The following list describes
each of the scientific and mathematical disciplines displayed on the
accompanying "whale" diagram. After each description are three items
Algorithmic
Complexity Theory:
One of the important
sources of contemporary conceptions of what is complex about complex
systems. Specifically, algorithmic complexity is a measure of complexity developed by the
mathematician Gregory Chaitin based on earlier work in Information Theory founded by
Claude Shannon and work on probability and information conducted by the by the Russian
mathematicians Kolmogorov and Solomonoff. Algorithm complexity theory defines and
measures complexity in terms of a computer algorithm (or computer program) which could
generate the data coming from a particular complex system. In other words, the degree of a
system's complexity is a matter of how large a computer program would be needed to generate
a bit string derived from the system under question (sequence of 0's and 1's, or the binary code
at the core of computer languages). Measures of complexity utilized in the study of Artificial
Life and similar cellular automata have been heavily influenced by Algorithmic Complexity
Theory.
Themes: Definition
and measure of complexity; relation of complexity to both
randomness and order; recognition of the novelty of emergent structures; predictability
and unpredictability of complex systems.
Researchers/Theorists:
Gregory Chaitin, Charles Bennett, Murray Gell-mann
Glossary: Algorithm;
Complexity (and Algorithmic Complexity); Logical Depth
Artificial Intelligence
(AI):
The design of "smart"
machines and robots which, obviously, have tremendous ramifications in
our "Information Age." By exploring what intelligence means to humans in order to mimic it
in
machines, AI has been instrumental in the recent explosion of research in the cognitive
processes of human beings. In addition, the development of intelligent machines has important
implications for computational theory. AI has facilitated the search for basic structures of a
complex system complex enough to be able to think. Consequently, AI has explored such
themes as the hierarchical relationship of cognitive mechanisms, devices for simplifying or
complexifying the dynamics of systems, and the elaboration of how interconnectivities effect the
functioning of a complex system. Artificial Intelligence was partly spawned from earlier work in
Cybernetics with servo-mechanisms, and has been influential in modern Computational Theory.
Themes: How
complex systems process information; insight into cognitive processes
occurring within and between human beings; the role of hierarchy in complex systems
Researchers/Theorists:
Herbert Simon, Marvin Minsky, Roger Shank, Douglass
Hofstadter, Danny Hillis. A significant and vociferous critique of some of AI's
conclusions applied to human cognition has been the philosopher John Searle.
Glossary: Complexity;
Hierarchy
Artificial Life:
The study of the
life-like patterns emerging in cellular automata and related electronic networks.
Pioneered by the computer scientist Chris Langton, and experimented with extensively at the
Santa Fe Institute. The study of Artificial Life is promising insights into natural processes leading
to the build-up of structure in self-organizing, complex systems. It is closely allied with research
into Random Boolean Networks (Stuart Kauffman) and Emergent Computational Theory.
Themes: Computer
simulations exhibiting self-organizing processes and emergent
structures
Researchers/Theorists:
Chris Langton; Doyne Farmer; Norman Packard; Thomas Ray;
William Sulis
Glossary: Artificial
Life; Cellular Automata; Boolean Networks; Emergence; Self-
organization
Autopoiesis:
A theory concerning
what accounts for the essence of a living organism as opposed to a
nonliving entity. Developed by the Chilean scientists Humberto Maturana and Francisco
Varela, the theory of autopoiesis suggests that a living organism can be understood as a
circular, autocatalytic-like process having its own survival as its main goal. The phenomenon of
self-organization has sometimes been understood in terms of autopoeisis. The theory's
emphasis on the circular "closure" of the living organism can be seen as a "remedy"
for the over
emphasis on "openness" found in "open systems" theory. Theories of autopoeisis have
been
used in discussions of the emergent structures in Artificial Life and other cellular automata.
Themes: How
self-organizational processes require some kind of boundary or
containment; the self-referential aspects of complex systems
Researchers/Theorists:
Humberto Maturana; Francisco Varela
Glossary: Autopoiesis;
Boundaries; Self-organization
Boolean Networks:
Electronic arrays
developed by the medical researcher and evolutionary biologist Stuart
Kauffman. These arrays are used to study self-organizing processes and the emergence of new,
unexpected structures. The nodes in these arrays are connected to other nodes according to
certain "boolean" or logical rules. Using the N/K Model of Boolean Networks yields insights
into how manipulating the rules, the number of traits, and the number of inputs, leads to various
self-organizing, emergent patterns. Of particular importance is the use of the construct of
"fitness landscapes" which are graphical representations of the adaptive or fitness values
of
various modifications of genetic (and analogous) materials. The study of random, Boolean
networks has provided important insights into how natural adaptive may occur, i.e., how
innovations arise and the conditions needed to facilitate innovation.
Themes: The
dynamics of adaptation, innovation, and learning; understanding the
emergence of order (Kauffman's "order for free") out of the nonlinear dynamics of the
networks
Researchers/Theorists:
Stuart Kauffman; William Macready
Glossary: N/K
Model; Random Boolean Networks
Catastrophe
Theory:
A mathematical
theory in the field of topology formulated by the French mathematician Renee
Thom. A catastrophe is a discontinuous change during the evolution of a system modeled by
structural equations and topological folds. Catastrophes are governed by control parameters
whose changes of values leads either to smooth transition at low values to abrupt changes at
higher, critical values. Catastrophes indicate points of bifurcation in dynamical systems.
Catastrophe theory provides critical insights into occurrences of abrupt change in complex
systems.
Themes: Insight
into abrupt changes in complex systems
Researchers/Theorists:
Rene Thom; Christopher Zeeman; Stephen Guastello
Glossary: Bifurcations;
Catastrophes
Chaos Theory:
The study of dynamical
systems characterized by sensitivity to initial conditions so that although
the behavior is constrained within a particular range, the future behavior of the system is largely
unpredictable. Unlike a random system which is also unpredictable, chaos is brought about by
deterministic rules. Such systems are constituted by nonlinear, interactive, feedback types of
relationships among the variables, components, or processes in the system. Chaos was first
glimmered by the great French mathematician Henri Poincare a century ago. However, it wasn't
until 1963 that the metereologist Edward Lorenz "discovered" chaos in data runs on a
computer program he was using to model the dynamics of the weather. The term "chaos" was
coined by the mathematicians Li and Yorke a decade later for a kind of aperiodic but bound
behavior in mathematical systems of coupled differential equations. Chaos Theory has become
an umbrella term for the study of many types of nonlinear, complex systems.
Themes: How
small changes can have a disproportionately large effect on a complex
system; the role of attractors in understanding the behavior of complex systems; revising
of the nature of the dichotomy between orderly and random
Researchers/Theorists:
Edward Lorenz; Jim Yorke; Ralph Abraham; Fred Abraham;
Robert May; Doyne Farmer; Norman Packard; Robert Shaw; James Crutchfield
Glossary: Attractors;
Chaos; Sensitive Dependence on Initial Conditions
Complex, Adaptive
Systems Theory:
The study of complex,
nonlinear, interactive systems which have the ability to adapt to a
changing environment. Such systems are characterized by the potential for self-organization and
exist in a nonequilibrium environment. CAS's evolve by random mutation, self-organization, the
transformation of their internal models of the environment, and natural selection. Examples
include living organisms, the nervous system, the immune system, the economy, corporations,
societies, and so on. The Santa Fe Institute is known as the major center in the world for the
study of CAS's.
Themes: How
complex, nonlinear, interactive systems adapt to a changing environment
along with other complex, adaptive systems in a co-evolutionary manner
Researchers/Theorists:
Murray Gell-mann, Brian Arthur, Chris Langton, Doyne Farmer,
Norman Packard, Stuart Kauffman, John Holland, William Sulis
Glossary: Adaptation;
Complex, Adaptive Systems; Complexity
Computational
Theory:
Research into the
functioning, capabilities, and limitations of computers. Pioneered by the work
of the remarkable English mathematician Alan Turing (who helped break the famous Enigma
Code used by the Germans during WWII), and John von Neuman (the Hungarian born but US
based mathematical prodigy), computational theory investigates such issues as the nature of
algorithms, computer languages, and the applicability and usefulness of various types of
computation to difficult problems in mathematics, the sciences, and other practical work with
real world complex systems. A major research agenda of computational theory has been to
delineate the nature of the complexity of various complex systems. Included in this is research
into what defines a computable versus a noncomputable problem. Moreover, computational
theory has provided us with the crucial distinction between hardware and software.
Themes: Computability
as a way of talking about the complexity of a system; a way of
typing complex systems according to their ability to process information (whether in
man-made computers or in the naturally-occurring systems like the brain, ecosystems,
and the immune systems.
Researchers/Theorists:
Alan Turing, John von Neumann, Douglass Hofstadter, John
Holland, Danny Hillis (and countless others as this has become a dominant scientific and
mathematical field)
Glossary: Church-Turing
Thesis; Information; Turing Machines
Condensed Matter
and Solid-state Physics:
That branch of
physics having do with solid state or condensed matter exhibiting such
phenomena as magnetism and modeled by such constructs as spin-glasses or how metal atoms
can be modeled in terms of their electron "spins" having an influence like positive or negative
feedback on neighboring atoms. The dynamics of "spin-glasses" have been influential in the
formulation of Kauffman's N/K models used in his Random Boolean Networks and other
complex, adaptive systems. Such models yield insight into the dynamics of interactive systems
through the changing of connectivity rules and the exploration of the ensuing emergent
phenomena.
Themes: How
to mode the behavior of interconnected systems in terms of coupling
between components and various means for moving the system into and out of
equilibrium states
Researchers/Theorists:
Philip Anderson; Daniel Stein; Richard Palmer; Bernard Derrida;
Gerald Weishbuch
Glossary: Coherence;
Feedback; Parameters (Order); N/K Models
Cybernetics:
The study of control
mechanisms such as thermostats, guided missile guidance systems, and
other early "smart" machines. Pioneered by the mathematicians Norbert Wiener and John von
Neumann, the term "cybernetics" comes from "cyber" or "steer" in Greek.
Cybernetics is
interested in how machines can be constructed to "steer" themselves such as in guided missiles.
After World War II, Cybernetics was instrumental in the development of Artificial Intelligence
and General Systems Theory. Cybernetics ideas spread to a host of other fields including
physiology, neuroscience, operations research, various engineering disciplines and so on. Along
the way, cybernetics became interested in machine learning and thus provided a foundation for
Artificial Intelligence and was the first field where ideas of self-organization were conceived.
Cybernetics has made much use of the concept of equilibrium and has conceived of self-
organization in terms of the self-regulation of equilibrium-seeking systems. Furthermore,
cybernetics posits the need for a "requisite variety" between the internal states of a system
and
the variation in its environment. In this way, cybernetics has laid important groundwork for the
study of adaptation of complex systems to a complex environments.
Themes: How
systems can be understood in terms of the dynamics of negative and
positive feedback; how systems can regulate their own behavior; adaptational,
tranformative, and learning processes in complex systems
Researchers/Theorists:
Norbert Wiener, W. Ross Ashby, Heinz von Foerster, Arthur
Burks, Gregory Bateson (applied to psychology and social systems), and Stafford Beer
(applied to businesses)
Glossary: Equilibrium;
Feedback; Information
Dynamical Systems
Theory (and Nonlinear Dynamical Systems Theory)(NDS):
The mathematical
discipline which studies how systems evolve over time according to the
dynamics of their equations. Emerging from classical mechanics, the study of differential
equations, and topology, dynamical systems theory utilizes the constructs of nonlinearity,
attractors, bifurcations, and phase (state) space to talk about transformations of system
behavior. Dynamical systems are usually considered deterministic systems, although they can be
influenced by random events. Much of the early work was done by Russian mathematicians
who had a head start on the study of nonlinear dynamics. Dynamical Systems Theory has
conceptualized many of the fundamental principles on which complexity sciences depend. It is
the grandparent of chaos theory.
A further development
of dynamical systems theory bringing in research into systems modeled
by nonlinear differential and difference equations. The mathematics of NDS were instrumental
in the development of Chaos Theory, particularly the concepts of attractors, bifurcation, phase
portraits, and measures of stability such as Lyapuonov Exponents. Prominent contemporary
theorists include the mathematicians Steve Smale and Ralph Abraham.
Themes: Transitions
systems through different attractor regimes; how systems can be
influenced by very small changes (fluctuations or perturbations)
Researchers/Theorists:
Henri Poincare; Steve Smale; Ralph Abraham; Leon Glass
(biology); Ary Goldberger (medicine)
Glossary: Attractors;
Bifurcation; Catastrophes; Chaos; Initial Conditions; Stability
Emergent Computation
Theory:
Research into the
computational capacities of emergent structures in complex, self-organizing
systems that can be used to measure the complexity of these structures. It recognizes emergent
phenomena by their information processing capacity. That is, one can understand the emergent
phenomena found in complex, adaptive systems by their their innate potential for processing
information. Growing-out of work in Chaos Theory and Artificial Life, Emergent Computation
Theory has postulated that a way to measure the complexity of a system is to ascertain what
specific type of Turing Machine can be most effectively model of a complex system's time
series measurements.
Themes: Emergent
structures as an intrinsic feature of complex systems to generate
innovative structures
Researchers/Theorists:
James Crutchfield; Melanie Mitchell; James Hanson
Glossary: Complexity;
Information; Time Series; Turing Machines
Evolutionary
Biology:
Biological theory
of evolution originating in the work of Charles Darwin. It studies the process
of evolution leading to the appearance and disappearance of species through the mechanisms of
random mutation and natural selection of the fitter mutants. As such evolutionary biology has
laid the foundation for our understanding of adaptation of living organisms to changes in their
environment. These ideas of adaptation are providing a template in which to understand
processes of adaptation in all complex, adaptive systems particularly the work of John Holland
and Stuart Kauffman.
Themes: How
processes of adaptation can be understood as the result of random
mutations, recombination of genotypes, and natural selection; the crucial role of the
"edge of chaos" as a zone where adaptive experimentation may be at is optimum.
Researchers/Theorists:
Charles Darwin (and his followers); Later on Jacques Monod,
Stephen Jay Gould, Richard Lewontin, Richard Dawkins, Stuart Kauffman
Glossary: Adaptation;
Edge of Chaos; Genetic Algorithms; N/K Model
Evolutionary
Systems Theory:
Syntheses of evolutionary
biology with congruent concepts from Cybernetics, General Systems
Theory, and Dynamical Systems Theory, serves to integrate many fields in terms of principles
of system development and transformation. The journal World Futures features articles on
Evolutionary Systems Theory.
Themes: General
constructs from the theory of evolution applied across a great many
complex systems; emphasis on evolutionary transformation
Researchers/Theorists:
Ervin Laszlo, Vilmos Csanyi, Rod Swenson, Sally Goerner
Glossary: Bifurcation;
Chaos; Complexity; Complex, Adaptive Systems
Far-from-equilibrium
Thermodynamics:
The study of self-organization
in physical systems founded by the Russian- born Belgian
physical chemist Ilya Prigogine, winner of the Nobel Prize in chemistry. Self-organization has
been studied from a thermodynamics perspective considering the relation between the build-up
of structure seen in thermodynamics versus the supposed tendency of an increase of entropy
(from the Second Law of Thermodynamics) to tear down form. Self- organizing, emergent
patterns are termed "dissipative structures." Many of the ideas are revisions of earlier
thermodynamic concepts applied to the build-up of organization in a physical systems.
Themes: Self-organization
understood as a process occurring in a nonlinear system at a
far-from-equilibrium system; how complex systems can take advantage of random
events in the build-up of new forms
Researchers/Theorists:
Ilya Prigogine; Gregoire Nicolis
Glossary: Dissipative
Structures; Equilibrium; Far-from-equilibrium; Self-organization
Fractal Geometry:
A geometrical pattern
or set of points which is self-similar on different scales. The geometry of
this pattern does not fall within the normal whole dimensions one, two, or three. Instead, a
fractal is "in-between" one and two or two and three and so on dimensions. For example, the
coast of England can be understood as a fractal, because as you observe from closer and
closer points of view (i.e., changing the scale) it keeps showing a self-similar kind of irregularity.
Fractal dimensionality is one way to measure the complexity of a dynamical system.
Furthermore, strange attractors have a fractal dimensionality. Fractals have become popular
through the amazing imagery of graphical depicted Mandelbrot or Julia Sets. The study of
Fractal Geometry has been a great aide in discovering universal principles in complex systems,
scaling phenomena being one of these. Moreover, fractals can represent power law
distributions.
Themes: Understanding
aspects of complexity in terms of repeated irregularities on
different scales; the benefits conferred on a system from having a fractal structure
Researchers/Theorists:
Benoit Mandelbrot; Michael Barnsley
Glossary: Attractor;
Chaos; Complexity; Fractal
Game Theory:
Originally developed
by the great mathematician John von Neumann and the economist Oscar
Morgenstern, Game Theory explores the various outcomes when interactive, semi-autonomous
agents engage in either cooperative and noncooperative behavior. For example, in the famous
Prisoner's Dilemma Game, two agents or "players" are arrested for armed robbery, and the
different outcomes of their resulting cooperative or noncooperative strategies in the face of the
district attorney's deal-making are assessed. Game Theory constructs are helpful in
understanding the global effect of local "rules" (i.e., the various strategies used by the
agents),
and thereby, it is another complementary framework for understanding adaptation.
Themes: Emergence
of global patterns in complex systems according to the rules or
strategies followed by interactive agents
Researchers/Theorists:
John von Neumann; Oscar Morgenstern; Bernardo Huberman;
Natalie Glance; Robert Axelrod
Glossary: Adaptation;
Emergence
General Systems
Theory:
Following from
earlier work in Cybernetics, Information Theory, and Evolutionary Biology,
General Systems Theory attempted to search for general principles of system across diverse
scientific disciplines. As such, it provides a precursor to the similar search for general principles
in Complex, Adaptive Systems Theory. Key ideas include negative feedback, stability,
equilibrium-seeking, self-regulation, and "open systems" referring to the need for vital systems
to be in active exchange with their environments.
Themes: The
search for general principles of the dynamics of living and other complex
systems
Researchers/Theorists:
Ludwig von Bertalanffy
Glossary: Adaptation;
Equilibrium; Self-organization
Genetic Algorithms:
A type of computer
program developed by the computer scientist John Holland whose strategy
of arriving at solutions is based on principles taken from genetics. Basically, the genetic
algorithm utilizes the mixing of genetic information in sexual reproduction, random mutations,
and natural selection at arriving at solutions. The use and study of genetic algorithms has been
instrumental in the development of a more general Complex, Adaptive Systems Theory.
Themes: Inquiry
into principles of learning and adaptation; designing evolving computer
programs
Researchers/Theorists:
John Holland
Glossary: Attractor;
Chaos; Complexity; Fractal
Information
Theory:
Formulated during
and after World War II, Information Theory focussed on measurements of
the amount of information a communications channel could contain. "Information" refers to
the
degree of variety versus redundancy capable of being transmitted electronically. Information
Theory has been a keystone in the development of the study of self-organization and
complexity as well as computational theory. Self-organization can be conceptualized in
Information Theory in terms of the paradoxical nature of "noise" (or random fluctuations or
perturbations) as either disorganizing or organizing. Complex systems can be understood as
information-processing mechanisms. Information is now being used as a general concept linking
all types of systems physical, social, computational.
Themes: Information
can be seen as the cognate in a social system as what energy is in a
physical system; search for general principles of information across many types of
systems
Glossary: Information;
Novelty; Redundancy
Researchers/Theorists:
Claude Shannon; Norbert Wiener; Henri Atlan (biology)
Neural Nets:
An outgrowth of
Artificial Intelligence, Neural Nets are electronic automata used to for machine
learning that are based on associative theories of human cognition. Using various algorithms,
they are often programmed to learn how to recognize a pattern. Changing the rules of
interaction between the "neurons" in the network can lead to interesting emergent behavior,
so
in that way, neural nets are another tool for investigating self-organization and emergence.
Many believe neural nets are a better model of the way the living brain works than the
operation of digital computers. The investigation of neural nets is providing a great many insights
into emergent patterns in complex systems. Moreover, the study of neural net pattern
recognition is providing insight into how the brain may function in its perception of patterns in
the environment.
Themes: Another
example of complex systems composed of interacting semi-autonomous
agents that can adapt and learn; insight into pattern recognition in complex system and
the build-up of internal models
Researchers/Theorists:
J.J. Hopfield; T. J. Sejnowski
Glossary: Adaptation;
Genetic Algorithms; Neural Nets
Self-organized
Criticality (SOC):
Research and theorizing
about natural, abrupt changes formulated by the physicist Per Bak.
Systems are viewed as evolving naturally, in a self- organizing manner, to a critical state at
which abrupt changes can occur which abrupt changes can occur. Examples of such systems
include plate tectonics leading to earthquakes, avalanches, sudden stock market dips or surges
as well as crashes, and so on. By considering such systems "weakly chaotic" and exploring
them in terms of power laws, Per Bak has contrasted them with "strongly chaotic" systems.
Some of the themes of SOC have been incorporated by Stuart Kauffman into his ideas on the
"edge of chaos."
Themes: Understanding
of abrupt, cascading or "avalanche" type of change in a
complex system; another picture of systems being in a poised state or readiness of
change; Information can be seen as the cognate in a social system as the energy in a
physical system.
Researchers/Theorists:
Per Bak; Chao Tang; Kurt Wiesenfeld
Glossary: Bifurcation;
Chaos; Power Law; Self-organization; Stability
Synergetics:
The study of self-organizing
systems initiated by the German physicist Hermann Haken, who
did early research on the emergence of coherence in lasers and other emergent phenomena in
physical systems. Synergetics emphasizes the exploration of order parameters which move the
focus of studying complex systems from the lower level of components up to the level of the
emergent structures. The term "Synergetics" has become roughly synonymous to complexity
science in Europe and Russia.
Themes: Understanding
emergent phenomena in terms of the order parameters
determining their coherent structure
Researchers/Theorists:
Hermann Haken
Glossary: Coherence;
Parameter (Order); Self-organization
System Dynamics:
Understanding the
dynamics of complex systems in terms of a network of interlocking negative
and positive feedback loops, e.g., how the functions of production, inventory, ordering, and
shipping are interrelated. Diagramming complex systems with the visual aides of System
Dynamics can help in indicating how changes will effect other parts or subsystems of the
system. System Dynamics also provides practice in thinking systemically about systems, i.e.,
conceiving of the overall "holistic" interaction of components. System Dynamics has been
influenced by Cybernetics and General Systems Theory, and more recently has included some
elements of Dynamical Systems Theory and Complex, Adaptive Systems Theory, Synergetics,
and Far-from-equilibrium Thermodynamics.
Themes: Another
way to conceptualize complex systems as interacting semi-autonomous
units influencing one another through positive and negative feedback
Researchers/Theorists:
Jay Forrester; George Richardson; Peter Senge
Glossary: Feedback
1. Thoughts
