HOME

TheInfoList



OR:

A complex system is a
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
composed of many components which may
interact Advocates for Informed Choice, doing business as, dba interACT or interACT Advocates for Intersex Youth, is a 501(c)(3) nonprofit organization using innovative strategies to advocate for the legal and human rights of children with intersex trai ...
with each other. Examples of complex systems are Earth's global
climate Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologi ...
,
organisms In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells ( cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fu ...
, the
human brain The human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of ...
, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
, a living cell, and ultimately the entire
universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...
. Complex systems are
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
s whose behavior is intrinsically difficult to model due to the dependencies, competitions, relationships, or other types of interactions between their parts or between a given system and its environment. Systems that are " complex" have distinct properties that arise from these relationships, such as nonlinearity,
emergence In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergenc ...
,
spontaneous order Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous o ...
,
adaptation In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links to their interactions. The term ''complex systems'' often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment. The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to reductionism, which attempts to explain systems in terms of their constituent parts and the individual interactions between them. As an interdisciplinary domain, complex systems draws contributions from many different fields, such as the study of
self-organization Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when suffic ...
and critical phenomena from physics, that of
spontaneous order Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous o ...
from the social sciences, chaos from mathematics,
adaptation In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
from biology, and many others. ''Complex systems'' is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including statistical physics,
information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...
, nonlinear dynamics,
anthropology Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of be ...
,
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
,
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
,
sociology Sociology is a social science that focuses on society, human social behavior, patterns of social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of empirical investigation an ...
,
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...
,
psychology Psychology is the science, scientific study of mind and behavior. Psychology includes the study of consciousness, conscious and Unconscious mind, unconscious phenomena, including feelings and thoughts. It is an academic discipline of immens ...
, and
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
.


Key concepts


Systems

Complex systems are chiefly concerned with the behaviors and properties of ''systems''. A system, broadly defined, is a set of entities that, through their interactions, relationships, or dependencies, form a unified whole. It is always defined in terms of its ''boundary'', which determines the entities that are or are not part of the system. Entities lying outside the system then become part of the system's ''environment''. A system can exhibit ''properties'' that produce ''behaviors'' which are distinct from the properties and behaviors of its parts; these system-wide or ''global'' properties and behaviors are characteristics of how the system interacts with or appears to its environment, or of how its parts behave (say, in response to external stimuli) by virtue of being within the system. The notion of ''behavior'' implies that the study of systems is also concerned with processes that take place over time (or, in
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, some other
phase space In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usuall ...
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
ization). Because of their broad, interdisciplinary applicability, systems concepts play a central role in complex systems. As a field of study, complex systems is a subset of systems theory. General systems theory focuses similarly on the collective behaviors of interacting entities, but it studies a much broader class of systems, including non-complex systems where traditional reductionist approaches may remain viable. Indeed, systems theory seeks to explore and describe ''all'' classes of systems, and the invention of categories that are useful to researchers across widely varying fields is one of the systems theory's main objectives. As it relates to complex systems, systems theory contributes an emphasis on the way relationships and dependencies between a system's parts can determine system-wide properties. It also contributes to the interdisciplinary perspective of the study of complex systems: the notion that shared properties link systems across disciplines, justifying the pursuit of modeling approaches applicable to complex systems wherever they appear. Specific concepts important to complex systems, such as emergence, feedback loops, and adaptation, also originate in systems theory.


Complexity

For a system to exhibit complexity means that the systems' behaviors cannot be easily inferred from its properties. Any modeling approach that ignores such difficulties or characterizes them as noise will necessarily produce models that are neither accurate nor useful. As yet no fully general theory of complex systems has emerged for addressing these problems, so researchers must solve them in domain-specific contexts. Researchers in complex systems address these problems by viewing the chief task of modeling to be capturing, rather than reducing, the complexity of their respective systems of interest. While no generally accepted exact definition of complexity exists yet, there are many archetypal examples of complexity. Systems can be complex if, for instance, they have
chaotic Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kid ...
behavior (behavior that exhibits extreme sensitivity to initial conditions, among other properties), or if they have emergent properties (properties that are not apparent from their components in isolation but which result from the relationships and dependencies they form when placed together in a system), or if they are computationally intractable to model (if they depend on a number of parameters that grows too rapidly with respect to the size of the system).


Networks

The interacting components of a complex system form a
network Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematic ...
, which is a collection of discrete objects and relationships between them, usually depicted as a graph of vertices connected by edges. Networks can describe the relationships between individuals within an organization, between
logic gate A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic ga ...
s in a circuit, between
gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a b ...
s in gene regulatory networks, or between any other set of related entities. Networks often describe the sources of complexity in complex systems. Studying complex systems as networks, therefore, enables many useful applications of
graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
and network science. Many complex systems, for example, are also complex networks, which have properties such as phase transitions and power-law degree distributions that readily lend themselves to emergent or chaotic behavior. The fact that the number of edges in a complete graph grows quadratically in the number of vertices sheds additional light on the source of complexity in large networks: as a network grows, the number of relationships between entities quickly dwarfs the number of entities in the network.


Nonlinearity

Complex systems often have nonlinear behavior, meaning they may respond in different ways to the same input depending on their state or context. In
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, nonlinearity describes systems in which a change in the size of the input does not produce a proportional change in the size of the output. For a given change in input, such systems may yield significantly greater than or less than proportional changes in output, or even no output at all, depending on the current state of the system or its parameter values. Of particular interest to complex systems are
nonlinear dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a ...
, which are systems of
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
s that have one or more nonlinear terms. Some nonlinear dynamical systems, such as the
Lorenz system The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lo ...
, can produce a mathematical phenomenon known as chaos. Chaos, as it applies to complex systems, refers to the sensitive dependence on initial conditions, or " butterfly effect", that a complex system can exhibit. In such a system, small changes to initial conditions can lead to dramatically different outcomes. Chaotic behavior can, therefore, be extremely hard to model numerically, because small rounding errors at an intermediate stage of computation can cause the model to generate completely inaccurate output. Furthermore, if a complex system returns to a state similar to one it held previously, it may behave completely differently in response to the same stimuli, so chaos also poses challenges for extrapolating from experience.


Emergence

Another common feature of complex systems is the presence of emergent behaviors and properties: these are traits of a system that are not apparent from its components in isolation but which result from the interactions, dependencies, or relationships they form when placed together in a system.
Emergence In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergenc ...
broadly describes the appearance of such behaviors and properties, and has applications to systems studied in both the social and physical sciences. While emergence is often used to refer only to the appearance of unplanned organized behavior in a complex system, emergence can also refer to the breakdown of an organization; it describes any phenomena which are difficult or even impossible to predict from the smaller entities that make up the system. One example of a complex system whose emergent properties have been studied extensively is cellular automata. In a cellular automaton, a grid of cells, each having one of the finitely many states, evolves according to a simple set of rules. These rules guide the "interactions" of each cell with its neighbors. Although the rules are only defined locally, they have been shown capable of producing globally interesting behavior, for example in Conway's Game of Life.


Spontaneous order and self-organization

When emergence describes the appearance of unplanned order, it is
spontaneous order Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous o ...
(in the social sciences) or
self-organization Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when suffic ...
(in physical sciences). Spontaneous order can be seen in
herd behavior Herd behavior is the behavior of individuals in a group acting collectively without centralized direction. Herd behavior occurs in animals in herds, packs, bird flocks, fish schools and so on, as well as in humans. Voting, demonstrations, rio ...
, whereby a group of individuals coordinates their actions without centralized planning. Self-organization can be seen in the global symmetry of certain
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
s, for instance the apparent radial
symmetry Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
of snowflakes, which arises from purely local attractive and repulsive forces both between water molecules and their surrounding environment.


Adaptation

Complex adaptive systems are special cases of complex systems that are adaptive in that they have the capacity to change and learn from experience. Examples of complex adaptive systems include the
stock market A stock market, equity market, or share market is the aggregation of buyers and sellers of stocks (also called shares), which represent ownership claims on businesses; these may include ''securities'' listed on a public stock exchange, ...
, social insect and ant colonies, the biosphere and the
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
, the
brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...
and the
immune system The immune system is a network of biological processes that protects an organism from diseases. It detects and responds to a wide variety of pathogens, from viruses to parasitic worms, as well as cancer cells and objects such as wood splinte ...
, the cell and the developing
embryo An embryo is an initial stage of development of a multicellular organism. In organisms that reproduce sexually, embryonic development is the part of the life cycle that begins just after fertilization of the female egg cell by the male spe ...
, the cities, manufacturing businesses and any human social group-based endeavor in a cultural and social system such as
political parties A political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific political ideology ...
or communities.


Features

Complex systems may have the following features: ;Complex systems may be open : Complex systems are usually open systems — that is, they exist in a
thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ...
gradient and dissipate energy. In other words, complex systems are frequently far from energetic equilibrium: but despite this flux, there may be pattern stability, see synergetics. ;Complex systems may exhibit critical transitions : Critical transitions are abrupt shifts in the state of
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
s, the
climate Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologi ...
,
financial system A financial system is a system that allows the exchange of funds between financial market participants such as lenders, investors, and borrowers. Financial systems operate at national and global levels. Financial institutions consist of complex, c ...
s or other complex systems that may occur when changing conditions pass a critical or bifurcation point. The 'direction of critical slowing down' in a system's state space may be indicative of a system's future state after such transitions when delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. ;Complex systems may be
nested ''Nested'' is the seventh studio album by Bronx-born singer, songwriter and pianist Laura Nyro, released in 1978 on Columbia Records. Following on from her extensive tour to promote 1976's ''Smile'', which resulted in the 1977 live album '' Sea ...
:The components of a complex system may themselves be complex systems. For example, an
economy An economy is an area of the production, distribution and trade, as well as consumption of goods and services. In general, it is defined as a social domain that emphasize the practices, discourses, and material expressions associated with th ...
is made up of organisations, which are made up of
people A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of prope ...
, which are made up of
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
- all of which are complex systems. The arrangement of interactions within complex bipartite networks may be nested as well. More specifically, bipartite ecological and organisational networks of mutually beneficial interactions were found to have a nested structure. This structure promotes indirect facilitation and a system's capacity to persist under increasingly harsh circumstances as well as the potential for large-scale systemic regime shifts. ;Dynamic network of multiplicity :As well as coupling rules, the dynamic
network Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematic ...
of a complex system is important. Small-world or scale-free networks which have many local interactions and a smaller number of inter-area connections are often employed. Natural complex systems often exhibit such topologies. In the human cortex for example, we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions. ; May produce emergent phenomena :Complex systems may exhibit behaviors that are emergent, which is to say that while the results may be sufficiently determined by the activity of the systems' basic constituents, they may have properties that can only be studied at a higher level. For example, empirical food webs display regular, scale-invariant features across aquatic and terrestrial ecosystems when studied at the level of clustered 'trophic' species. Another example is offered by the
termites Termites are small insects that live in colonies and have distinct castes ( eusocial) and feed on wood or other dead plant matter. Termites comprise the infraorder Isoptera, or alternatively the epifamily Termitoidae, within the order Blat ...
in a mound which have physiology, biochemistry and biological development at one level of analysis, whereas their social behavior and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level. ; Relationships are non-linear : In practical terms, this means a small perturbation may cause a large effect (see butterfly effect), a proportional effect, or even no effect at all. In linear systems, the effect is ''always'' directly proportional to cause. See nonlinearity. ; Relationships contain feedback loops :Both negative (
damping Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples i ...
) and positive (amplifying)
feedback Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...
are always found in complex systems. The effects of an element's behavior are fed back in such a way that the element itself is altered.


History

Although arguably, humans have been studying complex systems for thousands of years, the modern scientific study of complex systems is relatively young in comparison to established fields of science such as
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
and
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
. The history of the scientific study of these systems follows several different research trends. In the area of
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, arguably the largest contribution to the study of complex systems was the discovery of chaos in
deterministic Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and cons ...
systems, a feature of certain
dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a ...
that is strongly related to nonlinearity. The study of
neural networks A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...
was also integral in advancing the mathematics needed to study complex systems. The notion of self-organizing systems is tied with work in
nonequilibrium thermodynamics Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an ext ...
, including that pioneered by
chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...
and Nobel laureate Ilya Prigogine in his study of dissipative structures. Even older is the work by Hartree-Fock on the quantum chemistry equations and later calculations of the structure of molecules which can be regarded as one of the earliest examples of emergence and emergent wholes in science. One complex system containing humans is the classical political economy of the
Scottish Enlightenment The Scottish Enlightenment ( sco, Scots Enlichtenment, gd, Soillseachadh na h-Alba) was the period in 18th- and early-19th-century Scotland characterised by an outpouring of intellectual and scientific accomplishments. By the eighteenth century ...
, later developed by the
Austrian school of economics The Austrian School is a heterodox school of economic thought that advocates strict adherence to methodological individualism, the concept that social phenomena result exclusively from the motivations and actions of individuals. Austrian school ...
, which argues that order in market systems is spontaneous (or emergent) in that it is the result of human action, but not the execution of any human design. Upon this, the Austrian school developed from the 19th to the early 20th century the economic calculation problem, along with the concept of dispersed knowledge, which were to fuel debates against the then-dominant
Keynesian economics Keynesian economics ( ; sometimes Keynesianism, named after British economist John Maynard Keynes) are the various macroeconomic theories and models of how aggregate demand (total spending in the economy) strongly influences economic output ...
. This debate would notably lead economists, politicians, and other parties to explore the question of
computational complexity In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...
. A pioneer in the field, and inspired by
Karl Popper Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the ...
's and
Warren Weaver Warren Weaver (July 17, 1894 – November 24, 1978) was an American scientist, mathematician, and science administrator. He is widely recognized as one of the pioneers of machine translation and as an important figure in creating support for scien ...
's works, Nobel prize economist and philosopher
Friedrich Hayek Friedrich August von Hayek ( , ; 8 May 189923 March 1992), often referred to by his initials F. A. Hayek, was an Austrian–British economist, legal theorist and philosopher who is best known for his defense of classical liberalism. Hayek ...
dedicated much of his work, from early to the late 20th century, to the study of complex phenomena, not constraining his work to human economies but venturing into other fields such as
psychology Psychology is the science, scientific study of mind and behavior. Psychology includes the study of consciousness, conscious and Unconscious mind, unconscious phenomena, including feelings and thoughts. It is an academic discipline of immens ...
,
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
and
cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson ma ...
. Cybernetician
Gregory Bateson Gregory Bateson (9 May 1904 – 4 July 1980) was an English anthropologist, social scientist, linguist, visual anthropologist, semiotician, and cyberneticist whose work intersected that of many other fields. His writings include ''Steps to ...
played a key role in establishing the connection between anthropology and systems theory; he recognized that the interactive parts of cultures function much like ecosystems. While the explicit study of complex systems dates at least to the 1970s, the first research institute focused on complex systems, the Santa Fe Institute, was founded in 1984. Early Santa Fe Institute participants included physics Nobel laureates Murray Gell-Mann and Philip Anderson, economics Nobel laureate
Kenneth Arrow Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972. In economi ...
, and Manhattan Project scientists
George Cowan George A. Cowan (; February 15, 1920 – April 20, 2012) was an American physical chemist, a businessman and philanthropist. Education He conducted early research in the Manhattan Project. George served 39 years at Los Alamos National Lab ...
and Herb Anderson. Today, there are over 50 institutes and research centers focusing on complex systems. Since the late 1990s, the interest of mathematical physicists in researching economic phenomena has been on the rise. The proliferation of cross-disciplinary research with the application of solutions originated from the physics epistemology has entailed a gradual paradigm shift in the theoretical articulations and methodological approaches in economics, primarily in financial economics. The development has resulted in the emergence of a new branch of discipline, namely "econophysics," which is broadly defined as a cross-discipline that applies statistical physics methodologies which are mostly based on the complex systems theory and the chaos theory for economics analysis. The 2021
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
was awarded to
Syukuro Manabe is a Japanese-American meteorologist and climatologist who pioneered the use of computers to simulate global climate change and natural climate variations. He was awarded the 2021 Nobel Prize in Physics jointly with Klaus Hasselmann and Gi ...
, Klaus Hasselmann, and
Giorgio Parisi Giorgio Parisi (born 4 August 1948) is an Italian theoretical physicist, whose research has focused on quantum field theory, statistical mechanics and complex systems. His best known contributions are the QCD evolution equations for parton densit ...
for their work to understand complex systems. Their work was used to create more accurate computer models of the effect of global warming on the Earth's climate.


Applications


Complexity in practice

The traditional approach to dealing with complexity is to reduce or constrain it. Typically, this involves compartmentalization: dividing a large system into separate parts. Organizations, for instance, divide their work into departments that each deal with separate issues. Engineering systems are often designed using modular components. However, modular designs become susceptible to failure when issues arise that bridge the divisions.


Complexity management

As projects and
acquisitions Mergers and acquisitions (M&A) are business transactions in which the ownership of companies, other business organizations, or their operating units are transferred to or consolidated with another company or business organization. As an aspect ...
become increasingly complex, companies and governments are challenged to find effective ways to manage mega-acquisitions such as the Army Future Combat Systems. Acquisitions such as the FCS rely on a web of interrelated parts which interact unpredictably. As acquisitions become more network-centric and complex, businesses will be forced to find ways to manage complexity while governments will be challenged to provide effective governance to ensure flexibility and resiliency.


Complexity economics

Over the last decades, within the emerging field of
complexity economics Complexity economics is the application of complexity science to the problems of economics. It sees the economy not as a system in equilibrium, but as one in motion, perpetually constructing itself anew.Beinhocker, Eric D. The Origin of Wealth: E ...
, new predictive tools have been developed to explain economic growth. Such is the case with the models built by the Santa Fe Institute in 1989 and the more recent economic complexity index (ECI), introduced by the MIT physicist
Cesar A. Hidalgo Cesar, César or Cèsar may refer to: Arts, entertainment, and media * ''César'' (film), a 1936 film directed by Marcel Pagnol * ''César'' (play), a play by Marcel Pagnolt * César Award, a French film award Places * Cesar, Portugal * Ces ...
and the
Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
economist
Ricardo Hausmann Ricardo Hausmann (born 1956) is the former Director of the Center for International Development currently leading the Center for International Development’s Growth Lab and is a Professor of the Practice of Economic Development at the John ...
. Based on the ECI, Hausmann, Hidalgo and their team of
The Observatory of Economic Complexity The Observatory of Economic Complexity (OEC) is a data visualization site for international trade data created by the Macro Connections group at the MIT Media Lab. The goal of the observatory is to distribute international trade data in a visual ...
have produced GDP forecasts for the year 2020. Recurrence quantification analysis has been employed to detect the characteristic of business cycles and
economic development In the economics study of the public sector, economic and social development is the process by which the economic well-being and quality of life of a nation, region, local community, or an individual are improved according to targeted goals and ...
. To this end, Orlando et al. developed the so-called recurrence quantification correlation index (RQCI) to test correlations of RQA on a sample signal and then investigated the application to business time series. The said index has been proven to detect hidden changes in time series. Further, Orlando et al., over an extensive dataset, shown that recurrence quantification analysis may help in anticipating transitions from laminar (i.e. regular) to turbulent (i.e. chaotic) phases such as USA GDP in 1949, 1953, etc. Last but not least, it has been demonstrated that recurrence quantification analysis can detect differences between macroeconomic variables and highlight hidden features of economic dynamics.


Complexity and education

Focusing on issues of student persistence with their studies, Forsman, Moll and Linder explore the "viability of using complexity science as a frame to extend methodological applications for physics education research", finding that "framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics".


Complexity and biology

Complexity science has been applied to living organisms, and in particular to biological systems. Within the emerging field of
fractal physiology Fractal physiology refers to the study of physiological systems using complexity science methods, such as chaos measure, entropy, and fractal dimensions. The underlying assumption is that biological systems are complex and exhibit non-linear patt ...
, bodily signals, such as heart rate or brain activity, are characterized using
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
or fractal indices. The goal is often to assess the state and the health of the underlying system, and diagnose potential disorders and illnesses.


Complexity and modeling

One of Friedrich Hayek's main contributions to early complexity theory is his distinction between the human capacity to predict the behavior of simple systems and its capacity to predict the behavior of complex systems through modeling. He believed that economics and the sciences of complex phenomena in general, which in his view included biology, psychology, and so on, could not be modeled after the sciences that deal with essentially simple phenomena like physics. Hayek would notably explain that complex phenomena, through modeling, can only allow pattern predictions, compared with the precise predictions that can be made out of non-complex phenomena.


Complexity and chaos theory

Complexity theory is rooted in
chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to hav ...
, which in turn has its origins more than a century ago in the work of the French mathematician
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "Th ...
. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order. Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions of the system, though in practice this is impossible to do with arbitrary accuracy. Ilya Prigogine argued that complexity is non-deterministic and gives no way whatsoever to precisely predict the future. The emergence of complexity theory shows a domain between deterministic order and randomness which is complex. Cilliers, P. (1998). ''Complexity and Postmodernism: Understanding Complex Systems'', Routledge, London. This is referred to as the " edge of chaos". When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as it is within chaos theory, in which it prevails. As stated by Colander, the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions. For recent examples in economics and business see Stoop et al. who discussed Android's market position, Orlando who explained the corporate dynamics in terms of mutual synchronization and chaos regularization of bursts in a group of chaotically bursting cells and Orlando et al. who modelled financial data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity) with a low-dimensional deterministic model. Therefore, the main difference between chaotic systems and complex systems is their history. Chaotic systems do not rely on their history as complex ones do. Chaotic behavior pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'. On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist Murray Gell-Mann called "an accumulation of frozen accidents". In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations.


Complexity and network science

A complex system is usually composed of many components and their interactions. Such a system can be represented by a network where nodes represent the components and links represent their interactions. For example, the
Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, p ...
can be represented as a network composed of nodes (computers) and links (direct connections between computers). Other examples of complex networks include social networks, financial institution interdependencies, airline networks, and biological networks.


Notable scholars


See also


References


Further reading


Complexity Explained
* L.A.N. Amaral and J.M. Ottino
''Complex networks — augmenting the framework for the study of complex system''
2004. * * Walter Clemens, Jr.
''Complexity Science and World Affairs''
SUNY Press, 2013. * * A. Gogolin, A. Nersesyan and A. Tsvelik

Cambridge University Press, 1999. *
Nigel Goldenfeld Nigel David Goldenfeld (born May 1, 1957) is a Swanlund Chair, Professor of Physics Department in the University of Illinois at Urbana-Champaign (UIUC), the director of the NASA Astrobiology Institute for Universal Biology, and the leader of the ...
and Leo P. Kadanoff
''Simple Lessons from Complexity''
1999 * Kelly, K. (1995)
''Out of Control''
Perseus Books Group. * * Syed M. Mehmud (2011)
''A Healthcare Exchange Complexity Model''

Preiser-Kapeller, Johannes, "Calculating Byzantium. Social Network Analysis and Complexity Sciences as tools for the exploration of medieval social dynamics". August 2010
* *
Stefan Thurner Stefan Thurner (born 1969) is an Austrian physicist and complexity researcher. He has been professor for Science of Complex Systems at the Medical University of Vienna since 2009, external professor at the Santa Fe Institute since 2007, and guest ...
, Peter Klimek, Rudolf Hanel: ''Introduction to the Theory of Complex Systems'', Oxford University Press, 2018,
SFI @30, Foundations & Frontiers
(2014).


External links

* * * * * (Interdisciplinary Description of Complex Systems) * *
Complex systems
in scholarpedia.
Complex Systems Society

(Australian) Complex systems research network.


based on
Luis M. Rocha Luis M. Rocha is the George J. Klir Professor of Systems Science at the Thomas J. Watson College of Engineering and Applied Science, Binghamton University (State University of New York). He has been director of the NSF-NRT Complex Networks a ...
, 1999.
CRM Complex systems research group

The Center for Complex Systems Research, Univ. of Illinois at Urbana-Champaign
{{Authority control Complex dynamics Cybernetics Emergence Systems theory Systems science Mathematical modeling