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Sabelli, H. and Linnea Carlson-Sabelli. (1996). A cosmic
gene? A biological model of complex systems. In honor to James Miller.
Proc. International Systems Society.
40th meeting, Louisville, Kentucky, July 14-19. Edited
by M. L. W. Hall. Sustainable Peace in the World System, and the Next Evolution
of Human Consciousness. pp 531-542.
A
Cosmic Gene? A
biological model of complex systems. In
honor of James Miller. Hector
Sabelli and Linnea Carlson-Sabelli Chicago
Center for Creative Development and
Rush University 2400
Lakeview, Chicago, Illinois, USA. Abstract:
The continuity of evolution requires that the same fundamental forms must be
expressed at physical, biological, and psychological levels of organization.
Thus Pasteur inferred the asymmetry of physical elements, such as now postulated
by string theory, from the asymmetry of biomolecules. The overall anatomy of
mammals, the classes of taste receptors, and the neurophysiological organization
of color vision, share a pattern of tridimensional asymmetry: (1) a
unidirectional axis related to action; (2) a bidirectional but unbalanced
opposition that codes information; and (3) a diversification creating a
hierarchy of complexity. These three patterns of organization (asymmetry,
opposition, and bifurcation) correspond to the three pillars of mathematics
according to Bourbaki and Piaget: lattice, group and topological theories. We
postulate that this tridimensional form functions as a cosmic generator
present at all levels of organization (self-similarity of the universe). At each
level, the generator produces creative development, that, as
embryological development, is both determined and creative. The three cosmic
forms (asymmetry, opposition, and diversification) are necessary and sufficient
conditions for evolution. Departing from standard thermodynamics, process theory
postulates that processes are unidirectional actions (not mechanically
reversible), tend to symmetry (not uniformity), and create diversity and
complexity (rather than decay towards disorder). This model serves as a
foundation for the process method illustrated by companion articles in these
Proceedings. Key words:
asymmetry; catastrophe; color; creativity; development; entropy; process theory;
taste; union of opposites. Science was
born in ancient Greece as physiology (meaning the account of nature), a
comprehensive theory of processes and evolution, in which the spontaneous
creativity of biological matter was taken as evidence, and as a model, for
spontaneous creativity in physical processes.
Only later, with the 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. James Miller's general theory of living systems [Miller, 1978]
represents a magnificent return to the biological model of complex processes. In
the same spirit, process theory [Sabelli, 1989; Sabelli and Carlson-Sabelli,
1989] is a modern reformulation of comprehensive physiology. It provides a
method applicable to data analysis [Carlson-Sabelli et al, 1990, 1992, 1994,
1995, 1996; Sabelli et al, 1994, 1995 a, b], and a comprehensive approach to
medical [Sabelli et al 1994], psychological [Sabelli and Carlson-Sabelli, 1991,
in press] and social [Sabelli and Carlson-Sabelli, 1995] issues. This article
examines how comprehensive physiology also suggests a model for the fundamental
forms and forces of nature. Miller examined analogies of function between
systems from cells to societies. Here
we explore a complementary avenue, namely homologies between processes
at different levels of organization. Homology:
Life is full of forms that travel across time, space, and species. Arm, leg, fin
and wing all derive from the same origin, and have the same fundamental
structure, modified to perform different functions. Biologists say that they
homologous, meaning that they have the same cosmic form, the same
"logos" (as in "logic" and bio-"logy").
Homology is not confined to life forms. The continuity of evolution
requires that the same fundamental forms must be expressed at physical,
biological, and psychological levels of organization. The profound homology
between nature and mind is evident in the fact that mathematics, a product of
human thought, so admirably describes reality. Because we do it so
"naturally", we fail to realize a most surprising occurrence: the
certainty with which we can discover facts about nature by manipulating numbers
generated in our minds. Mathematical calculations have much to say about the
real world, allowing us even to determine with surprising accuracy
interplanetary travel. Through mathematics, the human mind must undoubtedly tap
into fundamental physical processes. This correspondence of thought with reality
is understandable, because perceiving, judging and knowing, and the brains that
perform these processes, are the product of animal evolution [Nicolai, 1976;
Vandervert, 1988; Barham, 1990]. Adopting an evolutionary perspective, systems
theory interprets the similarities between processes at different levels of
integration as homologies [Bertalanffy, 1968]. Form:
The discovery of the DNA code, the invention of computers, and the development
of communication [Shannon, 1964], catastrophe [Thom, 1975] and chaos [Yorke and
Li, 1975] theories, fractal geometry [Mandelbrodt, 1982], and complexity [Zurek,
1990] have placed form, form-ation, and in-form-ation center stage in
contemporary science. "Form" is understood to include the outer shape
and the internal structure of objects, and the temporal pattern of processes.
Formation constitutes a fundamental, and irreducible aspect of processes. A car
is a car because of the form in which its matter is shaped, not because of metal
is made of, or the fuel that energizes it. Death does not change the mass,
composition or energetic content of a body, but represents a change in the
pattern of exchange of energy. Biological
forms may provide revealing examples for the fundamental form of processes and
structures. Biology by necessity focuses on anatomical and molecular structure,
and on functional and developmental patterns. Pythagoras developed the first
numerical law of science by examining a psychophysical relation (between the
perception of sound and the length of the chord), and Cook [1979] identified
Fibonacci sequences among the fundamental life forms. One may thus learn about
fundamental forms of nature by examining patterns at the biological level. In
this manner Pasteur discovered the universality of asymmetry, a pattern now
confirmed at all levels of organization. Pasteur's
cosmic asymmetry: Based on the asymmetry of biomolecules, Pasteur
postulated that asymmetry is a feature of fundamental physical processes. This
audacious hypothesis has been confirmed by modern physics (non-conservation of
parity in beta decay [Yang and Lee, 1956]; asymmetric strings rather than
symmetrical particles as the fundamental components of matter [Scherk, 1991];
symmetry-breaking steps at every step of cosmological evolution [Anderson and
Stein, 1987]). It is also evident in biological, social and psychological
processes and structures [Clynes, 1969; Corballis and Beale, 1976].
Pasteur's asymmetry illustrates the concept of cosmic form
--"cosmic" means universal, ordered and beautifying (as in
"cosmetic"). Pasteur's
asymmetry highlights a shift of focus from composition to form. Pasteur's
inference also illustrates a method of reasoning that takes biological data as
fundamental, and capable of illuminating other disciplines, as contrasted to
exclusive attention to reduction of biological complexities to simpler physical
law. The high degree of abstraction
involved in the concept of asymmetry is what makes it useful, and capable of
providing insights into other fields of science. Following Pasteur's lead, this
article describes an abstract pattern of tridimensional asymmetry (figure 1)
shared by disparate biological processes, and suggests that its repetition may
serve to generate a multiplicity of patterns observed in physical and
psychological processes. Anatomical
form: tridimensional asymmetry:
Just as we learn much about a man by inspecting his hands, but we learn
more by examining his face and head, so we can learn much about the universe by
scrutinizing rocks, but much more by examining man, pointed out Nicholas of
Cusa. The overall anatomy of most animal species manifest 3 different forms of
asymmetry in the three dimensions of space (figure 1): there is direction of
locomotion and nutrition, an incomplete bilateral symmetry (two eyes, ears,
lungs, heart, limbs, etc), and a hierarchical organization of digestive
(endodermic), circulatory (mesodermic) and neural (ectodermic) along a third
axis. This triaxial organization is
likewise evident in the mammalian central nervous system: (1) dorso-ventral
asymmetry, as sensory areas are located dorsally, and ventral areas play motor
functions, corresponding to the direction of movement in humans; (2) asymmetric
bilaterality, a partial symmetry of right-left opposites that serves for
walking, apprehending, directional vision, and complementary thinking modes,
with one predominant side; (3) a hierarchy of complexity (corresponding in most
animals to the direction of movement, and in humans to the vertical dimension
singled out by gravity), generated by the bifurcation of simpler and older
spinal pathways into more recent structures with multiple parallel pathways. The
lower bulbo-spinal levels regulate simpler and essential functions such as
temperature, respiration, and posture, and have priority in the evolution of
species and in the development of the individual, as well as in mediating the
input and output for the higher levels. Diencephalic
and paleocortical levels coordinate simple social behaviors and emotions.
Neocortical levels are the substrate for personal and creative functions, and
control the function of the lower levels (cortical supremacy). Since brain has
been constructed and selected by natural evolution as the most accurate organ to
portray nature, its organization must correspond to the actual organization of
nature. We have thus proposed asymmetry, opposition and bidirectional
hierarchy as general principles. Evolutionary priority and informational
complexity are opposites in the bidirectional relation between levels of
organization. Simpler processes (low density of information) preexist, coexist
with, outlast and predetermine complex processes (priority of the simple).
Complex processes are made of, and are surrounded simple processes, yet they
predominate locally, because their higher density of information per unit of
matter/energy increases their efficacy and creativity (supremacy of the
complex). This concept offers
an alternative to reductionism, that stresses the simple material foundations,
explaining psychological processes as biological, as well as to philosophical
idealism, that divorces psychosocial processes from their material roots. Taste:
A similar logical structure is illustrated by the organization of taste
sensations (figure 1). Taste is a biological phenomenon, not a chemical
property; genetic traits determine that some individuals taste some substances
as bitter while others find them tasteless [Meiselman and Rivlin, 1986]. Taste
serves as a vehicle for communication between plants and animals. Plants produce
fruits that animals find pleasantly flavored, sweet-tasting to eat, and thereby
favoring seed dispersal. Many plants also produce noxious alkaloid toxins
dangerous to ingest in quantity. Animals
often find these defensive chemicals to be bitter-tasting. Taste thus provides
information essential for survival for plant-eaters. Taste
perception uses a logical arrangement that is formally similar to that of the
central nervous system (two unidirectional axes and two orthogonal opposites).
Salty taste, elicited by sodium and related cations, with lesser contribution by
the associated anions, measures an action, osmotic pressure, fundamental for the
regulation of water intake. Saltiness has no opposite, so it is a unidirectional
scale, and hence similar, in this abstract way, to the dorso-ventral asymmetry
that corresponds to action in the human body.
Sweet (which indicates nutritious carbohydrates), and bitter (that
signals the presence of potentially toxic alkaloids) are opposites (like right
and left) that can be combined together (as in chocolate) without neutralizing
each other. Sour detects hydrogen cations, and hence acids, which may be found
in green fruits and also as products of fermentation and decomposition of
biological matter; thus acidity is inversely related to complexity,
corresponding in this abstract respect to the vertical dimension in the human
central nervous system. It is a unidirectional scale, as alkaline substances do
not have an opposite taste. Color vision:
A similar logical structure is illustrated in the case of color vision.
Color has no physical existence: electromagnetic waves constitute a
continuum of frequencies. The eye creates color, three colors, to be exact,
which in their multiple combinations generate the infinite gradations of the
color wheel, and beyond the colors of the solar spectrum, the wealth of earth
colors, the colors of flesh and wood. Color is the art of life. Color is an
invention of flowers and bees, and of human hands painting faces in canvas, and
woman faces with cosmetics. Aristotle
considered color as a secondary property, not comparable with primary properties
such as weight and extension. With foolish arrogance has been labeled "an
illusion of the senses". On the contrary, color vision is a fundamental
product of biological evolution. The trifurcation of light into color in the
retina marks the transition from physical to biological processes. We propose
that such a trifurcation reveals the cosmic form of creation. Between the 1
dimensionality of light wave frequencies and the many dimensionality of cortical
colors, biological organization arises at the retinal level. Land [1959], the
inventor of Polaroid, discovered that two beams of polarized light of different
color, provided they are at opposite sides of a central wavelength, are
sufficient to produce the spectrum of color sensations.
With non-polarized light, three frequencies are needed. The retina has
three pigments sensitive to color, corresponding to orange, green and violet,
indicating a tridimensional organization. A different
pattern of organization emerges at the neural level. Neurons respond selectively
to colors with either excitation or inhibition; on-and- off discharges cancel
each other, thus showing to be mutually antagonistic.
A given cell responds to either yellow or
blue (but never to both simultaneously) according to the relative
intensity of the excitatory and the inhibitory inputs. Likewise green and red
are opponent processes in other cell types. Thus, at the neural level there are
4 primary neural colors, organized as two sets of opposites: red versus green,
and yellow versus blue. These oppositions can be demonstrated by contrast
experiments, by observations in color-deficient individuals, and by
consideration of the limits of the visual fields for each color [Hurtvich,
1981]. At the visual
cortical level, the combinations of these inputs allows us to distinguish an
extremely large variety of colors, perhaps an infinite number of them. At the
even higher level of organization, languages distinguish a much more limited
number. Significantly, artists construct a system of 8 colors, 3 primaries, 3
secondaries, black and white. Peculiarly, the retinal primary colors are
considered as secondary colors by artists, who choose red, yellow and blue as
primary colors. The primary colors form a remarkable logical structure (figure
2), as the sum of two primary colors generates a secondary color that is the
inverse of the third primary (e.g. blue + yellow = green = complementary of
red), and their various binary combinations generate an infinity of colors,
including two extremes, black and its inverse white. The addition of light beams
of complementary colors produces white light, and the combination of pigments of
complementary colors produces black. Colors thus have the properties of a group
(each element of the set has an inverse) and of a lattice (an ordered set with
an upper and lower element), two fundamental mathematical structures. Many features
of the neural organization of color can be represented by two orthogonal axes in
a plane. Note, however the metamorphosis from 3 retinal primaries to 4 neural
primaries: red and green are opposites at both the retinal and the neural level,
whereas blue and yellow, that appear as opposites at the neural level, are not
opposites at the retinal level. Thus the neural tetrad of colors appears to be
organized according to the same formal structure as our bodily axes and our
perception of taste (figure 1): there one pair of opposites (red and green) and
two unidirectional axes (blue and yellow), although the latter behave as
opposites in some contrasts experiments. In all three cases we have 1 set of
opposites, 3 dimensions, and 4 primaries. The color
metaphor serves to express a number of basic concepts about processes.
First, that there are three complementary classes, not two opposites.
Second, for each color there is a complementary opposite, an anti-color,
a negative, a negation. Third, the sum of two colors is equal to the complementary
opposite of the third. Thus, yellow
and red combine to form orange which is the absence of blue, the negative of
blue, the anti-blue, the no-blue. The logical
organization of colors fits human ideas and feelings, so colors acquire symbolic
meanings (emotional, political, religious). Even more strikingly, the algebra of
colors describes types and interactions of elementary particles. Quantum
chromodynamics:
According to currently accepted physics, quarks (or anti-quarks), entities that
never are observed as independent particles combine as triplets to make hadrons
(such as protons and neutrons), and as pairs to make mesons. Regarding the
superstrong force that binds them together, classes of quarks and of anti-quarks
can be described as colors. There are three "colors" of quarks, and
three colors of "anti-quarks", while all observable particles are said
to be "white". As in the
case of mixing lights, "white' can be produced in two ways: adding together
three primary colors, or mixing a primary color and its complementary
anti-color. As quarks do not really
have color, one may conceive of this description as a happy analogy of no deep
consequence, but the fact that fundamental physical entities conform to the same
mathematical scheme as visual colors may also reflect a true homology. Development and
catastrophes: Having observed the transformations through which eggs
become adult organisms, Aristotle proposed that embryological development may
serve as a model for all processes. It is still the most common model for
social, economic, and psychological growth, maturation and individuation.
Aristotle proposed that the form of adult organism is contained in its
seed. Form is thus embodied in
material structure, not separated from it, as postulated then by Plato and in
our times by Whitehead [Emmet, 1966]. More than twenty centuries later Mendel
inferred that biological form and its development were encoded in a multiplicity
of genes, and Avery specified that the DNA molecules contained
development-directing information in their structure. The discovery of the
double-helix structure of DNA demonstrated how specific oppositions served to
carry and reproduce information. The DNA molecule itself also embodies linear
order, and a hierarchical relation between genes. Likewise significantly, the
pivotal process of differentiation is described by the tridimensional model of
catastrophes that embodies in still another way the cosmic form of two
asymmetric axes, and one bipolar opposition. Whereas
traditional models focused on fixed sequences of predetermined stages, actual
development is also diversifying and creative, as illustrated by human
individuation. Even embryological development is epigenetic, i.e. there is an
increase in complexity which cannot be accounted for by the unfolding, growth,
or decomposition of pre-formed structures, already present in the egg [Waddington,
1968]. Development may thus serve
as a model for evolution, which is both creative and constrained by the laws of
physics; note that the term evolution itself means unfolding, implying a
predetermined path. Also physical processes may represent the unfolding of an
implicated order; in fact, matter and mind may share the same implicate order [Bohm,
1985]. Creativity in
biological development has been modeled by the concept of a predetermined
branching of channels that canalize the differentiation into tissues [Waddington,
1975], a process which inspired catastrophe theory [Thom, 1975], a mathematical
description of qualitative changes from one opposite to another. The simplest
catastrophes are governed by two control variables --a bifurcating control
parameter that at low values leads to a continuous outcome, while at high values
the outcome is discontinuous; and an asymmetric control parameter that at mid
values is associated with large changes between the modes, while at extreme
values is associated with small changes around the modes. A catastrophe is hence
a surface in 3 dimensions. The two dimensions determined by the control
parameters appear to reflect the sum and difference of opposing forces. Choices as
catastrophes: Using the phase plane of opposites (figures 1 and 2 of
Sabelli and Carlson-Sabelli, in These Proceedings) to measure separately
attraction and repulsion between individual persons in the clinical study of
interpersonal choices [Carlson-Sabelli et al, 1992, 1994], we found that the
difference between opposite motivations provides information regarding the
direction of the outcome (asymmetric control parameter), while both opposing
forces contribute to provide psychological energy (bifurcating factor as the sum
of opposites). Thus, the bifurcating parameter could be calculated as the sum of
the underlying opposing motivations, while the asymmetric parameter was the
difference between them. These results suggest to us that catastrophes, the
simplest form of non-linear, i.e. creative interaction, result from the union
and difference of opposites. The relations
between sum and energy, and between difference and information, are intuitive in
the case of psychological processes, but may be equally applicable to physical
interactions [Sabelli and Carlson-Sabelli, 1992].
Taking catastrophes as the simplest case for the formation of
tridimensional organization, we proposed that structure formation is governed by
control parameters similar to those that govern catastrophes. The bifurcating
factor b is a function of total energy flow (action), and therefore sums
opposite actions, while the asymmetric factor is a function of the information,
and therefore of the difference between the opposites. Complex patterns and
structures organize when opposing forces are equal and intense. The formation of
matter itself represents a similar process of structure formation in high
intensity energy processes. Based on the
catastrophe model, Sheldrake [1981] has proposed the existence of morphogenic
fields that have a causal role in the development and maintenance of form at all
levels of complexity, thus replacing the concept of genetic programs in biology
--as contrasted to the current model, that extends it to physics. Mathematical
forms:
Three axes, with three different forms of asymmetry, are thus observed in
disparate biological processes, such as body anatomy, taste, color vision, and
developmental catastrophes. We can portray these three types of asymmetry as
forms: an arrow for order, two different and opposing arrows for opposition, an
a Y for bifurcation.
Significantly,
the three forms of asymmetry appear to correspond to the three disciplines that
Bourbaki and Piaget considered as the pillars of mathematics: lattice theory,
that studies order; group theory, that studies opposition; and topology, that
studies change with continuity, as in the bifurcations of rubber geometry.
Within topology, McNeill's thoroid model [1994] also highlights some of the
features of the cosmic generator discussed here.
A companion
article [Sabelli and Carlson-Sabelli, 1996] describes these cosmic patterns as
integers, 1 for unidirectional order, 2 for roughly symmetric opposition, and 3
for the creation of structure, and from these creating further complexity,
beginning with 4 for the repetition of opposition, 6 for the coexistence of
trifurcation and bifurcation, and chaos as result of repeated bifurcations.
These numerical qualities are present in the examples discussed above.
From physiology
to physics: The similarities in the structure of bodily axes,
tastes, and colors, suggest that the tridimensional tetrad of opposites may
represent a fundamental form of biological processes, and perhaps also of
physical processes. The main focus of current physics is on fundamental forces
and particles. Physics does not study morphogenesis directly, nor does form
enter in its fundamental equations explicitly, but form and structure constantly
emerge in its descriptions, as illustrated by the fundamental role of group
theory, symmetry, quantum numbers, and orbital forms.
The usefulness of studying fundamental components is supported by the
enormous advances accomplished by high energy physics and by molecular biology,
yet knowledge of composition and of general principles is not sufficient to
account for the specific processes that give a particular form to a mountain, a
continent or a galaxy. Further, analysis may not reveal true elements: the once
postulated indivisible atoms were divided into "elementary" particles,
in turn protons and neutrons were shown to be made of quarks, and now quarks
appear to be formed by still smaller particles, suggesting that matter can be
broken down infinitely, so the "smallest particle" is defined by the
amount of energy applied. In this light, the quest for fundamental forms may be
an essential complement to the elusive quest for "elementary
particles". In the same manner as genetic information is encoded in the
molecular structure of DNA, we may expect that physical forms, such as patterns
of change and material structures must embody the laws of nature. Asymmetry is a
fundamental aspect of physical processes and entities. Contemporary string
theories portray the most fundamental entities as line-like rather than
point-like particles, hence implying asymmetry. Physical action, defined as the
product of energy x time, is asymmetric. Action
is the fundamental constituent of nature. Nothing is simpler than action (the
Planck constant is an action), and everything is action: matter is equivalent to
energy (Einstein), and energy exists only as flow. Action, and hence time, flows
in only one direction, yet mechanics portrays time as reversible (thus negating
the creation of novelty). Only thermodynamics allows for anisotropy
(differentiation between series of events read forwards or backwards), and even
in this case the monotonic increase in entropy is diminished in significance
because it is viewed as a statistical property of large number of entities or
events, not applicable to individual cases, which can be reversible. Postulating
action asymmetry as a fundamental axiom of nature thus suggest a change from
current theory, and would align physics with evolutionary theory. Likewise opposition
represents a fundamental aspect of physical processes. Light, as other forms
of energy, illustrates the association of asymmetric flow with orthogonal
opposites, as the electric and magnetic fields of the sinusoidal electromagnetic
wave are perpendicular to each other and to the direction of wave motion (figure
3). Positive and negative, proton and electron, attraction and repulsion, matter
and void, every physical process involves opposites. A large number of physical
processes and entities can be understood in terms of symmetry, hence the
enormous role of group theory in physics. Change, difference, and communication
are particular instances of opposition. Information is communication, news of a
difference [Bateson, 1979], and can be coded in a binary code, as it is done
routinely in computers and many other digital devices. Even more fundamentally,
Bohr's principle of complementarity [Capra, 1975] indicates that to account for,
or to explain, a certain event, one needs two distinct modes of description; and
further, these two forms of representation are mutually incompatible.
As the Planck
constant has the dimensions of action, we speculate
that the most elementary form of action is embodied in the creation and
destruction of pairs of oppositely charged particles in the vacuum within the
boundaries of the Planck's constant. Within
the idealistic epistemology that has dominated quantum mechanics, this is
interpreted as uncertainty. Notwithstanding,
the creation and disappearance of particle pairs is a physical reality --for
instance, it creates a measurable pressure between closely positioned walls.
The process thus results in a measurable asymmetry--the net pressure
created by the creation of particle pairs.
It obviously involves the separation and union of opposites (figure 4A),
and an increase and a decrease in the number of entities (figure 4B) which may
be interpreted as "complexity". The
difference between the form of the void and the form of existence appears to be
the symmetry of the oppositely charged particles created within the Planck
boundaries, and the asymmetry of the oppositely charged protons and electrons
that constitute matter. Physical
systems are obviously organized in a hierarchy of complexity.
Simplicity and complexity are related to separation and union. In the
above example, separation increases complexity from void to twoness, while union
reduces complexity from two to none. In physical systems, separation can
increase complexity, just as division and differentiation do in biological
systems. On the other hand also
union can increase complexity, as in system formation. Most systems theories
focus on levels of organization according to system formation: subatomic,
atomic, molecular, biological, social, planetary, solar, galactic, etc. Cosmic forms
and emergent forms: Useful as this is, the hierarchy of systems portrays only
one aspect of complexity. Thus the
biological and the psychological level are widely different in complexity,
although they may be co-extensional. Further,
social processes are in many ways simpler and older than psychological processes
[Sabelli, 1989; Sabelli and Carlson-Sabelli, 1995].
Thus complexity has another dimension not reflected by system formation,
but fundamental to understand the relation of priority : supremacy discussed
above. Further, most natural processes and structures have a fractal geometry [Mandelbrodt,
1982; West and Goldberger, 1987]. Fractal structures characteristically have
patterns that repeat at many levels (self-similarity). Further, fractal geometry
and chaos theory demonstrate how the repetition of a simple form, or the
iteration of a simple equation, can create unbound complexity, including both
chaos and organized structures. We thus propose a self-similar universe
resulting from the iteration of the same cosmic form. Simpler levels can be
expected to have simple but universal forms. These simple forms appear to be
repeated, iteratively, at each of the more complex levels of organization --in
other words, there are units, oppositions, tridimensional structures, and a
zero, at the subatomic, atomic, molecular, biological, social and psychological
level, creating a fractal self-similarity between levels of organization. In
addition to these universal forms, complexity results from the creation of new
forms via the interaction of simpler processes. A cosmic
generator:
As only the laws of logic and the laws of physics may be expected to
apply to all levels of organization, these observations suggest that a tridimensional
tetrad may reflect be a fundamental pattern of organization already present
in elementary physical processes. It is significant that both mathematics and
physics may lend support to this view, and even more indicative that the model
suggests concepts applicable to physics and to logic. The same form
is manifested in action, information and structure, but out of phase in time:
each action prior to the structure that it produces, each structure prior to the
action it produces. We propose that this tridimensional tetrad is a cosmic
generator that drives and organizes novel and more complex (multidimensional)
forms. Adopting a process perspective, we focus on asymmetry as action, and on
form as formation. A cosmic form is a cosmic action, a gene, a program, a seed.
The term "cosmic gene" represents a metaphor based on analogy, a
legitimate and widespread method of reasoning in modern science,
but it points to the possible existence of a fundamental homology, as the
cosmic form is also embodied in DNA. The existence
of homologies implies common developmental paths. In the case of biological
development, morphogenesis is explained in terms of programs, analogous to those
of a computer, embodied in the DNA structure. The concept of creative
development proposed here extends the notion of genetic programs to physical
processes. Just as the same DNA is present in every cell of the organism,
regardless of their differences, the same cosmic form would be shared by all
processes and structures. Postulating a
cosmic form does not deny diversity. Enormous species differences can be
produced by minor changes in the genetic material, as illustrated by the 99%
overlap of human and chimpanzee DNA [King and Wilson, 1975]. In the same manner,
the same basic laws of nature can produce unbound diversity. Just as genetic
information is contained in the form of DNA, the laws of nature can be described
as cosmic forms. As portrayed by the logistic equation, fundamental processes
leading to diversification and complexity include opposition [Sabelli and
Carlson-Sabelli, 1996] and triadicity [Yorke and Li, 1975].
The multiplication of color classes by the combination of 3 primary
colors also indicates that trifurcation is a generator of diversity and
complexity. Thus a cosmic form that includes opposition and triadicity can
function as a program that guides development, creating diversity. This
completes the analogy with the genetic role of DNA structure. The model
implies that nothing is simpler than all 3 asymmetries, not that this is the one
and only universal form. Naturally something is gained by recognizing the cosmic
forms in a given processes, but the purpose is not to reduce the
multidimensionality of higher processes, but to describe it in an orderly
fashion. In summary,
processes as well as structural units (subatomic, atomic, molecular, cellular,
etc) have at least three axes: one asymmetric dimension that corresponds to
action, or temporal change; one asymmetric dimension that corresponds to
complexity, or hierarchy; and one pair of opposites which codes information. All
reality is a process organized along two types of dimensions (unidimensional
action and hierarchy vs bidimensional opposition such as in communication), and
two types of opposition. Action (energy
x time) and hierarchy (structure, from matter to life to mind) are
unidirectional dimensions, and they complement and oppose each other as temporal
priority gives power to the simple, while at each moment of time the most
complex has supremacy. Priority and
supremacy each are asymmetric relations, defined along dissimilar axes, even if
they oppose each other in a certain way.
There is
another type of opposition, such that existing between positive and negative
communication (true or false, harmonic or conflictual, sweet or bitter, from A
to B or from B to A), determining a bidimensional plane.
These opposites are similar in nature (they are both electrical charges,
tastes, messages, etc). Information is carried by the difference between
opposites (asymmetry), as well as by their sum (e.g. bittersweet is a distinct
taste, favored by some). A natural logic:
Rational thinking as well as unconscious psychological processes fit the
model presented here: (1) There is a unidirectional flow of consciousness
(William James) which includes an inborn awareness of physical time. (2) There
is a constant awareness of opposites as interlocutors, as well as a tendency to
think in opposites, as every idea evokes its contrary, that serves to organize
many primitive societies. Oppositions coexist in the unconscious (Freud) but
also in conscious thought. (3) There is an inborn awareness of tridimensional
space, whether awake or asleep, as well as a widespread tendency to think in
triads, and to create tripartite classifications (from the Trinitarian concept
of God to Freud's tripartite model of the mind). Further, higher degrees of
complexity, as well as chaos, occur during both wakefulness and sleep.
As truth is the correspondence of thought with reality, rationality must
consist in the correspondence of thinking processes with natural processes. As
scientists and as clinicians we may thus benefit from a model of processes. It
is known that certain patterns of thinking, such as black and white thinking,
promote psychiatric dysfunction, including neuroses [Adler, 1954], depression
[Beck et al, 1979], and borderline disorders.
As adaptation to ever changing circumstances is required for physical and
emotional health, static thinking is likewise dysfunctional. Notwithstanding,
traditional logic focus on the permanence of identity, the mutual exclusion of
opposites (principle of no-contradiction), and the exclusion of third
alternatives. According to Freud, conscious thinking followed these laws of
logic; only the unconscious allowed uninterrupted change and the coexistence of
opposites. These static portraits
of rational thinking derive from static views of nature, that must be replaced
by evolutionary views. This is
particularly important in psychiatry, as correcting dysfunctional cognitive
affective structures have been shown to have psychotherapeutic value [Beck,
1979]. It may also be useful to correct dysfunctional social attitudes. This
psychotherapeutic value recommends consideration of this model of creative
development, provided that we remain aware of the intrinsic fragility of any
over-arching scheme. Practical
applications:
"So what?" is the standard question that professional scientists and
practitioners raise when confronted with speculative models. Whereas disregard
of the intrinsic value of understanding seems flat, and requiring theory to be
immediately translatable into testable hypotheses reflects ignorance of the time
table of science, it seems useful to ask pragmatic questions, because they guide
us to look for experimental predictions and practical methods that are not
derivable from earlier models. Each form of asymmetry suggests particular
research strategies and hypotheses. Temporal
asymmetry indicates the need to collect time series data, and leads us to
replace the static methods of traditional and mathematical logic by dialectic,
dynamic logic [Sabelli, 1984, 1995]. Focusing on mood processes [Carlson-Sabelli
et al, 1990 Sabelli et al, 1990] reveals data that cannot be uncovered by
measuring mood states, no matter how exactly. Likewise measuring the entropy of
processes (as measured by a time series of observations [Sabelli et al, 1994,
1995; Carlson-Sabelli et al, 1996] provides a concept of entropy as symmetry and
diversification that contrast with the notion of entropy as disorder derived
from the study of the entropy of states. Consideration
of opposites provides alternative hypotheses as discussed by Lakatos' modern
classic [Lakatos, 1976]. The coexistence of opposites provides a method, the
diamond of opposites [Carlson-Sabelli et al, 19] as a method to measure
coexisting opposite processes which has been applied in biological
[Carlson-Sabelli and Sabelli, 1996], sociological [Sabelli and Carlson-Sabelli,
1995], and psychological [Carlson-Sabelli et al, 1992, 1994] research. The
diamond of opposites also provides an alternative to the Venn diagrams of
mathematical logic, that exclude opposition.
The principle of duality in projective geometry allows one to discover
new theorems by an almost mechanical procedure [Kline, 1955]. All statements of
projective geometry can be "dualized", i.e. a second true statement
can be obtained merely by interchanging the words point and line in a theorem
(e.g. as two points determine a line, two lines determine a point). This
symmetry of point and line in projective geometry corresponds to a more general
duality of entity and relation. It is noteworthy that projective geometry is
more physiological and logically more fundamental than both Euclidean
non-Euclidean geometries (which can be derived as special cases). Triadic
thinking promotes creativity, as discussed by Torre [1996] and by
Carlson-Sabelli and Sabelli [1996] in these proceedings.
Consideration of a hierarchy of complexity lead us to study processes in
multiple dimensions. In the study of heart rate variability, a measure of
established prognostic value, methodical analysis in 1, 2, 3 and multiple
dimensions [] reveals patterns beyond those observable with time-domain and
spectrum analysis alone. Pilot studies indicate the possibility of detecting
psychosis by measuring the dimensions of cardiac rhythms in the
electrocardiogram [Sabelli et al, 1995 a,b].
The attractor
of evolution: The form of the cosmic gene is by necessity mirrored in
the form of the cosmic attractor. Process theory thus postulates that the
universe tends towards a complex attractor that includes a point attractor, a
cyclic attractor that alternates between opposites, and a tridimensional
structure. And further, as these
nested attractors interact, we expect the development of an enormous complexity.
Hence the maximization of physical entropy, biological evolution, and cosmic
creation, are different aspects of the same process of creative development,
organized by the asymmetry of action, the symmetry of opposition, and the
hierarchy of complexity. We speculate that these forms are necessary and
sufficient to create unbounded complexity. Symmetry increases in multiple
dimensions, at the very least the three dimensions of physical space; the
tendency towards tridimensional symmetry might be sufficient to create
complexity. This speculation is
suggested by the fact that period three implies chaos [Yorke and Li, 1975]. We
take period three as a simple model for tridimensionality, and chaos as a simple
case of complexity. We thus
speculate that a tendency to trisymmetry creates complexity. As illustrated by
empirical studies already quoted, these concepts have both methodological and
theoretical implications. Let us state
these concepts in simple words. A person's life is a paradigmatic example of
creative development, including its various aspects --entropy maximization,
evolution, and creation. Throughout
life, our cells grow, reproduce, and die. We grow up and we grow old, at each
time, from birth to death. In the course of our life we create our person,
including our own spirit (or shrink it with the help of head-shrinkers of
psychotherapeutic, ideological or religious persuasion), undoubtedly because we
are born with spirit, so we participate in, and contribute to create (and to
destroy), spirit in the universe. Thus creation and destruction coexist at each
point, and develop organization and complexity, not just random disorder. The
pattern of life is homologous to the form of our body, both reflecting the
fundamental laws of the universe: asymmetric action, opposition, and simple
complex hierarchy. The form of the cosmic gene is by necessity mirrored in the
form of the cosmic attractor, that some call God and some call entropy. Acknowledgements:
We are thankful to the Society for the Advancement of Clinical
Philosophy, to Mrs. Margaret Trobaugh, and to Mrs. Maria McCormick, for their
invaluable support for this research.
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Tridimensional asymmetry
in the overall anatomy of most animal species, in the organization of taste, of
color, and of social categories. Figure 2: The
color cube: a lattice and a group. Red + Green =
White White - Red =
Green = Blue + Yellow Blue + Orange =
White White - Blue =
Orange = Red + Yellow
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of the Planck constant. |
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