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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 II. Co-Creation, Evolution and
Entropy. 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 924-935.
How is the universe, that it creates a human heart?
II. Co-Creation, Evolution and Entropy
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 non-technical presentation of a scientific model
of nature as a co-creative process. It is offered as an alternative to
determinism and contingency, the two leading scientific paradigms. A co-creation
is an interaction that generates novelty. The interaction of complementary
opposites naturally generates novelty, complexity, and diversity. The principle
of least action implies that action is directed by equal and complementary
information. Coupled to action, opposition generates symmetry and organization,
not equilibrium or disorder. Evolution is a creative development, determined by
the interaction between primordial asymmetric action and symmetry-generating
opposition. The production of entropy measures this asymmetric
production of symmetry. Statistical entropy of numerical series increases with
symmetry and diversity, not with disorder. As biomolecules, and in contrast to
random, periodic or chaotic series, biological time series such cardiac beat
intervals are asymmetric, and more so in coronary illness. Their entropy
decreases, while order increases, in coronary illness and in depression, i.e.
with decay, at variance with standard thermodynamics. Coronary illness results
at least in part from a disproportion between high psychological and lower
cardiac action, while depression may result from an inhibition of action by
overwhelming conflict or biological deficit.
Entropy is augmented by the creation as well as by the
destruction of organization, but evolution necessarily precedes and exceeds
decay. Organization emerges and mediates the flow from primordial asymmetry
(action) to attractive symmetry (entropy). Creativity can be promoted by
increasing and equalizing the energy of complementary opposites. Key words: co-creation,
coronary illness, depression, entropy, evolution, information, fractal, least
action, modules, process theory. How does the heart move that mirrors what moves us?
The traditional homeostatic model assumed that heart rate tends to
equilibrium, and varies only as the result of external disturbances. We now know
that excessive regularity of the pulse predicts imminent death, indicating that
variation is an intrinsic and fundamental feature of cardiac health. Cardiac
timing is modulated by the opposing accelerating and decelerating action of
opposite the sympathetic and the parasympathetic nerves. As these two nerves can
be simultaneously active, and antagonize each other, the same heart rate can
obtain with a wide range of neural inputs. Heart rate is approximately 90 per
minute, and regular, in the denervated heart; the same average rate, but with
complex variations, can occur during the simultaneous activation of both
sympathetic and parasympathetic nerves. Heart rate is a linear continuum;
sympathetic and parasympathetic regulation oppose each other in this dimension,
but synergize each other in creating complexity of pattern. The relation between
these opposites must then be represented in a plane (the "diamond of
opposites") rather than as polarities in a linear continuum, and their
relation can be examined in two dimensional plots of cardiac beat series, such
as phase portraits and return maps as illustrated by Carlson-Sabelli et al [This
Volume]. The sympathetic / parasympathetic system offers thus a model for
complementary opposites: every process represents a sequence of accelerations /
decelerations generated by synergic (sympathetic) and antagonistic
(parasympathetic) interactions. As interactions are mutual and repetitive,
oppositions generate a bipolar feedback. Through these nervous inputs, brain
organizes the timing of cardiac beats, as manifested by the occurrence of
transient patterns of ("complexes"), associated with
behavioral, emotional and intellectual activity (figure 1, Part I). Complexes
are patterns of repetition or recurrence, separated by transitions, net
accelerations or decelerations that interrupt recurrence. The pattern of cardiac
timing is not reducible to equilibrium, periodicity, or chaos. Complexes are
transient, asymmetric, and creative. In contrast equilibrium, periodic and
chaotic orders are stable, symmetric, and recurrent. Cardiac complexes have less
recurrences than random series. As recurrence represents repetition of pattern,
this indicates novelty. The production of novelty seems to be a defining feature
of life. We thus embark into the search for an organized but ever-changing
universe.
Creative Development Cosmic Seed: Our objective is
to find the simplest process that will generate biological-like patterns. Our
starting point is the four primary processes described in Part I. Flux, action,
opposition, and structure formation are universal components of all processes,
that repeat at all levels of organization, and in many different
respects. Physical, chemical, biological, social, personal levels of
organization are generated by the combination of these primary processes. Our
hypothesis is that action and information are necessary and sufficient to
generate all other commonly observed patterns. This is process theory. The
equation At+1 = At + g sin(At) embodies its two
basic postulates: the linear growth of action is modelled by addition, and the
cycling of complementary opposites by the sine function. Morphogenesis and dimensiogenesis:
Primary processes may be conceptualized as dimensions common to all processes.
Mathematics defines dimensions simply as the number of independent numbers
required to describe the state of a variable. Physical theory and measurement
hinge on the definition of dimensions. Process theory stresses the unity of
energy and time as action. Physical dimensions are sufficient to describe simple
and general processes; a larger number of dimensions, as yet unidentified, must
be embodied in biological processes. Physics focuses on general patterns rather
than on particulars, omitting form and organization, which are essential in
biology. Process theory thus adds the patterns of the primary processes as
dimensions to describe information and organization at any level of complexity.
Flux may be measurable by an extension of the concept of temperature -we already
speak of emotional temperature-, using standard statistical techniques.
Intensity and timing estimate action at any level of organization. Information
can be measured as opposition. The correspondence between fundamental dimensions
(action, information) and cosmic forms (asymmetry, opposition) suggest that
dimensions may be understood as forms, and, conversely, form may be measured as
dimension. Numbers measure not only quantity (cardinals) and order (ordinals);
they also portray form, as stressed by both the Greek founders of science and
modern researchers such as Gödel and Jung. Modern technology allows one to code
forms as digital sequences of numbers. Galileo stressed the intimate relation
between scale and function, a view expanded by Engels in his famous dialectic
law according to which changes in quantity produce changes in quality, either
gradually or suddenly; for instance, water freezes at 0oC while
gradual increases in population changes a village into a city. We thus portray
forms as dimensions: action is asymmetry, information is complementary
opposition (harmony), structure is tridimensional distance. Physical, chemical,
biological, social, and psychological organization are composite forms of higher
dimensionality. Evolution is a process of dimensiogenesis. Determined novelty: Although primary
processes are generic, their interaction generates novelty, the differentiation
of classes, and the generation of unique beings. A unique child is procreated by
woman and man; three primary colors create an infinity of tints. Diversification
is evident at all levels of organization, e.g. the sequence of
"symmetry-breakings" in cosmological evolution, tissue differentiation
in embryological development, psychological individuation. Development is
predetermined by genes yet each individual is unique. We thus propose to
consider evolution as a creative development, meaning that both creative
and predetermined, as the interaction between primary processes necessarily
generates novelty, complexity, and diversity. Transcendental numbers such as π,
the sequence of which is determined, yet unpredictable, exemplify the notion of
determined creativity at a simpler level of organization. Π
has a high degree of novelty (as biological data do), is strictly determined (as
periodic series are) yet lacks pattern (as random distributions do). The
transcendental character of π as a number
represents the incommensurability of linear and circular order, a union of
opposites. Π
appears to be random, meaning that its decimal sequence cannot be differentiated
from random series. Intriguingly, π's
decimal sequence is less recurrent than any random sequence of 10 values that we
have tested. We interpret lower-than-random recurrence as the generation of
novelty. Thus π appears to us as paradigmatic of determined generation of
novelty. We speculate that evolution may in fact be propelled by such determined
creativity. Determined numerically irrational relations such as π
may account for apparent random occurrences in nature. Π
is generated by the interaction of asymmetry and opposition in the process
equation; in the same equation, as g, π produces
bifurcation.
Action and information as cocreative dimensions Action produces interactions. Progress must meet
resistance, and resistance creates complexity, as illustrated by the logistic
equation (see Part I). Progress also finds co-creators, synergic or
"sympathetic" co-actors that accelerate the process in rate,
intensity, direction or complexity. Interactions accelerate or decelerate
actions, they change velocity, direction, or complexity. The only thing
interactions cannot do is to allow the process to proceed unchanged. Repetitive
interactions constitute a feedback. As a process generates both accelerating and
decelerating interactions, the feedback is bipolar, positive or negative. The principle of least action and complementary
information: The effect produced by an action depends also on
information; for instance, the velocity of a car depends upon the action of its
engine (that consumes gas) and the information provided by transmission,
aerodynamic shape, and the drivers' control. The system is optimal when the
information available allows one to take full advantage of the energy consumed,
and vice versa, when energy empowers the available information. In terms that
readily suggest its extension to all levels of organization, the principle of
least action states that, of all the possible paths consistent with the
conservation of energy, a physical system will move along the path that
minimizes either time lapsed or energy consumed or both. Action thus proceeds
with maximal local efficiency, implying optimum information. Least action is a
conservation principle: the least action is all the action, and the available
information is the optimum information. Together, they co-determine the
resultant effect. How does a particle choose the path of least action, as if
there is an intelligence associated with physical action?
Information explains the why of the least action principle: a system
functions optimally as result of the symmetric complementarity of action and
information, i.e. for the 450 resultant of two equal and
orthogonal opposites. Modelling action and information as orthogonal opposites
suggest to portray their effect as the hypotenuse. Intriguingly, the effect of a
unit of action and a unit of information equals 1.41.. the square root of 2,
another irrational number with an apparently random decimal sequence. Likewise
the circumpherence, that curve of a given length which encloses the biggest
area, generates pi. Significantly, least action describes quantum mechanical
paths (Feynman), and guarantees that the rate at which heat and entropy are
generated by current flows is a minimum. Action and flux as co-creative opposites:
Disordering flux is both a product and a source of action. Action becomes flux
(e.g. friction generates heat) to a greater extent than flux generates action,
but the opposite transformation is equally fundamental. Life feeds on sunlight
that, making an electron in the chlorophyll molecule jump to a higher molecular
orbital, provides both energy and information. Life feeds on heat, requiring
temperatures that maintain water liquid and do not denaturate proteins. and
consciousness emerges, as far as we observe, only around 370C. Thus
the spontaneous tendency for different temperatures to equilibrate generates the
conditions necessary for the development of complexity, rather than inert
uniformity. Flux is also a product and a source of opposition. When it interacts
with organized processes and structures, heat can generate information. Random
collisions are not evenly distributed, so they produce Brownian movement, that
has characteristics similar to those obtained in biological time series (but not
with random data) in wavelet and recurrence portraits. In the iterative
mathematical equation At+1 = At + b * At, where
b is a random sequence from -1 to 1, the combination of unidirected action and
bipolar random variation produces time series in which novelty and pattern
resemble physiological data. Such biotic patterns are not generated by combining
addition with any unipolar random, such as At+1 = At + u *
At, where u is a random sequence from 0 to 1. The difference between
unipolar and bipolar rectangular random distributions is not simply a
shift in scale. Complementary opposites as the cyclic engines of change:
Circular opposition, together with action, generates spiral convergence to an
equilibrium point. Convergence is a process that advances like a screw. Its
putative attractor, equilibrium, varies, as illustrated by the
"equilibrium" of supply and demand, as the opposite forces themselves
change. Equilibrium is a rare and transient event, observed only under
artificial laboratory conditions. Spiral change constructs galaxies, ammonites,
and Fibonacci's series and its golden ratio φ . Action
and opposition also generate helices, as in proteins, nucleic acids and
dialectic reasoning, and tridimensional waves, such as light. The logistic
equation demonstrates that simple opposition to growth generates bifurcation
cascades, chaos, and infinite periodicities as described by Sarkovskii's
novelty-creating series (3, 5, 7 ... infinity... 2x3, 2x5, 2x7...infinity... 2nx3,
2nx5,... infinity... 2n.. 22, 2, 1). The
process equation At+1 = At + g sin(At)
demonstrates that the iteration of linear growth and bipolar opposition
generates in addition biological-like patterns [Kauffman and Sabelli, This
Volume]. As its gain is increased, bipolar feedback produces convergence, then
bifurcation into opposite processes that together generate chaos, and biotic
patterns. During the chaotic phase, an infinite number of cycles are generated,
while during the biotic phase there are multiple infinitations, as also obtained
in Sarkovskii's series. The biotic patterns resemble actual biological data in
their low recurrence rate and their asymmetry. The generation of biotic patterns
by this simple equation shows that novelty-generating organization needs not be
limited to biology, but may occur in physical evolution. The fundamental bifurcation in the process equation
suggests to us that diversification and ordering may function as
complementary processes in the creation of life-like organization. For instance,
mutations generate genetic diversity, and natural selection creates order. An
evident feature during the chaotic regime is the coexistence of expansion,
bifurcations and periodic ordering. Complexity of pattern (convergence <
periodic <chaotic < biotic), except for the intermixing of chaotic and
periodic patterns, increases with the range of action At,
illustrating the relation of quantity and quality. Complexity also increases
with the feedback gain g. This is noteworthy because g can be interpreted as a
measure of self-acceleration or self-information. This may be the seed of a
crucial step in evolution: consciousness. But feedback needs not be internal: it
also results from mutual, repeated external interactions.
Entropy as symmetry, not disorder Opposite mechanical forces neutralize each other,
generating transient equilibrium, but simple iterative equations show that
opposite processes also generate cycles, bifurcations, and chaos. Beyond chaos,
the union of asymmetric action and opposition generates biotic patterns. Yet
entropy is often defined as disorder, interpreting the second law as spontaneous
tendency towards decay, rest, and uniformity. It is pointed out that cool spoons
immersed in hot soup become warm, while two objects at the same temperature
never diverge, one cooling down while the other warms up; likewise glasses break
into pieces when they fall, while these pieces never spontaneously reassemble to
reconstitute the cup. Notwithstanding it is evident that life has spontaneously
originated from matter, and that living organisms continue to evolve. The
identification of entropy with disorder creates a contradiction between the
increase in entropy and the generation of complexity in cosmological and
biological evolution. To overcome this contradiction, Schrödinger proposed that
living organisms decrease their internal entropy, which is exported as waste
into the environment. This process allows for the development of biological
organization, but does not explain it. In the standard scientific viewpoint,
complexity and of life are the fruit of accident. An alternative view originates
with Prigogine's far-from-equilibrium thermodynamics. Irreversibility exists at
the microscopic level --in contrast, the standard explanation of entropy as the
macroscopic result of time-symmetric microscopic mechanics allows for potential
reversibility. Time has a constructive role. Physically, chaotic processes far
from equilibrium create dissipative structures --they are not stable
attractors. Thermodynamic entropy is defined as a state function. The
statistical distribution of particle positions and velocities is considered to
represent the total physical entropy of a process. Reducing entropy to mechanics
allows for potential reversibility, and leads to equating entropy with
uniformity and disorder. Statistical mechanics thus fails to explain why either
evolution or irreversibility occur. It must explain the tendency to maximize
entropy as the result of initial conditions, which are both arbitrary and
untestable, as there is nothing in the equations of mechanics or of probability
to account for it. When entropy is measured as a state, organized processes may
appear to be random: their temporal order disappears when the time series is
collapsed to construct the histogram from which the statistical entropy of the
series is calculated --thus infinite complexity may appear as total disorder.
From the process perspective adopted here, the entropy of a process is measured
by the entropy of its time series, not by a state function. Nor does physical
entropy exhaust the entropy of each of the multiple levels of organization that
are present in any process. To measure organization we are developing biostatistical
entropy as concept and as a method that quantifies novelty, diversity,
asymmetry, dimensions and pattern. As
illustrated by Carlson-Sabelli et al [This Volume] with measures of entropy and
recurrence in random, periodic, chaotic, and biological time series, the entropy
of the time series increases with diversity and symmetry, while recurrence
entropy increases with pattern, whether periodic order or biological
organization. Likewise statistical variability and entropy increase, while
recurrence decreases, from point attractor to periodic to chaotic to biotic
patterns in the process equation. Thus statistical entropy is an abstract
measure of the diversity and symmetry of the numerical data, and it does not
vary with their order or disorder. Organization is portrayed by both a higher
recurrence entropy for short and medium sequences, and a lower than maximal
entropy for long sequences [Carlson-Sabelli et al [This Volume]. Eddington proposed that the second law of thermodynamics
is the most fundamental law of nature. We may thus expect spontaneous increase
in entropy to drive evolution, as proposed by Lotka. We view unidirectional time
as the primordial asymmetry that accounts for irreversibility and order, and
reinterpret the second law as a determined asymmetric flow towards symmetry,
rather than as a tendency to a more probable state. Creative systems such as
biological organisms are open systems that feed on energy and excrete entropy.
In our view, the essential feature of the process is the unidirectional flow:
energy input ®
organization ®
entropy output. Asymmetry feeds organization in its way towards symmetry. The
internal entropy of biological systems is decreased in some respects and
increased in other respects. Thus the entropy of cardiac beat time series is
lowered by the asymmetry of their distribution, but their recurrence entropy is
relatively high. Entropy is lower in coronary illness and in depression than in
normal subjects. To a biologist, it is not surprising that illness leads to a
reduction in the flow of energy and the production of entropy, but, as illness
is paradigmatic of decay, these results contradict mechanical thermodynamics. As a process, the rate of entropy production increases
faster within organisms than in their environment. The free energy flow density
in human brain (150,000 ergs sec-1 g-1) is much higher
than that of any other system --e.g, it is 500 ergs sec-1 g-1
for the biosphere and only 2 ergs sec-1 g-1 for the sun,
calculated physicist Chaisson. Considering also the temperatures (sun 15,000,0000K,
biosphere 2800K, brain 3090K), we have an enormous
difference in entropy: 485 for brain, 1.78 for the biosphere, and 0.000133 for
the sun. Albeit these numbers are rough calculations, they point to a
correlation between entropy production and complexity, not with disorder. Even
ideal gases do not tend to disorder and rest: a gas spontaneously expands until
it is constrained by its container: apparent equilibrium results from
opposition, not from the depletion of free energy. Statistical mechanics assumes
that molecular configurations to be found at any one instant in the ensemble are
the same as those we would see in the original real system were we to observe it
for a very long time; this assumption cannot apply to an open and expanding
system. The expansion of a gas, or of the universe, separates its constituents,
and may thus render distinguishable entities previously undistinguishable. It
thus creates information, not disorder. Layzer has argued that the expansion of
the universe more than compensates for the disordering tendency of entropy
maximization. Spontaneous processes do not only randomize but also
differentiate, as evident at all levels of organization, e.g. the sequence of
"symmetry-breakings" in cosmological evolution, embryological tissue
differentiation, psychological individuation. The current interpretation of entropy as disorder,
uniformity and decay is a philosophical overlay that does not stem from the
mathematical formulation. Undoubtedly friction reduces movement to heat, use
produces wear and tear, and life leads to death, but just as evidently heat and
action produce work, life emerged from inorganic processes, and it necessarily
precedes death. Entropy is augmented by the creation as well as by the
destruction of organization. The maximization of entropy is an asymmetric
tendency towards symmetry, and symmetry constructs structures, not only
equilibrium. The consumption of energy may serve to construct or to destroy: the
increase in entropy is an enantiodromia of evolution and decay (from the
Greek, enantios opposite, and dromos course). Instead of entropic equilibrium, processes appear to
evolve toward greater complexity. Point attractor models have been found
insufficient to understand heart rate variations, and appear also insufficient
to understand physical processes. One cannot do physics by analogy, but one must
pay attention to the fundamental fact that also biological processes are
physical phenomena. We do not confuse our ideas, still in development, with
actual physics, but note that Pasteur's asymmetry was another way to learn about
reality. Universalizing from biological data is not extrapolating to the
universe what we have learned in one of its corners, but to take the evidence
found there seriously, requiring that our world views be consistent with them.
Universalizing from biological data means to place limits as to what kind of
hypotheses we make. If life proceeds from birth to death, physical time cannot
be reversible. If illness decreases entropy, then entropy is not associated with
decay.
Co-Creative Evolution Also biological evolution appears to be governed by the
unidirectionality of time, the coexistence of opposites, and the creativity of
combinations. There are evolutionary, involutionary, and neutral changes in
biological history, but an overall progress towards greater complexity is
evident. Complexity increases because evolution necessarily precedes and exceeds
decay. Nature cannot destroy what it has not as yet created. Simple materials
are used in the formation of more complex systems. Products created by simpler
organisms are necessary for the evolution of more complex ones. Micro-organisms
synthesize vitamins. Plants generate oxygen. Food chains are the material bases
for evolution. The generation of complexity necessarily precedes and exceeds
decay. Simple components by necessity appear and accumulate before they are
integrated into more complex systems. As proposed by Empedocles, in the first theory of
evolution, both cooperation and conflict contribute to generate novelty and
complexity. Species co-evolve, with each other and with the environment. They
feed each other energy and information. Organisms cooperate, as illustrated by
Margulis' discovery of the endosymbiosis of bacteria as mitochondria in
nucleated cells. We exist in symbiosis with our intestinal flora, and depend on
the oxygen generated by plants. Predation between species, and competition
within a species, are complementary to cooperation. Altruistic traits are
prominent in maternal behavior, but are more general --including apes saving
human children, as observed more than once in zoos. Certainly chimpanzees and
humans share more than 90 % of our genes, but this fact actually contradicts the
sociobiologists' claim that altruism is an expression of genetic selfishness,
directly related to the proportion of the genome we share. In any case, genes
have no self. Sexual reproduction and mutations generate novelty and
diversity. Undoubtedly mutations are "random" in some respects, but
not in others: bacteria rapidly develop resistance to commonly used antibiotics.
Sexual choice and other behaviors, as well as the biological and physical
environment function as complementary processes in the creation of life-like
organization. Competition does not eliminate diversity, as it wipes out the
unfit, rather than limiting survival to the fittest at a particular time and
place --a strategy that would render the species unable to evolve. Behavior is
governed by a complex and dynamic hierarchy of needs and wants, from adequate
temperature, oxygen and water to love, freedom and creativity, not solely by
survival. Not only humans but also animals die of loneliness or captivity.
Natural selection is not the action of a physical environment upon passive
organisms: it is an interaction between biological behavior and a largely
biological environment. Sexual selection is entirely a biological communication.
Thus in higher organisms, as Piaget stressed, brain directs evolution. Thereby
adaptation and creativity direct evolution, in a Lamarckian fashion, not through
genetics, but through behavior. As discussed above, self-information via
internal or external feedback creates complexity. Physical priority and psychological supremacy:
Hierarchies are asymmetric, but interactions are bidirectional. The heart
supplies oxygen and nutrition to the brain; in turn brain controls the heart,
illustrating the concept of priority of energy and supremacy of information.
Mood (information) is largely predetermined by the amount of sunlight, and by
levels of oxygenation (energy). In all processes the simpler levels predominate
globally because they have more energy, more extension, more duration, and
temporal priority. The more complex processes predominate locally, because they
have greater density of energy flow and of information (priority of the
simple and supremacy of the complex). Evolution creates hierarchies in levels of organization
(mathematical, physical, chemical, biological, social, psychological), just as
it creates a hierarchy of brain structures (Jackson's spinal, bulbar,
mesencephalic, diencephalic, cortical levels), and in psychological functions (Maslow's
hierarchy of needs and wants). Hierarchies of complexity differ from hierarchies
determined by the extension of systems (atom, molecule, cell, organism, society,
planet); extension does not separate the biological and the psychological
levels, and places the social above both of them. Social behaviors occupy an
intermediate position between biological needs that determine economic
priorities and the psychological desires and relations that organize personal
life. As a totality, society has greater energy and complexity than individuals
(priority), but each individual mind has greater energetic and informational
density (supremacy). Also, social processes have temporal priority over
individual psychological processes in evolution, in individual life, and in
personal interactions. Social species (ants, birds) antedate
psychologically-minded humans. Humans began their history as animals with a rich
social behavior. Only later on a psychological self emerged. Social systems
existed first; individuation occurred within the context of an already rich
social life; tribal communion antedates individual freedom. As soon as we are
born, we have a social identity, as members of a sex, a generation, a social
class, a nation, and even a religion; only later we develop as individual
persons. In each relation, we begin by treating the other according to her or
his role (patient and doctor, worker and manager, etc) and only later we
personalize the relation. Biological existence precedes mind, but brain controls
our bodily function and health. Likewise, economics predetermine feelings and
ideas, but beliefs, ideas and choices, science and politics, control the
economy. Mathematics and psychology are equally relevant in all sciences.
Economic and spiritual values are equally relevant to social progress. History
shows a progressive personalization of social processes. Fractal self-similarity, homology and complexes:
The four primary processes and other simple patterns such as those included in
Fibonacci's spiral order and in Sarkovskii's novelty-generating series) repeat
at multiple levels of organization, generating fractal self-similarity.
Opposition is manifested in different, multiple, potentially infinite
pairs; for instance, bipolar flux and complementary information are two forms of
symmetry below and above asymmetric action, and action itself contains a
symmetry, namely energy potential. Chaos repeats the irregular patterns of
microscopic flux, and magnifies it through its sensitivity to initial
conditions. Color triads occur among subatomic particles and in vision.
Mendeleiev's table embodies linear order (atomic number), periodicity (families
of elements) and bifurcation (the lanthanides and the transition metals). Time,
opposition and co-creativity appear at the social level as the fundamental
patterns of age and generation, sex, and complementary classes. Primary forms
are embedded in many different ways in complex processes, but not in
every possible way, not in all respects, not all the time.
Physical evolution may determine how these basic forms become imprinted in
physical and biological structures. Biological evolution is imprinted into
anatomical structure, embryological development, and, most dramatically, in the
metamorphosis of amphibia and butterflies. Arm, leg, fin, wing, illustrate the
evolutionary concept of homology, namely a common origin that yields common
features. A simple level of organization, let us say, chemical,
contains as a particular subclass the more complex ones, such as biological;
everything that is biological is also chemical, but most molecules are not
contained in biological organisms. Thus the complex level contains within
itself, as its foundation, the simpler level. It is made of simple components.
Thus complexity is coded in the pattern in which the simpler components are
organized. Simple processes provide the basic patterns of complex processes. In
turn, complex processes organize the simpler physical actions that embody them.
For instance, feeling and thinking are encoded in sequences of action
potentials, which in turn are embodied in the physical movement of ions. The
same forms must therefore exist at all levels within an organism. Accordingly,
the lower and the higher levels --such as the timing of the heart and the
behavior of the organism-- must have each other's form (isomorphism). The
complex is homologous to the simple, but in turn it imparts its form. System components differentiate internally.
Miller's theory of living systems shows how subsystems function as
"organs". Systems have a "heart" that distributes energy for
action, and a "brain" that informs and coordinates. As the supplier of
energy, the heart reflects energy consumption as timing, and it is thus
modulated by a simple accelerating / decelerating opposition, the sympathetic /
parasympathetic nerves that mediate brain control. Thus cardiac patterns of
timing (complexes) reflect behavioral patterns. Complexes are patterns imposed
on simpler organs by the information delivered by the more complex level.
Complexes determined at a higher level overcome whatever attractors may function
at a simpler level of integration --this is what we call supremacy. Semantic creativity:
Alphabetical levels of organization [Pattee] consisting of a small number of
classes of exchangeable modules (atoms, nucleotides, letters) create unlimited
variety at higher levels (molecules, genes, language). Just as sexuality
procreates unique individuals, language constantly generates new sentences.
Alphabetical levels are common. Even the simple process equation generates
several alphabets as cycles: the cycle of 4, 3 and 6 (as colors), and 12 values
(as musical notes). System formation is thus creative. Each entity is a
system, a composite of many modules. As modules, from physical particles
to human persons, are exchangeable units, they can move from one system to
another, but belong more or less permanently to their class. System components
co-create their environment. Every entity creates an individual-centered
system, with its material self as a center, a surrounding field of energetic
interactions, and a larger field of communications. Complementation defines the
asymmetric relation between a concrete entity and its infinite environment --the
system it determines as its complementary opposite. Logical creativity: Human reasoning
is creative, because it generates new ideas from the refutation of old ones. To
be creative, method must include both logical no contradiction and dialectic
contradiction. Opposition is a certainty, but opposites imply and exclude each
other. We thus recognize the validity of dialectic inferences: if A then no-A,
but separated in time, space or respect. Where the opposite actually occurs, how
do opposites coexist, is a matter of empirical research. A two-valued logic must
be bipolar, including 1 and -1 rather than only 0 and 1, and more appropiatedly,
must include complementaries such as 1 and i (the square root of -1); such
bidimensional framework allows one to represent the coexistence of opposites.
The principle of no-contradiction should not be discarded by positing many
simultaneous worlds, or asserting that the entire mass of the universe was
concentrated in a point outside time and space, a conclusion that may also could
be taken as a refutation of the hypothesis that the expansion of the universe
has been linear, at the same rate as observed now. This is a rather unlikely
hypothesis in view of the non-linearity of any known process, and the
observation of galaxies older than the hypothetical genesis. Continuing creation: Instead
of a hypothetical big bang, we envision continuously evolving elementary
processes, each starting with convergence to an apparently static, linear
change, i.e. a period one composed of unidirectional advance (time) and constant
value (energy conservation). Feedback leads to bifurcations (opposition), and
create sinusoidal variation (harmony). These cycles occur in at least two
dimensions, real and imaginary. Thereby they generate tridimensional waves, like
sine and cosine, and the electrical and magnetic components of light, which are
the minimum of information. Greater feedback generates chaos, and period three,
and hence, by Sarkovskii's theorem, every other period and iterative
infinitations. Biological-like patterns result form bipolar feedback (random or
sinusoidal). There is a continuous creation: from particles to atoms to
molecules to organisms to social animals to human persons. 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, not toward disorder. The painter and his heart:
Iterative equations give us an opportunity to move from metaphor to science. The
painter of "Reflections" (Part I, figure 2) used a computer rather
than a brush. Pairing and crossing over process equations, and representing the
outcome in two dimensions to investigate the co-creation of opposites, we found
the landscape that fractally repeats itself (figures 1 and 2). A two-dimensional
representation of two independent of process equations produces much simpler
patterns. As shown in figure 1, a self-reflecting wave, which we call the seed,
is generated within a wide range of initial values, while within another wide
range of values, its mirror image is obtained. At the transition, both forms are
generated. Then, as illustrated in figure 2, the trajectory spins off to create
more complex forms, such as the factory with its smokestack, and fractally
repeating images of what we see as an oriental rendition of a landscape. Primed
by an awareness of opposition, asymmetry and symmetry, we are intrigued by shape
of the seed. Figure 1: Co-creative equations: the seed.
Patterns generated by paired equations a' = a + 0.1 * b sin(b), in the x axis,
and b' = b + 0.01 * a cos(a), in the y axis. Initial value for b = 0.001.
Initial value for a: Top: 6.37347. Middle: 6.373475. Bottom: 6.3736
We are engaged even more with the heart of the painter.
Medically, illness often affects the human heart --in a heart with feelings
there is more than enough heart to attack. The greater asymmetry of cardiac beat
time series in coronary illness, together with the fostering role of rushing
competitiveness and anger in this illness, suggests to us that coronary
illness results at least in part from a disproportion between high psychological
action and lower cardiac action. Depression facilitates coronary illness,
even when it involves a lowering of psychological energy as result of biological
deficit or overwhelming defeat, perhaps because it heightens anger and anxiety.
Process theory inspires these hypotheses, and provides methods to test them.
Socially, hearts need to be addressed. Individualism takes a great toll on the
human heart, both as indifference to the suffering inflicted on others, and as
acceptance of socioeconomic coercions that significantly contribute to illness
in each of us. Living in the wealthiest country, where infant mortality exceeds
that of any other industrialized country, we regard co-creation also as a
mission. Creation continues, and we participate as active protagonists. As
chaotic and biotic processes are extremely sensitive to initial conditions, even
our individual acts can have significant consequences, demanding ethical action.
Co-creating gives meaning to our life. Figure 2: Co-creative equations: Increasingly
larger views of patterns generated by paired equations as in figure 1, for
initial value for a = 6.3734761 (between middle and higher value in
figure 1). |
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