Toward encompassing relationship discontinuities through phase diagrams and catastrophe theory

Reimagining Intercourse between the Righteous Unrightly Challenged (Part #8)

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Chains of argument? Conventional discourse on relationships has long focused on use of logical modes privileging a chain of argument -- challenging non-sequiturs (typically fruitlessly). Such modes are increasingly called into question by the contradictory perspectives cultivated in other domains -- typically "elsewhere". More generally this could be caricatured as people variously pointing and enjoining: come this way, follow us, go that way, don't follow them, etc.

Consensus: This pattern is notably only too evident with respect to controversial issues (climate change, etc). The very possibility of consensus regarding explanation in support of informed strategy has become questionable (The Consensus Delusion: mysterious attractor undermining global civilization as currently imagined, 2011). Agreement may itself preclude the dynamics of further intercourse.

Anticipating some crisis to break the logjam, non-decision-making might be said to be the name of the game (The Art of Non-Decision-Making -- and the manipulation of categories, 1997). Some analogue to separation, break-up or divorce is then the obvious option. In any archetypal gathering of the wise, how to respond to those gathered who point variously to different "ways" -- and at each other as exemplifying "the problem"?

Phase diagram of styles of credible relationship: One interesting way of reframing the situation is through re-intepretation of the pattern of the classical phase diagram whereby the relationships between the fundamental states of matter are indicated, as discussed separately (Metaphorical geometry as a cognitive vehicle, 2014). How might the fundamental conditions of relationship be understood in such terms?

Such an approach suggests that the degree of connectivity and discontinuity in the experience of relationships and argumentation might be fruitfully compared with that variously characteristic of such states (solid, liquid, gas, plasma) and the nature of the bonding which distinguishes them. Understanding of the relationship between the forms of continuity could then benefit from the manner in which states of matter are displayed together in a phase diagram capable of highlighting transition boundaries and "critical points". Of some relevance, the phase diagram metaphor has been explored with respect to the distinction between data, information, knowledge and wisdom (The Isdom of the Wisdom Society: embodying time as the heartland of humanity, 2003). The following suggests an adaptation to intercourse -- including harassment.

Simplified phase diagram interrelating states of matter of different degrees of bonding/connectivity suggestive of contrasting connectivity in relationships

Connectivity and bonding: The diagram can be used to distinguish conditions characterized by "solid" relationships, notably under any extreme "pressure" of circumstances -- especially coercion. There is then a requirement that links between points made in any argument be "crystal clear" -- that points should be "aligned". This contrasts with the more "fluid" condition characteristic of many negotiations where matters and their connectivity are subject to reinterpretation. Metaphorical use is made of "liquidity". This flexible condition is more evident as exchanges in a relationship become more "heated" and controversial. When they have been "frozen" solid, of particular concern is the possible need to "unfreeze" categories under certain circumstances -- -- as separately argued (Framing the Global Future by Ignoring Alternatives: unfreezing categories as a vital necessity, 2009; Systemic Crises as Keys to Systemic Remedies a metaphorical Rosetta Stone for future strategy? 2008).

With further "excitement", the characteristic connectivity is further reduced, as is evident in movements of opinion characteristic of any "wind of change" -- and its eddies. The ionization characteristic of high temperatures is consistent with the polarization in such debate.

Unforeseen forms of coherence and credibility: The diagram is valuable in indicating the possibilities of transitions between phases (forms of relationship and their sustaining modes of argument), 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). These might have especially valuable properties and functions with respect to credibility and coherence of forms of relationship.

The diagram offers a means of discussing the conditions of "pressure" and "heat" (metaphorically characteristic of relationships) under which credible bonding of particular kinds could form -- emphasizing the nature of coherence under those conditions. This usefully frames recognition of inspirational discourse primarily characterized by the fiery "heat" of the presentation -- irrespective of whether the arguments are otherwise considered incredible.

The axes of the diagram might then be variously associated with

• "pressure axis", engendering: agreement, probability (certainty), resolution through coercion
• "temperature axis", engendering: disagreement, hope, improbability (uncertainty), irresolution

Positive vs. Negative: Using the axes for this purpose raises the valuable question as to how widespread metaphorical use of "positive" and "negative are to be be related to it -- given the manner in which they are associated with the other attributions. In physical terms, positive pressure is associated with higher pressure. In relation to temperature, negative is associated with lower temperature.

More complex is any association of hope/despair to the schematic. Greater hope can be readily associated with greater agreement (under pressure), which may well evoke a degree of despair at options forsaken. Similarly, greater hope may be associated with the inspiration of heated debate, which may in turn evoke a degree of despair at options ignored.

Idyllic weather? In the light of appreciation of the complexities of the weather, the phase diagram frames any (questionable) assumption regarding the nature of the ideal pattern of discourse with which ultimate sustainability might be associated. What would it be like if it all "worked", "came together" and "everyone agreed" -- as implied by some idyllic scenarios? The question is asked by Robert Adler (Happy Planet: we can make the world sustainable, but would you want to live there, New Scientist, 5 July 2014).

At one extreme it could then be argued that the pattern would be that of an "air conditioned" environment. This would restrict discourse to particular areas of the phase diagram -- excluding conditions associated with excessive "pressure" or "temperature", then to be deprecated (as with "bad weather"). Some might well favour further restriction to the "solid" phases of argumentation -- in which connectivity was highest. What if there was "universal consensus"? Is this to be understood in terms of a "critical point" in the phase diagram where contrasting phases are strangely reconciled?

Ecosystem of argument phases: Clearly this extreme example makes the point that a more "natural" pattern of dynamically related phases is desirable. The looser connectivity of the "liquid" phases have their place. Valued creativity may be recognized as associated with "brainstorming" -- namely gaseous phases involving higher temperatures. This may include levels of disagreement -- namely the very low connectivity of the highest temperatures. Expressed otherwise, the challenge is then how to ensure a sustainable weather pattern, somehow incorporating dynamically the complete mix of phases.

It is necessarily impossible to argue conventionally for such a mix since it calls upon a variety of modes of argument between which there are complex phase transitions. It is in this sense that aesthetic appreciation of changing conditions of weather offers greater insight -- as with the understanding of people of the land, or sea, or poets. The possibility of relationships across phase boundaries can be usefully discussed in terms of correspondences -- as variously appreciated and deprecated (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007).

Framing discontinuities in relationship in terms of catastrophe theory? As questioned above, given the catastrophic experience of harassment of any kind, what might indeed be the seven "elementary" catastrophes to be distinguished in any relationship as framed by catastrophe theory as one approach to dynamical systems.

Human relationships do indeed merit understanding in terms of the complexity of such systems -- rather than in the light of simplistic "mechanical" relationships, as can be too readily assumed. (Brian R. Flay, Catastrophe Theory in Social Psychology: some applications to attitudes and social behavior, Behavioral Sciences, 23, 1978, pp. 335-350; Derek Evan and Antonette M. Zeiss, Catastrophe Theory: a topological reconceptualization of sexual orientation, New Ideas in Psychology, 2, 1984, 3, pp. 235-251; Ian Stewart and P. L. Peregoy, Catastrophe Theory Modeling in Psychology, Psychological Bulletin 94, 1983, 2, pp. 336-362; Wolfgang Wildgen, Semantic Description in the Framework of Catastrophe Theory, 1981). Curiously, as the dates of these papers indicate, the perceived relevance of catastrophe theory has decreased with increasing perception of the catastrophic incidence of harassment of every form. This could be seen as confirmed in the latest comprehensive summary by Tim Poston and Ian Stewart (Catastrophe Theory and its Applications, 2014). Violence in relation to sexuality is only briefly discussed in passing (p. 411).

Given the fundamental is nights of catastrophe theory, there would seem to be a case for reviewing the set of 7 distinct systemic catastrophes identified by that theory -- asking the question as to how they might help to reframe interpersonal relationships in which harassment is perceived to be a factor. If nothing else, this would seem to offer a new language through which to frame the complexities of any slide towards catastrophic harassment.

The possibility of such an application has been discussed separately in the form of Clues from catastrophe theory, force dynamics and manoeuvering (2002) as part of a more general discussion (Navigating Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms through movement, 2002). With the set of "vices" considered there as comparable with the 7 elementary catastrophes, vice might then be a form of behavioural discontinuity or disarray -- in which the elegance of well-coordinated control is somehow lost. Reference was made to the work of Denis Postle (Catastrophe Theory: predict and avoid personal disasters, 1980) and R. D. Hinshelwood (Models of Demoralisation. British Journal of Psychotherapy 5, 1988, pp. 218-227) in demonstrating how catastrophe theory may be used by an individual to map their own behaviour and the critical areas on that map at which stress and breakdown are possible.

Given the pattern of questions engendered by experience of harassment, of potential relevance is the association between the style of question and the experience of the catastrophe, as can be speculatively explored (Conformality of 7 WH-questions to 7 Elementary Catastrophes: an exploration of potential psychosocial implications, 2006). Adaptation of the following images, typical of discussion of catastrophe theory, was made in another speculative exploration of potential relevance (Reframing the Dynamics of Engaging with Otherness: triadic correspondences between topology, Kama Sutra and I Ching 2011).

Suggestive attribution of complementary "languages" as control factors of a characteristic "behaviour surface" of catastrophe theory
Applied to Sudden Lost Meaning: A Catastrophe? (Management Decision, 1994) by Patricia Karathanos, et al.	Applied to a Catastrophe theory map of civic accountability in the psychological therapies (Psychotherapy and Politics International, October 2010) by Denis Postle

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