Relational theory

In physics and philosophy, a relational theory is a framework to understand reality or a physical system in such a way that the positions and other properties of objects are only meaningful relative to other objects. In a relational spacetime theory, space does not exist unless there are objects in it; nor does time exist without events. The relational view proposes that space is contained in objects and that an object represents within itself relationships to other objects. Space can be defined through the relations among the objects that it contains considering their variations through time. The alternative spatial theory is an absolute theory in which the space exists independently of any objects that can be immersed in it.

Someone who has constructed a relational theory or promotes relational theorising is called a relationist.

The relational point of view was advocated by in physics by Gottfried Wilhelm Leibniz, Ernst Mach (in his Mach's principle), and it was rejected by Isaac Newton in his successful description of classical physics. Although Albert Einstein was impressed by Mach's principle, he did not fully incorporate it into his general theory of relativity. Several attempts have been made to formulate a full Machian theory, but most physicists think that none have so far succeeded. For example, see Brans–Dicke theory.

Relational quantum mechanics and a relational approach to quantum physics have been independently developed, in analogy with Einstein's special relativity of space and time. Relationist physicists such as John Baez and Carlo Rovelli have criticised the leading unified theory of gravity and quantum mechanics, string theory, as retaining absolute space. Some prefer a developing theory of gravity, loop quantum gravity for its 'backgroundlessness'.

A recent synthesis of relational theory, called R-theory,^[1] continuing the work of the mathematical biologist Robert Rosen (who developed "Relational Biology" and "Relational Complexity" as theories of life (^[2]) takes a position between the above views. Rosen's theory differed from other relational views in defining fundamental relations in nature (as opposed to merely epistemic relations we might discuss) as information transfers between natural systems and their organization (as expressed in models). R-theory extends the idea of organizational models to nature generally. As interpreted by R-theory, such "modeling relations" describe reality in terms of information relations (encoding and decoding) between measurable existence (expressed as material states and established by efficient behavior) and implicate organization or identity (expressed as formal potential and established by final exemplar), thus capturing all four of Aristotle's causalities within nature (Aristotle defined final cause as immanent from outside of nature). Applied to space-time physics, it claims that space-time is real but established only in relation to existing events, as a formal cause or model for the location of events relative to each other; and in reverse a system of space-time events establishes a template for space-time. R-theory is thus a form of model-dependent realism. It claims to more closely follow the views of Mach, Leibniz, Wheeler and Bohm, suggesting that natural law itself is system-dependent.

Relational order theories

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 systems, or networks, of relationships. Basic physics has assumed and characterized distinctive regimes of relationships. For common examples, gases, liquids and solids are characterized as systems of objects which have among them relationships of distinctive types. Gases contain elements which vary continuously in their spatial relationships as among themselves. In liquids component elements vary continuously as to angles as between themselves, but are restricted as to spatial dispersion. In solids both angles and distances are circumscribed. These systems of relationships, where relational states are relatively uniform, bounded and distinct from other relational states in their surroundings, are often characterized as phases of matter, as set out in Phase (matter). These examples are only a few of the sorts of relational regimes which can be identified, made notable by their relative simplicity and ubiquity in the universe.

Such Relational systems, or regimes, can be seen as 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. In the commonly observed transitions between phases of matter, or phase transitions, the progression of less ordered, or more random, to more ordered, or less random, systems is recognized as the result of correlational processes (e.g. gas to liquid, liquid to solid). In the reverse of this process, transitions from a more-ordered state to a less ordered state, as from ice to liquid water, are accompanied by the disruption of correlations.

Correlational processes have been observed at several levels. For example, atoms are fused in suns, building up aggregations of nucleons, which we recognize as complex and heavy atoms. Atoms, both simple and complex, aggregate into molecules. In life a variety of molecules form extremely complex dynamically ordered living cells. Over evolutionary time multicellular organizations developed as dynamically ordered aggregates of cells. Multicellular organisms have over evolutionary time developed correlated activities forming what we term social groups. Etc.

Thus, as is reviewed below, correlation, i.e. ordering, processes have been tiered through several levels, reaching from quantum mechanics upward through complex, dynamic, 'non-equilibrium', systems, including living systems.

Quantum Mechanics

Lee Smolin^[3] 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".^[4] Smolin and a group of like minded researchers have devoted a number of years to developing a loop quantum gravity basis for physics, which encompasses this relational network viewpoint.

Carlo Rovelli initiated development of a system of views now called Relational quantum mechanics. This concept 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.

The physical content of the theory is not to do with objects themselves, but the relations between them. As Rovelli puts it: "Quantum mechanics is a theory about the physical description of physical systems relative to other systems, and this is a complete description of the world".^[5]

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.

Cosmology

The conventional explanations of Big Bang and related cosmologies (see also Timeline of the Big Bang) project an expansion and related ‘cooling’ of the universe. This has entailed a cascade of phase transitions. Initially were quark-gluon transitions to simple atoms. According to current, consensus cosmology, given gravitational forces, simple atoms aggregated into stars, and stars into galaxies and larger groupings. Within stars, gravitational compression fused simple atoms into increasingly complex atoms, and stellar explosions seeded interstellar gas with these atoms. Over the cosmological expansion process, with continuing star formation and evolution, the cosmic mixmaster produced smaller scale aggregations, many of which, surrounding stars, we call planets. On some planets, interactions between simple and complex atoms could produce differentiated sets of relational states, including gaseous, liquid, and solid (as, on Earth, atmosphere, oceans, and rock or land). In one and probably more of those planet level aggregations, energy flows and chemical interactions could produce dynamic, self replicating systems which we call life.

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.

This picture of progressive development of order in the observable universe as a whole is at variance with the general framework of the Steady State theory of the universe, now generally abandoned. It also appears to be at variance with an understanding of the Second law of thermodynamics which would view the universe as an isolated system which would at some posited equilibrium be in a maximally random set of configurations.

Two prominent cosmologists 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. David Layzer ^[6] and Eric Chaisson.^[7]

Layzer speaks in terms of the rate of expansion outrunning the rate of equilibration involved at local scales. Chaisson summarizes the argument as "In an expanding universe actual entropy … increases less than the maximum possible entropy"^[8] thus allowing for, or requiring, ordered (negentropic) relationships to arise and persist.

Chaisson depicts the universe as a non-equilibrium process, in which energy flows into and through ordered systems, such as galaxies, stars, and life processes. This provides a cosmological basis for non-equilibrium thermodynamics, treated elsewhere to some extent in this encyclopedia at this time. In terms which unite non-equilibrium thermodynamics language and relational analyses language, patterns of processes arise and are evident as ordered, dynamic relational regimes.

Biology

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^[9] Smolin,^[10] Chaisson, Stuart Kauffman^[11] and Ulanowicz.^[12]

This realization has proceeded from, among other sources, a seminal concept of ‘dissipative systems’ offered by Ilya Prigogine. 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. A familiar example of such a structure is the Red Spot of Jupiter.

In the 1990s, Eric Schnieder and J.J. Kaye^[13] 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) 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.^[14] 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^[15] 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 correlation processes entailed in the expansion and cooling processes of the universe.

Two investigators, Robert Ulanowicz^[12] and Stuart Kauffman, .^[16] have suggested the relevance of autocatalysis 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 thermodynamic definition of the life process, which might briefly be summarized as stable, patterned (correlated) processes which intake (and dissipate) energy, and reproduce themselves.^[17]

Ulanowicz, a theoretical ecologist, has extended the relational analysis of life processes to ecosystems, using information theory 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 and, more fully, Leo Buss^[18] 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 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.

Related areas of current interest

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-László Barabási,^[19] and Mark Buchanan^[20]

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."^[21]

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 processes of correlation in creating all ordered systems.

Emergence

The relational regime approach includes a straightforward derivation of the concept of emergence.

From the perspective of relational theories of order, emergent phenomena could be said to be relational effects 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 separately and independently, would not have such effects.

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 found. It could impede fluid flow, as a part of a retaining wall. If it were placed in a wind tunnel, it could be said to induce turbulence in the flow of air around it. In contests among rivalrous humans, it has sometimes been a convenient skull cracker. Or it might become, though itself a composite, an element of another solid, having 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 article for a useful description of how varying components can, in a composite, yield effects within an external field of use, or relational setting, which the components alone would not yield).

This perspective has been advanced by Peter Corning, among others. In Corning's words, "...the debate about whether or not the whole can be predicted from the properties of the parts misses the point. Wholes produce unique combined effects, but many of these effects may be co-determined by the context and the interactions between the whole and its environment(s)." ^[22]

That this derivation of the concept of emergence is conceptually straightforward 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 articles.

The term "emergence" has been used in the very different sense of characterizing the tiering of relational systems (groupings made of groupings) which constitutes the apparently progressive development of order in the Universe, described by Chaisson, Layzer, and others, and noted in the Cosmology and Life Organization portions of this page. See for an additional example the derived, popularized narrative Epic of Evolution described in this encyclopedia. From his perspective, Corning adverts to this process of building 'wholes' which then in some circumstances participate in complex systems, such as life systems, as follows "...it is the synergistic effects produced by wholes that are the very cause of the evolution of complexity in nature."

The Arrow of time

As the article on the Arrow of time 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’ . That is, the expanding universe is a sustained process which as it proceeds yields changes of state which do not appear, over the universe as a whole, to be reversible. The changes of state in a given system, and in the universe as a whole, can be earmarked by observable periodicities to yield the concept of time.

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.^[23]

Economics

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.

Albert-László Barabási, Igor Matutinovic^[24] and others have suggested that economic systems can fruitfully be seen as network phenomena generated by non-equilibrium forces.

As is set out in Thermoeconomics, a group of analysts have adopted the non equilibrium thermodynamics concepts and mathematical apparati, discussed above, as a foundational approach to considering and characterizing economic systems. They propose that human economic systems can be modeled as thermodynamic systems. Then, based on this premise, theoretical economic analogs of the first and second laws of thermodynamics are developed.^[25] In addition, the thermodynamic quantity exergy, i.e. measure of the useful work energy of a system, is one measure of value.

Thermoeconomists argue that economic systems always involve matter, energy, entropy, and information.^[26] Thermoeconomics thus adapts the theories in non-equilibrium thermodynamics, in which structure formations called dissipative structures form, and information theory, in which information entropy is a central construct, to the modeling of economic activities in which the natural flows of energy and materials function to create and allocate resources. In thermodynamic terminology, human economic activity (as well as the activity of the human life units which make it up) may be described as a dissipative system, which flourishes by consuming free energy in transformations and exchange of resources, goods, and services.

The article on Complexity economics also contains concepts related to this line of thinking.

Another approach is led by researchers belonging to the school of evolutionary and institutional economics (Jason Potts), and ecological economics (Faber et al.).^[27]

Separately, some economists have adopted the language of ‘network industries’.^[28]

Particular Formalisms

Two other entries in this encyclopedia set out particular formalisms involving mathematical modeling of relationships, in one case focusing to a substantial extent on mathematical expressions for relationships Theory of relations and in the other recording suggestions of a universal perspective on modeling and reality Relational theory.

See also

• Relationalism
• Relationism
• Systems theory

References