasing and equalizing the energy of complementary opposites, and further, by expanding pairs into triads.

 

Structures are co-creations, i.e. tridimensional and relatively stable patterns generated by interactions. Pattern and stability result from complex equilibration of opposite forces. Three dimensions are the least necessary to accommodate complementary opposite waves. All processes contain, create, and destroy structure (subatomic particles, biological organisms, etc). Material structure also is a universal feature of processes. Matter itself is a structure, a tridimensional separation between masses of energy: this is Descartes' definition of matter as extension. Stable structures conserve information. They conserve "memories" of the processes that generate them. All structures embody in their three dimensions the unipolar asymmetry of action, the bipolar asymmetry of information, and the hierarchical asymmetry of co-creation. Even our anatomy embodies the unidirectionality of physical action as front and back, the symmetry of opposition as right and left, and the hierarchy of organization from head to toe. Likewise the earth, and any other astronomical body, displays asymmetry in three dimensions: rotation as action, opposition as the gradient from equator to two poles, and a vertical distribution of energy, the states of matter, and biological inhabitants.

 

Threeness is a cosmic form that reoccurs at all levels of organization and in all respects. Threeness seems crucial to organization: material structure has three dimensions; the triangle is the only mechanically stable polygon. Mathematically, Sarkovskii's remarkable theorem demonstrates that period three implies periods of any order, an infinite sequence of marches towards infinity ("infinitations"), and chaos. For the universe as a totality, as well as for gases, action is an expansion in three dimensions, while black holes represent a contraction in three dimensions. Mother, father and child make a family. Action, information and organization are universal features of processes, as illustrated by physical energy, information and matter. Social and intellectual categories are often triadic (e.g. executive, legislative and judicial power, id, superego and ego). As illustrated by catastrophes, the interaction of opposites generates at least one more dimension. Whereas forkings are relatively common in nature, trifurcations are rarer but highly creative. The tridimensional expansion of the universe generates galactic organization. The combination of three colors of quarks organizes subatomic particles. The distinction of three primary colors in the retina epitomizes the emergence of biological from physical processes. 

 

In conclusion: Four primary components are found in all processes. In part II of this article we explore how two primordial forms, asymmetric action and complementary opposition are sufficient for generating periodic, chaotic, biotic and evolutionary processes.

 

For easy reading, we have omitted references and scientific data in this primer of process theory, presented in companion articles in this volume, and in more technical publications of process theory listed below.

 

Sabelli, H. (1989). Union of Opposites: A Comprehensive Theory of Natural and Human Processes. Lawrenceville, VA: Brunswick Publishing.

Sabelli H., Carlson-Sabelli L., Javaid J. (1990). The Thermodynamics of Bipolarity: A Bifurcation Model of Bipolar Illness and Bipolar Character and Its Psychotherapeutic Applications. Psychiatry: Interpersonal and Biological Processes. 53:346-367.

Sabelli H. and Carlson-Sabelli L.(1991). Process Theory as a Framework for Comprehensive Psychodynamic Formulations. Genetic, Social, and Gen. Psychology Monographs. 117:5-27.

Carlson-Sabelli L, Sabelli HC, and Hale A. 1994). Sociometry and Sociodynamics." In Psychodrama since Moreno. Karp, Watson and Holmes, Editors.

Carlson-Sabelli L., Sabelli H., Patel, M., Messer, J.,  Zbilut, J., Sugerman, A., Walthall K., Tom, C. and Zdanovics, O. (1995). Electropsychocardiography. Illustrating the application of process methods to comprehensive patient evaluation. Complexity and Chaos in nursing  2: 16-24.