Variations on any theory of correspondences

Theories of Correspondences -- and potential equivalences between them in correlative thinking (Part #5)

It could be inferred that the algebraic theory of correspondences of science has displaced the symbolist variant, much as some religions are notable for constructing their places of worship on the precise location of the deprecated "pagan" forms performing an "analogous" function in earlier times. The nature and degree of similarity will be explored below.

But, despite statements such as those of Jung, that the symbolist theory of correspondences is "obsolete", it should be noted that it continues to be influential as such in a variety of domains. For example the Swedenborgian variant continue to be promoted through Swedenborgian groups, as the "science of correspondences" (cf Geoffrey S. Childs, Correspondences: a key to distinctiveness, Journal of the Correspondences Committee, 1990-1992, and bibliography) [the Wikipedia entry lists notable people influenced by these views in the past].

But, more intriguing is the degree to which surrogates have emerged that are not apparently related to either the algebraic or the symbolist variants. The theory of correspondences in its "obsolete" sense, can fruitfully be understood as having gone underground -- or even been forced underground by the dominance of cognitive styles in mainstream science and religion through the first half of the past century. "Underground" may however mean incorporated into the body of esoteric knowledge characteristic of the many rosicrucian, masonic and other secret societies.

A fruitful set for further study might therefore include:

Metaphor and analogy: These are variously distinguished and widely used, both as fundamental to cognitive processes (notably in the hardest of sciences) and for purposes of communicating complex insights to a wider audience. It is for example interesting that a new source of motivation for work on the foundations of algebraic geometry, in general, and on intersection theory, in particular, resulted from the solution of an outstanding problem in number theory (the Riemann hypothesis for fields of algebraic functions in one variable over a finite field of constants) by André Weil in 1940 using an "analogue of the theory of correspondences". The work of George Lakoff, with various collaborators, has given considerable credibility to this mode of reasoning. Its role in governance may be fundamental (cf Documents relating to Metaphor for Governance). One approach to analogy of historical interest, because of its relationship to the symbolist theory of correspondences, is the theory of universal analogy of Charles Fourier (1772-1837). An unfortunately narrow approach to similarity and analogical reasoning by Western cognitive scientists is discussed below.
Isomorphism: This is of technical significance in mathematics but is more generally recognized as a kind of mapping between objects, which shows a relationship between two properties or operations. According to Douglas Hofstadter: "The word 'isomorphism' applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where 'corresponding' means that the two parts play similar roles in their respective structures." (Gödel, Escher, Bach, p. 49) From a mathematical perspective, I. E. Segal (Equivalences of Measure Spaces, American Journal of Mathematics, 73, 2, 1951, pp. 275-313) clarifies the varieties of isomorphism, relatings weak equivalence of measure spaces to varieties of isomorphism of function-spaces over measure spaces..
Homology: This is a form of analogy or isomorphism distinctly characteristic of various disciplines. In the case of anthropology, homology refers to analogy between human beliefs, practices or artifacts due to genetic or historical connections. In biology, the analogy to which homology refers is that of structures arising from shared ancestry. In mathematics, homology (and cohomology) is a procedure to associate a sequence of abelian groups or modules with a given mathematical object. In sociology, homology is a form of structural 'resonance' between different elements making up a socio-cultural whole.
Cobordism: In mathematics, this is a relation between manifolds, based on the idea of boundary. Two manifolds M and N are cobordant if their union is the complete boundary of a third manifold L; L is then called a cobordism between M and N. By this means an equivalence relation on manifolds is obtained. Cobordism theory has become part of the apparatus of extraordinary cohomology theory.
Correlation: In probability theory and statistics, correlation indicates the strength and direction of a linear relationship between two random variables. It is an indication of the departure of two variables from independence. There are a number of coefficients that measure the degree of correlation. From a psycho-social perspective, "correlative thinking" has been noted as characteristic of premodern cultures, as discussed in more detail below.
General systems: In search for invariants across specialized disciplines, the Society for General Systems Research was founded in 1954 (see Yearbook of the Society for General Systems Research), later renamed International Society for the Systems Sciences. Essentially the initiative aimed at overcoming the growing isolation of specialized disciplines. Considerable attention has been given to isomorphism between distinct disciplines or between systemic levels, notably as subsequently developed through living systems theory. The commonalities and contrasts with cybernetics also merit attention.
Isophor: Combining isomorphism and metaphor, this term has been used by Kathleen Forsythe to depict a feeling response to one thing in terms of another. An isophor is then something that is "experienced emotionally and, (that) as such, define(s) the experience of understanding." (Isophor: poiesis of experience, 1987 ). Elsewhere Forsythe (Cathedrals of the Mind, 1986) argues that: "Analogy and its poetic expression, metaphor, may be the "meta-forms" necessary to understanding those aspects of our mind that make connections, often in non-verbal and implicit fashion, that allow us to understand the world in a whole way." With the isophor there is no separation between thought and action, between feeling and experience. The experience itself is evoked through the relation. She suggests that the experience of one thing in terms of another, the isophor, is the means by which domain is mapped to domain and that consciousness of this meta-action, when recognized, lies at the heart of cognition. Forsythe has postulated the development of an epistemology of newness in which learning is the perception of newness and cognition depends on a disposition for wonder leading to this domain of conception-perception interactions. She argues that the notion of metaphor is commonly understood to mean the description of one thing in terms of another -- presupposing an objective reality. This objectivity may be questioned especially if, as suggested by Maturana, (objectivity) is placed in parentheses.
Design: In all its forms, including sacred geometry, design is dependent on appropriate correspondences. This is most notably to be seen in use of design in marketing and communications.
Parallelism in rhetoric: As a rhetorical and poetic device (notably in Hebrew biblical poetry and Chinese poetry), two or more parts of the structure may be given a similar form so as to give the whole a definite pattern. Roman Jakobson pioneered The secular study of parallelism in poetic-linguistic traditions around the world was pioneered by Roman Jakobson (The Poetry of Grammar and the Grammar of Poetry, 1987).
"Magic": This term may be variously understood. Those skilled in any art or science are notably valued when their solutions to a challenge are described as "magic". Loosely defined, a social (or romantic) occasion is typically most highly valued if it is "magical". A more precise understanding of what makes such occasions magical was the focus of "natural magic" or "sympathetic magic", notably promoted by Marsilio Ficino (B. Copenhaver. Natural magic, hermetism, and occultism in early modern science, 1990) and contrasted with "demonic magic". As understood by its current practitioners (notably neo-pagans and wiccans), the "magical art of correspondences", based on an underlying theory of "correspondences", is held to be the basis of magic itself. These correspondences are considered to be hidden relationships among entities within the universe -- especially between human beings and the external world. They are understood as
- links that unite seemingly disparate realms;
- a window on the structure of the cosmos;
- a lens between the macrocosm ('as above') and microcosm ('so below');
- based on analogical reasoning, which seeks similarities of pattern -- a "right-brain" approach (artistic, poetic, holistic) -- rather than "left-brain" cause-and-effect reasoning which scientific materialism insists is alone valid.
Divinatory systems are considered especially powerful tools in finding and analyzing correspondences, notably with the aid of "tables of correspondences". In contrast to the pathetic conflation of magic with sorcery (as in the Encarta encyclopedia), under any focus on demonic magic, careful attention can fruitfully be given to the distinction between demon and daimon. The latter (cf Kairos -- the opportune moment for self-referential re-identification, 2007) been held to be intimately related to the still voice of conscience (as notably consulted by Socrates prior to his death), the artists muse, and duende as highly valued in Spanish culture.
Symbolism: Seemingly disassociated from the (past) "symbolist movement" in the arts and the inspirations it derived from the "symbolist theory of correspondences", symbolism is increasingly recognized to have a far greater presence in contemporary culture than most realize. As noted by symbolism.org: " More than an ancient, esoteric discipline, it really serves as the centerpiece for an entirely new modern philosophy and understanding of the world. While symbols seem to increasingly 'migrate' to contemporary culture - defining such things as leading brands, products, films, events and celebrities - few understand the dynamics and cycles of their movement, their overall language and what they tell us. In effect, we are much more busy creating symbols than trying to understand them".
Archetypal psychology: As developed by James Hillman, from the work of Carl Jung, archetypal psychology is a polytheistic psychology, in that it attempts to recognize the myriad fantasies and myths -- gods, goddesses, demigods, mortals and animals -- that shape and are shaped by the psychological lives of humans. The ego is understood to be but one psychological fantasy within an assemblage of fantasies.
Synaesthesia: The term synaesthesia is normally used to indicate a condition in which the stimulation of one sensory modality gives rise to an experience in another modality. This may be understood as a form of cognitive fusion. In an auditory synaesthete, for example, an auditory experience may give rise to an experience in the visual modality. Synaesthetes often experience correspondences between the shades of color, tones of sounds, and intensities of tastes that provoke alternate sensations (see Synaesthesia: union of the senses; Richard E. Cytowic, Synesthesia: phenomenology and neuropsychology -- a review of current knowledge, 1995). Ironically a symbolist poet, inspired by Baudelaire's views of synaesthesia, has been criticized for lack of scientific merit at a time when attention is being given to then phenomenon (Louis W. Marvick, Rene Ghil and the Contradictions of Synesthesia, Comparative Literature, 51, 4 1999, pp. 289-308)
Transdisciplinarity: Disciplines are defined by distinct methods which are necessarily disassociated from any interdisciplinary or transdisciplinary methodology intended to elicit connectivity between their respective cognitive styles. The systems sciences have offered one approach to this difficulty; proposals for unified science have offered another. These proposals have not however been able to encompass disciplines held to be non-scientific.
Psycho-cultural equivalence: Marisa Zavalloni (Identity and Hyperidentities: the representational foundation of self and culture, Papers on Social Representations, 2, 3, 1993) outlines based on three sets of equivalence:
- Linguistic equivalence means that in terms of identity, an adjective, a verb, a noun, anadverb are interchangeable, thus to be adventurous, adventure, to act adventurously all point to different accounts of a same underlying, referential complex.
- Psychological equivalence refers to the affective- representational circuit, namely if an identity word appears on one psychological dimension, it will necessarily appear on all the other dimensions. When one of these dimensions is in a foreground position (as the focus of consciousness) the other will be activated as background thinking.
- Affective equivalence means that the different feelings that are activated in association with the psychological dimensions comprising the affective-representational circuit, are experienced simultaneously either in foreground or background positions. These feelings are all part of the original affect which was triggered when a feature of the external world became encapsulated in an identity word. As a postcolonialist critic, Gayatri Chakravorty Spivak (Can the Subaltern Speak? 1988) introduced a more complex notion of affective equivalence in clarifying the position of Deleuze and Foucault:
  Their suggestion, summarized, is that, since capital decodes and deterritorializes the socius by releasing the abstract [cf. Nietzsche's slave logic] as such, capitalism manages the crisis by way of the generalized psychoanalytic mode of production of affective value, which operates via a generalized system of affective equivalence, however spectacular in its complexity and discontinuity.
Mutuality of affection: A degree of equivalence in affective and romantic relationships -- promoted as the ideal of courtly love -- is a major concern in interpersonal relationships. Victor S. Johnston (Why We Feel: the science of human emotions, 1999) describes a set of feelings particularly adjusted to the paradoxical challenges of survival: an elaborate emotional monitoring system for the mutuality of affection, protection, and concern. If the reciprocity is broken by recklessness, a "pop out feeling" indicates the loss of the "investment". An extreme example is unrequited love, namely love that is not reciprocated, even though reciprocation is usually deeply desired.

More generally, Daniel Goleman (Social Intelligence: the new science of human relationships, 2006) summarizes a wide range of research on social neuroscience indicative of the manner in which identity is established and sustained by cyclic psychosocial processes. Whereas the circulatory system is a closed loop, the emotions are an open loop system sustained by cognitive processes that allow others to help manage individual emotions more appropriately. Goleman uses the term "looping", which readily recalls the anxiety that people may feel to be "kept in the loop" -- perhaps to be usefully understood as a felt sense of equivalance. Empathy creates a feedback loop as people work towards a "fit" between their own perceptions and the reality of another -- such that looping enables a person to feel within themselves the distress expressed by another. On the other hand, looping too tightly -- excessive mutual entrainment -- can be experienced as suffocating in a relationship. He distinguishes between "positive" and "negative" (or toxic) loops.
Value-centred "equivalence":
- Value equivalence (in media preferences): The concepts of trust and credibility may be and framed as 'value equivalence' -- namely a comparison of value differences between user and media affecting whether or not alternatives to the available, dominant mass media will be sought and used. Value equivalence may then explain user preference, trust, selection, and uses of both mass and alternative media. (T. B. Christie. The role of value equivalence in news media selection, American Association for Public Opinion Research, 2003)
- Moral equivalence: This is used to challenge assumptions of moral superiority, notably in comparing acts of aggression between states or peoples. In some cases it may then be argued that the two parties could be viewed as "equally" culpable in a struggle for (moral) supremacy. Critics have for example claimed that the intervention of the USA in various arenas should be considered as morally equivalent to some interventions by the Soviet or Nazi regimes. Similar judgments have been made with respect to the Israeli actions against Palestinians, in comparison with some Nazi acts against the Jews. The term "romantic equivalence" has been similarly used with regard to efforts to compare the rights of Israelis to live in peace and of Palestinians to regain all of their land. The applicability of moral equivalence in the case of the USA was notably challenged by Jeane Kirkpatrick (The Myth of Moral Equivalence, Imprimis, 15, January 1986, 1) following her period as the first woman US Ambassador to the United Nations. Such views were effectively echoed by a subsequent US Ambassador to the United Nations, Madeleine Albright, the first woman to become US Secretary of State. When asked by an interviewer with regards to the effect of sanctions against Iraq: "We have heard that half a million children have died. I mean, that's more children than died in Hiroshima...is the price worth it?". Albright replied: "I think this is a very hard choice, but the price -- we think the price is worth it." (We Think the Price is Worth It, Fair, 2001) Such views regarding Iraq (and elsewhere) continue to be echoed by the leadership of the Coalition of the Willing. Albright was notable for her failure to take any action with regard to the genocide in Rwanda. Righteousness necessarily precludes any possible recognition of moral equivalence, no matter the degree of atrocity for which the righteous are responsible.
- Retributive justice: From this perspective there is an expectation that punishment should in some way be equivalent to the crime. Proportional punishment, scaled relative to the severity of the offending behaviour, is thereby considered as a morally acceptable response to crime. This is not necessarily interpreted to mean that the punishment has to be precisely equivalent to the crime.
Spiritual equivalence: Some interfaith groups promote initiatives that assume a degree of equivalence between the deepest insights of different religions or spiritual traditions -- although such equivalence is profoundly deplored by others as anathema or blasphemy (even to the point of being punishable by death). As consistent with a general "law of equivalence of form", a "spiritual equivalence of form" may also be understood in terms of the degree of similarity and dissimilarity of intentions. Others, such as the Asymmetric Threats Contingency Alliance, recognize a degree of equivalence between spirituality and science. A spiritual equivalence between jaguars and shamans is sometimes made explicit in the widespread belief that, under the influence of hallucinogens, some shamans transform into jaguars in body as well as spirit.

Focusing on John Locke, the process philopher Greg Moses (American Pluralisms: pragmatism, Locke and Cruse, 1995) argues with regard to spiritual equivalence:
What the contemporary mind stands greatly in need of is the divorce of the association of uniformity with the notion of the universal, and the substitution of the notion of equivalence. Sameness in difference may be a difficult concept for us -- it is. But the difficulty is historical and traditional, and is the specific blight of the modern and Western mind.
How much of the contemporary mind is still preoccupied with uniformity as the best fulfillment of unity? Note the continuing complaint that diversity is less important than universal human values.

As an early advocate, and bureaucratic casualty, of what today is called multicultural education, Locke fought valiantly for cultural approaches which embrace difference, because of the deeper unity that is signified:

What we need to learn most is how to discover unity and spiritual equivalence underneath the differences which at present so disunite and sunder us, and how to establish some basic spiritual reciprocity on the principle of unity in diversity. If for instance, one difference that divides us is racial, then it will be important to select representative expressions from across race lines in order to discover spiritual equivalences between them. Having investigated such equivalences, we would be better equipped to unify ongoing differences and mediate against further conflicts.

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Variations on any theory of correspondences