Metaphorical geometry as a cognitive vehicle

The-O Ring and The Bull Ring as Spectacular Archetypes (Part #2)

As noted above, in methodological terms, the following argument could be considered an exploration of connectivity -- of the connectivity within the meta-pattern which supposedly connects, as previously discussed (Walking Elven Pathways: enactivating the pattern that connects, 2006). The four "theos" each imply a particular form (or degree) of connectivity and might even be distinguished by the connectivity which they consider "legitimate" -- and consequently how they consider each other to be "illegitimate". The question is then the form through which connectivity can be provided or implied.

The question might be framed differently by recognizing that the "theos" have different degrees of preference for a "solid" argument, in contrast to one which might be more "flexible" (if not characterized by "liquidity"), or one which was "inspiring". This suggests that connectivity in argumentation might be fruitfully compared with the fundamental states of matter (solid, liquid, gas, plasma) and the nature of the bonding which distinguishes them. Understanding of the relationship between the forms of connectivity could then benefit from the manner in which states of matter are displayed together in a phase diagram capable of highlighting "critical points". Of some relevance, the phase diagram metaphor has been explored with respect to the distinction between data, information, knowledge and wisdom.

Different degrees of connectivity implied by phase diagram of states of matter
Typical phase diagram (reproduced from Wikipedia)	Adaptation to theo* information (reproduced from Patterns Essential to Individual and Global Health? 2010)

Comparing patterns of argumentation of the "theo" modalities to the "geometry" of states of matter also opens the way to exploring phase transitions between "theo" modes, the existence of possible correspondences to so-called non-classical states (glass, quasicrystals, magnetically ordered, quantum spin liquid, etc), low-temperature states (superfluids, etc), and high-energy states (see Wikipedia List of states of matter). How might this clarify the nature of inspiration, insight and "design concept" -- or the conditions of "pressure" and "heat" (metaphorically characteristic of argument) under which credible bonding of particular kinds could form, as suggested by the following table? Framed in this way, this notably highlights a degree of overlap between the "theos", especially in the light of the range of "states of matter"..

	Suggestive use of states of matter as metaphors of degrees of connectivity in argumentation (tentative)
	"solid"	"liquid"	"gas"	"plasma"
"theorem"	"axiomatic"
"theory"	"principles"	credible applications	hypothesis	opinion, idea, possibility
"theology"	"doctrinal principles"	required belief	revelation	inspiration
"theosophy	"experiential principles"	credibility	revelation	inspiration

Given the manner in which the "theo" modalities are challenged by humour, could this be understood in terms of phase transitions, especially in the light of efforts to reverse engineer human cognitive capacities (Matthew M. Hurley, et al. Inside Jokes: using humor to reverse engineer the mind, 2011)? The above presentation raises the question of how connectivity in argument described as "flaky" (unexpected, illogical, unreliable) is to be distinguished from what is otherwise valued (in chess) as "Knight's move thinking" (as discussed below).

The experience of certain forms, through the manner in which insight is carried by their geometry, offers a means of engaging with that integrity. Geometrical patterns, as experienced by the body in movement, offer an interface between ideographic and mythopoeic cognition -- as argued in the case of dance, especially in its ritual forms (Mark Johnson, The Body in the Mind: the bodily basis of meaning, imagination, and reason, 1987; Maxine Sheets-Johnstone, The Primacy of Movement, 1999). As an example, walking a labyrinth is valued for that reason.

More fundamentally, rather than geometry, this may be a question of number and its intimate experiential relation to time (Marie-Louise von Franz, Number and Time, 1974; George Lakoff and Rafael Nuñez, Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001). For von Franz:

To sum up: numbers appear to represent both an attribute of matter and the unconscious foundation of our mental processes. For this reason, number forms, according to Jung, that particular element that unites the realms of matter and psyche. It is "real" in a double sense, as an archetypal image and as a qualitative manifestation of the realm of outer-world experience. Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still unexplored mid-point between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and unrepresentational. (pp. 52-53)

The geometry is experienced through modalities in addition to those of seeing, so fundamental to the association of the "theo" modalities with text in its many forms. This sense of the geometry, and the cognitive experience of its constraining force, is notably articulated by mathematician Ron Atkin (Multidimensional Man: can man live in three dimensions? 1981), as separately summarized (Comprehension: social organization determined by incommunicability of insights). The significance is evident in the efforts of environment designer Christopher Alexander (A Pattern Language, 1977; The Timeless Way of Building, 1979) and the cognitive equivalent it may imply (5-fold Pattern language, 1984).

Such arguments reinforce the implication that the four "theos" merit consideration as cognitive masks for modalities governed by number (and geometry). This frames the significance of a fifth modality, denoted here by "thea", potentially indicative of the emergent quintessence to which von Franz and Jung refer -- ironically a term now used by physics to refer a hypothetical form of dark energy, postulated to explain the accelerating universe. Of potential relevance is use of five by Peter Senge (The Fifth Discipline: the art and practice of the learning organization, 1990).

Introducing the feminine could be understood as a necessary methodological provocation. Put bluntly, none of the "theos" is able or motivated to engage with the sexual reality so familiar to ordinary mortals. This is despite the ambitions of each "theo" to be comprehensive in its worldview and its engagement with reality -- and to make claims in this regard, implying that other perspectives are irrelevant or erroneous.

This systemic "negligence" of " otherness" -- associated especially and symbolically with the feminine -- can be illustrated as follows:

theory: questionable capacity to handle and encompass disagreement and alternative perspectives, or to envisage their emergence.
theorem: indifference to whatever has not been integrated within the coherence of the theorem, especially from the male perspective by which it tends to be engendered
theology: well-recognized controversy regarding the status of women, irrespective of detailed declarations by men concerning sexual appropriateness
theosophy: inability to articulate fruitful relations encompassing the feminine -- typically reinforcing the male dominance associated with the perspective through which wisdom is articulated

None of the "theos" offers an experiential articulation of sexual attraction or intercourse -- fundamental to successful suggestibility in a market economy. This is most striking in the case of what mathematics might contribute to that understanding, as discussed separately (Reframing the Dynamics of Engaging with Otherness: triadic correspondences between Topology, Kama Sutra and I Ching, 2011).

More tragically, this is evident in any strategic discussion relating to population and resources (Formally ignoring a fundamental systemic process: the economy vs. the fucking? 2012), as discussed with respect to the Royal Society report on People and the Planet (2012). Those involved in such discussion reserve their engagement with sexual attraction and intercourse for shadowy "extracurricular" contexts to which reference can only be made through euphemism, if at all. This recalls the period in which participants at meetings of the World Health Organization debated the health dangers of smoking in smoke-filled rooms -- without for a moment recognizing the incongruity, the symbolic message, or the appropriateness.

If reports relating to global challenges, produced from any "theo" perspective, can be readily rated as essentially "unsexy", what does this imply for their capacity to engender interest and remedial action? It is ironic that the evolution of the four "theo" modalities has resulted in a form of cognitive "infertility" -- except in domains with which they are not preoccupied. The irony is all the greater in a period in which the infertility of human couples is a matter of increasing concern -- especially as a consequence of environmental factors variously exacerbated by the "theos".

It is from this perspective that "metaphorical geometry" is explored in the light of the "dimensions" which the feminine brings to any more inclusive engagement with reality by the "theo" modalities. This necessarily raises questions with regard to the connectivity of the argument. Is there a form of connectivity that is missing from the coherence which the "theos" variously purport to encompass -- effectively a missing link, in the light of the argument of Terrence Deacon (What's Missing from Theories of Information? 2010; Incomplete Nature: how mind emerged from matter, 2011)?

Curiously with respect to connectivity and coherence the "theos" have indeed been variously able to articulate understanding of patterns of connectivity unrelated to their particular logic. This is most evident in the case of musical and architectural harmony and associations within a poem. Such patterns may engender appreciation, even imposed as a norm, as with sacred music. However it has not been possible to generalize their relevance, whether to the coherence of the mindset of particular "theo" or to the challenges of wider society, as separately discussed (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). Under the guise of "whatever works", this applies in particular to the credibility of connectivity associated with flirtation and to whatever it may lead. Use of spin and cosmetics offer examples of interesting case studies.

More generally, and less explicitly, the focus of any "theo" on explanation (in whatever terms) obscures other means of ensuring a degree of credible connectivity and coherence. This is most evident in design in its most general sense, but most clearly with respect to humour and story telling as framed by the Italian proverb: Si non è vero, è ben trovato (Even if it is not true, it is well conceived).

Framed in this way, there is a case for recognizing the inadequately explored role of correspondences of various kinds (Theories of Correspondences and potential equivalences between them in correlative thinking, 2007). Under what conditions is a degree of correspondence to be considered fruitful -- a question made evident by moonshine mathematics (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

Relevant to the method of this argument, and its exploitation of metaphor, Kenneth Boulding made the fruitful point that:

Our consciousness of the unity of the self in the middle of a vast complexity of images or material structures is at least a suitable metaphor for the unity of a group, organization, department, discipline, or science. If personification is only a metaphor, let us not despise metaphors - we might be one ourselves. (Ecodynamics; a new theory of societal evolution, 1978. p. 345)

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Metaphorical geometry as a cognitive vehicle