Engaging with mathaphors, isophors, analogies and correspondences

Wholth as Sustaining Dynamic of Health and Wealth (Part #9)

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Mapping correspondences: Missing from the bridging initiatives (noted above) is any systematic attempt to map the axiomatic structures of theology in relation to the axiomatic formalizations of mathematics, in the light of the logic implied in each case. As evoked by Sarah Voss, the question is then whether those of mathematics offer mnemonic aids to the process of engendering spiritual experience -- to eliciting wholth according to the argument here. Problematic in both cases is the aridity of the language of those axioms (framed statically in terms of categories) in relation to the need to enable the cognitive engagement intrinsic to the dynamics of the experiential quality of wholth.

A striking example of the fruitful role of correspondences emerged in the course of development of symmetry group theory -- in relation to discovery of the so-called Monster Group of incomprehensibly high dimensionality. Work on the unexpected nature of the correspondences gave rise to the expression in mathematics of monstrous moonshine theory. This is acclaimed as one of the most profound discoveries in mathematics whose significance is yet to be fully understood (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

The challenge of symmetry group comprehension is another matter (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008). However the possibility of formal correspondences between the axiomatic structures of mathematics and theology is more readily conceivable than those made credible by moonshine mathematics.

Given the concern here with connectivity within a "meta-pattern", comparison between the distinct and shared understanding of correspondences merits consideration (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007). Especially interesting are the distinctions and overlaps between its various uses, most notably in the light of their historical role in the symbolist tradition:

• Correspondence (mathematics), with several related meanings
• Correspondence analysis, a multivariate statistical technique
• Correspondence rules (quantum mechanics)
• Correspondence theory of truth (philosophy), a theory in epistemology
• Correspondence principle (physics), that theories must agree with experimental evidence
• Correspondence (theology), the relationship between spiritual and physical realities

Metaphors and analogies: Striking emphasis has been given to the role of metaphor from a cognitive psychological perspective by George Lakoff and Mark Johnson (Metaphors We Live By, 1980; Philosophy in the Flesh: the embodied mind and its challenge to Western thought, 1999). This has been explicitly related to mathematics (George Lakoff and Rafael E. Núñez, Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000).

Possibilities of relevance to this arguments are indicated by the theologian and feminist scholar, Sallie McFague who argues for a different way of knowing, exemplified in her case by its implications for knowing divinity (Life Abundant: rethinking theology and economy for a planet in peril, 2000). In particular she argues for the individual freedom to engage in metaphoric reframing of God according to different circumstances -- rather than being dependent on particular models (Metaphorical Theology: models of God in religious language, 1982; Models of God: theology for an ecological, nuclear age, 1987). Her case for producing metaphors taking appropriate account of environmental factors could be adapted, both to reframing the science-religion relationship and to framing a meta-pattern with which individuals could have as intimate relationship as with deity.

Especially interesting are the insights into cognitive processes offered by fluidity, as developed in the work of Douglas Hofstadter (Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995). The approach contrasts with the rigidity conventionally associated with categories. In collaboration with Emmanuel Sander, this has now been further developed (Surfaces and Essences: analogy as the fuel and fire of thinking, 2013) who argue that:

We are constantly faced with a swirling and intermingling multitude of ill-defined situations. Our brain's job is to try to make sense of this unpredictable, swarming chaos of stimuli. How does it do so? The ceaseless hail of input triggers analogies galore, helping us to pinpoint the essence of what is going on. Often this means the spontaneous evocation of words, sometimes idioms, sometimes the triggering of nameless, long-buried memories.

The dynamics of such fluidity, notably in the light of the unusual insights of Viktor Schauberger, are a rich source of metaphor of relevance to governance, as separately explored (Enabling Governance through the Dynamics of Nature: exemplified by cognitive implication of vortices and helicoidal flow, 2010).

Mathaphors: The term was introduced by Voss, as noted, as a means of expanding understandings of spirituality, namely through metaphors drawn from mathematics. In an interview by Tom McFarlane (Mathematics, Ministry, and Mediation: an interview with Sarah Voss, Holos: forum for a new world view, 2009), Voss indicates:.

Mathaphors, however, have current as well as historical importance. Today's culture is largely caught up in the truths of science, which consistently uses mathematics as the primary language for both exploration and communication. To me, that means mathematics is also an exquisite candidate forcontemporaryspiritual exploration.Lewis Thomas, author of many books on science, medicine, language, and philosophy, once referred to mathematics as the universal language of the future.

Isophors: In various papers to the American Society for Cybernetics, Kathleen Forsythe (Cathedrals in the Mind: the architecture of metaphor in understanding learning, 1986) makes the point that: It can be argued that metaphor is the fundamental core of our conceptual system as surely as the logic of form which we use in argument and debate. She cites Gregory Bateson: "...metaphor is not just pretty poetry, it is not either good or bad logic, but it is in fact the logic upon which the biological world gas been built, the main characteristic and organizing glue of this world of mental process....

Forsythe then argues:

However, because our conceptual system is not something we are normally aware of, we have failed to account for its metaphorical nature in our discussion of truth and meaning. Yet its pervasiveness suggests a central and basic role in the underlying architecture of thought. Metaphor can create new meaning, create similarities and so define a new insight and new perception of reality.. Such a view has no place in the dominant objectivist picture of the world.

She further notes:

The pervasiveness of metaphor in our conceptual system suggests a central and basic role in the underlying architecture of thought. Metaphor represents the ability to understand one thing in terms of another as we ascribe an understood pattern to unknown phenomena and perceive their structural integrity within the environment of our experience. We can then begin to perceive the environment of learning as one in which analogical thinking serves as architecture, analytical thinking serves as engineering and the imagination ensures that the interactions which create life and meaning are always being realized anew. The implications for this approach to applied epistemology provide insights into the design and development of learning systems that support the creative nature of learning.

As separately indicated (Being the Universe : a Metaphoric Frontier, 1999), Forsythe also 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.

Forsythe uses the term isophors for isomorphisms experienced in the use of language. Isophors are distinct from metaphors in that they are experienced directly. 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 we map domain to domain and that our consciousness of this meta-action, when we observe ourselves experiencing this, lies at the heart of cognition. She 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. This notion presupposes an objective reality. This objectivity may be questioned and if, as suggested by Maturana, (objectivity) is placed in parentheses:

... we can begin to appreciate clearly the role we play in the construction of our own perception of reality. for this reason, the notion of the experience of one thing in terms of another, the isophor, suggests that it is this dynamic constructing ability that involves conception and perception -- unfolding and enfolding, that this gives rise to the coordination of actions in recursion which we know as language.

As discussed separately (Significance: Metaphor, analogy, symbol and pattern, 1995), Forsythe stresses the relationship between metaphor and the pattern language developed by Christopher Alexander:

The architecture of how we structure the reality of our imagination is metaphoric. Metaphors are bridges that order the nature of our collective and individual humanity. Metaphor provides the reality to the pattern language of thought for it is the mechanism of ordering newness. Language only lives when each person has his or her own version that must constantly be re-created in each person's mind as he or she interacts with others in the environment. It is only through understanding these inner patterns that we can begin to consciously bring the outer pattern of our lives into harmony.

The potential of such a pattern language for enabling engagement with a meta-pattern has been variously explored separately (5-fold Pattern Language, 1984; In Quest of a Strategic Pattern Language: a new architecture of values, 2008; Openness and Closure in Pattern Language: geometry versus resonance, 2012).

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