Relational order theories
Encyclopedia
A number of independent lines of research depict the universe, including the social organization of living creatures which is of particular interest to humans, as system
System
System is a set of interacting or interdependent components forming an integrated whole....

s, or networks, of relationships.

Relational systems, or regimes, are often seen as differentiated—and thus defined—by reductions in degrees of freedom among the elements of the system. This diminution in degrees of freedom in relationships among elements is characterized as correlation. The correlation process is sometimes seen as tiered through several levels, reaching from quantum mechanics upward through complex, dynamic, ‘non-equilibrium’, systems, including living systems.

The quantum mechanics level

Lee Smolin
Lee Smolin
Lee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...

  proposes a system of "knots and networks” such that "the geometry of space arises out of a … fundamental quantum level which is made up of an interwoven network of … processes”. Smolin and a group of like minded researchers have devoted a number of years to developing a loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

 basis for physics, which encompasses this relational network viewpoint.

Carlo Rovelli
Carlo Rovelli
Carlo Rovelli is an Italian physicist who has worked in Italy, the USA, and France. His work is mainly in the field of quantum gravity. He is among the founders of the Loop Quantum Gravity theory.-Life and career:...

 and associated persons have, in parallel and in communication with Smolin and associates, begun to elaborate a system called Relational quantum mechanics
Relational quantum mechanics
Relational quantum mechanics is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and...

, which has at its foundation the view that all systems are quantum systems, and that each quantum system is defined by its relationship with other quantum systems with which it interacts. Rovelli has proposed that each interaction between quantum systems involves a ‘measurement’, and such interactions involved reductions in degrees of freedom between the respective systems, to which he applies the term correlation.

These lines of inquiry are developed at more length by the authors and other investigators, and in the linked pages in this encyclopedia. The linked pages are more technical and detailed in nature than this very summary reflection of some of the central elements.

Though the proponents of these theories seem confident that they are on the right track, they are candid in reflecting that their work requires considerable investigation and elaboration in competition with and integration with other perspectives on quantum mechanics, Einsteinian relativity, string, and other fundamental theories of physics.

The cosmological level

The conventional explanations of Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

 and related cosmologies (see also Timeline of the Big Bang
Timeline of the Big Bang
This timeline of the Big Bang describes the history of the universe according to the prevailing scientific theory of how the universe came into being, using the cosmological time parameter of comoving coordinates...

) projects an expansion of and related ‘cooling’ of the universe which entails a cascade of phase transitions involving fundamental forces, quark-gluon transitions to simple atoms, complex atoms, simple and complex molecules, and aggregations of these entities into galaxies, stars, planets, etc. (Strictly speaking, phase transitions can both manifest correlation and differentiation events, in the direction of diminution of degrees of freedom, and in the opposite direction disruption of correlations. However, the expanding universe picture presents a framework in which there appears to be a direction of phase transitions toward differentiation and correlation, in the universe as a whole, over time) At least at the level of aggregation of baryons, each correlated and differentiated system thus evolved can be considered, from the relational point of view, as a network of relationships.

David Layzer and Eric Chaisson
Eric Chaisson
Eric J. Chaisson is an American astrophysicist and science educator best known for his research, teaching, and writing on the interdisciplinary science of cosmic evolution....

  have provided slightly varying but compatible explanations of how the expansion of the universe allows ordered, or correlated, relational regimes to arise and persist, notwithstanding the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

.

Layzer spoke in terms of the rate of expansion outrunning the rate of equilibration involved at local scales, while Chaisson summarizes the argument as “In an expanding universe actual entropy … increases less than the maximum possible entropy“ thus allowing for, or requiring, ordered (negentropic) relationships to arise and persist.

Chaisson depicts the universe as a non-equilibrium process, at least in this sense, in which energy flows into and through ordered systems, such a galaxies, stars, and life processes. This provides a cosmological basis for non-equilibrium thermodynamics
Non-equilibrium thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium; for they are changing or can be triggered to change over time, and are continuously and discontinuously...

, treated elsewhere to some extent in this encyclopedia at this time. In terms which unite non-equilibrium thermodynamics language and relational analyses, patterns of processes arise and are evident as ordered, dynamic relational regimes.

Basic levels

There seems to be agreement that life is a manifestation of non-equilibrium thermodynamics, both as to individual living creatures and as to aggregates of such creatures, or ecosystems. See e.g. Brooks and Wylie Smolin, Chaisson, Stuart Kauffman and Ulanowicz.

This realization has proceeded from, among other sources, a seminal concept of ‘dissipative system
Dissipative system
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter....

s’ offered by Ilya Prigogine
Ilya Prigogine
Ilya, Viscount Prigogine was a Russian-born naturalized Belgian physical chemist and Nobel Laureate noted for his work on dissipative structures, complex systems, and irreversibility.-Biography :...

. In such systems, energy feeds through a stable, or correlated, set of dynamic processes, both engendering the system and maintaining the stability of the ordered, dynamic relational regime.

In the 1990s, Eric Schnieder and J.J. Kaye began to develop the concept of life working off differentials, or gradients (e.g. the energy gradient manifested on Earth as a result of sunlight impinging on earth on the one hand and the temperature of interstellar space on the other). Schneider and Kaye identified the contributions of by Prigogine and Erwin Schrödinger What is Life? (Schrödinger)
What is Life? (Schrödinger)
What Is Life? is a 1944 non-fiction science book written for the lay reader by physicist Erwin Schrödinger. The book was based on a course of public lectures delivered by Schrödinger in February 1943, under the auspices of the Dublin Institute for Advanced Studies at Trinity College, Dublin...

 as foundations for their conceptual developments.

Schneider and Dorion Sagan have since elaborated on the view of life dynamics and the ecosystem in “Into the Cool “. In this perspective, energy flows tapped from gradients create dynamically ordered structures, or relational regimes, in pre-life precursor systems and in living systems.

As noted above, Chaisson has provided a conceptual grounding for the existence of the differentials, or gradients, off which, in the view of Kaye, Schneider, Sagan and others, life works. Those differentials and gradients arise in the ordered structures (such as suns, chemical systems, and the like) created by in correlation processes entailed in the expansion and cooling processes of the universe.

Two investigators, Robert Ulanowicz and Stuart Kauffman, . have suggested the relevance of autocatalysis
Autocatalysis
A single chemical reaction is said to have undergone autocatalysis, or be autocatalytic, if the reaction product itself is the catalyst for that reaction....

 models for life processes. In this construct, a group of elements catalyse reactions in a cyclical, or topologically circular, fashion.

Several investigators have used these insights to suggest essential elements of a definition of the life process, which might briefly be summarized as stable, patterned (correlated) processes which intake (and dissipate) energy, and reproduce themselves.

Ulanowicz, a theoretical ecologist, has extended the relational analysis of life processes to ecosystems, using information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

 tools. In this approach, an ecosystem is a system of networks of relationships (a common viewpoint at present), which can be quantified and depicted at a basic level in terms of the degrees of order or organization manifested in the systems.

Two prominent investigators, Lynn Margulis
Lynn Margulis
Lynn Margulis was an American biologist and University Professor in the Department of Geosciences at the University of Massachusetts Amherst. She is best known for her theory on the origin of eukaryotic organelles, and her contributions to the endosymbiotic theory, which is now generally accepted...

 and, more fully, Leo Buss
Leo Buss
Leo W. Buss is a Professor in Yale University's departments of geology, geophysics, and ecology and evolutionary biology.-Life:He graduated from Johns Hopkins University with a B.A., M.A., and Ph.D in 1979....

 have developed a view of the evolved life structure as exhibiting tiered levels of (dynamic) aggregation of life units. In each level of aggregation, the component elements have mutually beneficial, or complementary, relationships.

In brief summary, the comprehensive Buss approach is cast in terms of replicating precursors which became inclusions in single celled organisms, thence single celled organisms, thence the eukaryotic cell (which are, in Margulis’ now widely adopted analysis, made up of single celled organisms), thence multicellular organisms, composed of eukaryotic cells, and thence social organizations composed of multicellular organisms. This work adds to the ‘tree of life’ metaphor a sort of ‘layer cake of life’ metaphor., taking into account tiered levels of life organization.

Social organization

Social network theory has in recent decades expanded into a large field reaching across a large range of topics. Among other things, social network analyses are now applied to political, professional, military, and other closely attended subject matters. See e.g. the explanation, references and links in the Social Network
Social network
A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...

 article in this encyclopedia.

The internet, because of its low cost, broad reach, and combinatorial capacity, has become a prominent example of social networking, as is evident in this encyclopedia, Youtube, Facebook, and other recent developments. As a readily available illustration of a dynamic relational network system, at the human technology level, the internet has become a subject for analyses of how networks of relationships can arise and function.

Second law of thermodynamics

The development of non equilibrium thermodynamics and the observations of cosmological generation of ordered systems, identified above, have engendered proposed modifications in the interpretation of the Second Law of Thermodynamics, as compared with the earlier interpretations on the late 19th and the 20th century. For example, Chaisson and Layzer have advanced reconciliations of the concept of entropy with the cosmological creation of order. In another approach, Schneider and D. Sagan, in “Into the Cool’ and other publications, depict the organization of life, and some other phenomena such as benard cells, as entropy generating phenomena which facilitate the dissipation, or reduction, of gradients (without in this treatment visibly getting to the prior issue of how gradients have arisen).

The ubiquity of ‘power law’ and log normal distribution manifestations in the Universe

The development of network theories has yielded observations of widespread, or ubiquitous, appearance of power law and log normal distributions of events in such networks, and in nature generally. (Mathematicians often distinguish between ‘power laws’ and ‘log normal’ distributions, but not all discussions do so.) Two observers have provided documentation of these phenomena, Albert-Laslo Barabasi,, and Mark Buchanan

Buchanan demonstrated that power law distribution occur throughout nature, in events such as earthquake frequencies, the size of cities, the size of sun and planetary masses, etc. Both Buchanan and Barabasi reported the demonstrations of a variety of investigators that such power law distributions arise in phase transitions.

In Barabasi’s characterization “…if the system is forced to undergo a phase transition … then power laws emerge – nature’s unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self organization and paved with power laws.”

Given Barabasi’s observation that phase transitions are, in one direction, correlational events yielding ordered relationships, relational theories of order following this logic would consider the ubiquity of power laws to be a reflection of the ubiquity of combinatorial process of correlation, expressed in phase transitions.

Emergence

There has been considerable comment on the concept of ‘emergence’ in recent decades. See Emergence
Emergence
In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....

 This summary of relational regime theories will not create a detailed analysis or a summary of literature, as this might be done elsewhere. However, one can note and briefly illustrate that the relational regime approach includes a straightforward derivation of the concept of emergence.

That is, from the perspective of relational theories of order, emergent phenomena could be said to be relational effects or characteristics of an aggregated and differentiated system made of many elements, in a field of relationships external to the considered system, when the elements of the considered system, taken alone, would not have such an effect.

For example, the stable structure of a rock, which allows very few degrees of freedom for its elements, can be seen to have a variety of external manifestations depending on the relational system in which it may be involved. It could impede fluid flow, given some conditions. In a regime of gases, it will exclude most components of the gas from the space it occupies, ( or incorporate some of them, depending on its structure). In contests among rivalrous humans, it has sometimes been a convenient skull cracker. Or it might become a composite element of another solid, with similarly reduced degrees of freedom for its components, as would a pebble in a matrix making up cement.

To shift particulars, embedding carbon filaments in a resin making up a composite material can yield ‘emergent’ effects. (See the composite material
Composite material
Composite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...

 article for a useful description of how varying components can, in a composite, yield effects within a field of use which the components alone would not yield).

That this derivation of the concept of emergence is conceptually straightforward and this brief reflection of this derivation uses simple illustrations does not imply that the relational system may not itself be complex, or participate as an element in a complex system of relationships – as is illustrated using different terminology in some aspects of the linked emergence and complexity
Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

 articles.

The Arrow of time

As the article on the Arrow of time
Arrow of time
The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...

 in this encyclopedia makes clear, there have been a variety of approaches to defining time and defining how time may have a direction.

The theories which outline a development of order in the universe, rooted in the asymmetric processes of expansion and cooling, project an ‘arrow of time’ – i.e. a sustained process which as it proceeds yields changes of state which do not appear, in the aggregate, to be reversible, over the universe as a whole.

Given the challenges confronting humans in determining how the Universe may evolve over billions and trillions of our years, it is difficult to say how long this arrow may be and the eventual end state it targets. At this time some prominent investigators suggest that much if not most of the visible matter of the universe will collapse into black holes which can be depicted as isolated, in a static cosmology.

Economics

Albert-Laslo Barabasi, Igor Matutinovic and others have suggested that economic systems can fruitfully be seen as network phenomena generated by non-equilibrium forces.

At this time there is a visible attempt to re-cast the foundations of the economics discipline in the terms of non-equilibrium dynamics and network effects, led by researchers belonging to the school of evolutionary and institutional economics (Jason Potts), and ecological economics (Faber et al.). The Complexity economics
Complexity economics
Complexity economics is the application of complexity science to the problems of economics. It studies computer simulations to gain insight into economic dynamics, and avoids the assumption that the economy is a system in equilibrium.- Models :...

 article in this Encyclopedia elaborates on this and related developments.

Outside this group, some economists have adopted the language of ‘network industries’.

See also

  • Autocatalysis
    Autocatalysis
    A single chemical reaction is said to have undergone autocatalysis, or be autocatalytic, if the reaction product itself is the catalyst for that reaction....

  • Autocatalytic set
    Autocatalytic set
    An autocatalytic set is a collection of entities, each of which can be created catalytically by other entities within the set, such that as a whole, the set is able to catalyze its own production. In this way the set as a whole is said to be autocatalytic...

  • Emergence
    Emergence
    In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....

  • Dissipative systems
  • Ecosystem
    Ecosystem
    An ecosystem is a biological environment consisting of all the organisms living in a particular area, as well as all the nonliving , physical components of the environment with which the organisms interact, such as air, soil, water and sunlight....

  • Phase
    Phase (matter)
    In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

  • Phase transition
    Phase transition
    A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

  • Self-organization
    Self-organization
    Self-organization is the process where a structure or pattern appears in a system without a central authority or external element imposing it through planning...

  • Self-organized criticality
    Self-organized criticality
    In physics, self-organized criticality is a property of dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune...

  • System
    System
    System is a set of interacting or interdependent components forming an integrated whole....

  • Systems theory
    Systems theory
    Systems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...

  • Theory of Social Systems
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