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7 November 2017 | Draft

Reimagining Intercourse between the Righteous Unrightly Challenged

Attraction and harassment in psychodynamic terms beyond the binary blame-game

-- / --

Mapping processes of harassment and terror systemically
Framing a psychosocial ecosystem in terms of control factors
Missing dimensions -- exploring the shadow and crafting the unsayable?
Mutual perceptions and boundaries -- recognizing the experiential challenge
Promoting ostentatious inequality: dubious complicity in an unmentionable game of unquestionable dimensions?
Cultural distinctions and contradictions regarding harassment
Toward encompassing relationship discontinuities through phase diagrams and catastrophe theory
Encompassing the "attraction-harassment" dynamic with a notation of requisite ambiguity?
Patterning psychosocial relationships in 3D or more?

Produced on the occasion of multiple accusations by women against male celebrities, and a major political crisis amongst UK Members of Parliament implicated in that process.
(Westminster sex scandal: Theresa May to call for 'culture of respect', BBC News, 6 November 2017;
Why a tide of sexual allegations has swept through Westminster, The Guardian, 4 November 2017).


Considerable attention is now focused on sexual harassment by men, whether systemically or in the light of cases involving prominent celebrities. The question here is whether this focus is in danger of obscuring other forms of harassment which also merit a degree of attention. The more general perspective may offer greater understanding of the issue as well as more viable possibilities for remedial action. As a currently dramatic example of the unquestionably righteous engaging with those who have long considered themselves to be unquestionably righteous, rethinking their relationship may also offer insight into other situations in the global arena characterized by that same mindset.

It is curious to note that "harassment" is not studied in systemic terms -- using the extensive insights of system dynamics for example -- although there are many references to the phenomenon being "systemic". As noted by Colleen Sheppard (Inclusive Equality: the relational dimensions of systemic discrimination in Canada., 2010):

While our understanding of discrimination has been revolutionized by the recognition of adverse effect and systemic discrimination, the problem of sexual harassment has in many respects failed to incorporate the full implications of a systemic analysis and continues to focus on the moral blameworthiness of the individual perpetrator. Sexual harassment does not fit comfortably into the paradigm of systemic discrimination: we tend to view sexual harassment as a problem of aberrant individual wrongdoing rather than a systemic problem. As Margaret Thornton notes, the "privileging of the sexual in sexual harassment means that the focus is on the aberrant behaviour of individuals rather than the structural or systemic manifestations of discrimination." Although sexual harassment has resisted a systemic analysis, it is essential to examine the broader structural and institutional factors that heighten vulnerability to harassment. (p. 80)

Any discussion of more than simplistic form quickly acknowledges that both the phenomenon and dialogue about it are complex (Rachel Kaser, Facebook video series details the complexity of sexual harassment, 2017). Yet almost no attempt is made to draw upon the extensive insights of complex system dynamics, nonlinear systems or catastrophe theory. In the light of the latter, for example, what might be the seven "elementary" catastrophes to be distinguished in any relationship -- variously understandable in terms of harassment? With an increasingly obvious need to engage with ambiguity and its cultivation, is it somewhat naive to assume that the challenge can be fruitfully addressed through the conventional modalities of "linear thinking"? I Am Right and You Are Wrong (Edward de Bono, 1992)? Every nation has to either be with us, or against us (Hillary Clinton, 13 September 2001)?

The concern here is to recognize that "harassment", although currently framed as primarily sexual, takes a number of forms of which the gender-based variety is but one. Arguably there is a tendency with any highly charged issue -- whether based on gender, ideology, religion, race, cultural norms, or status -- to distort the meaning of terms through dubiously restrictive definitions. This serves the purpose of excluding interpretations which are believed to dilute the primary strategic concern and the opportunity of particular groups of victims. A higher degree of focus on one form may however successfully distract from focus on another. Furthermore, does the tendency to engage in one indicate the probability of engaging in another?

Harassment can indeed also be understood as male-on-male, most notably in segregated institutions (prisons, the military, many workplaces), just as it can include female-on-female in similar contexts, or adult-on-minor (as recently widely publicised with respect to the clergy). Rather than being primarily sexual it can also be recognized in terms of the variety of forms of coercion and bullying, most obviously in the workplace, educational environments and in those provided by dominant groups for the variously challenged (the elderly, the physically or mentally disabled, the chronically ill, and the like). Even more problematic is the institutionalization of coercion through the continuing incidence of slavery and bondage -- with its particular sexual implications.

The terror potentially associated with harassment can be recognized in the exposure to bullying. However, given the prevailing concern with terrorism, it is clear that great care is effectively taken to distinguish the terror experienced by some -- the bullied, the sexually harassed, and those exposed to racketeering or to "shootings" -- from that undertaken to promote ideological agendas. This is deemed far less acceptable -- incomprehensibly scandalous. However it remains unclear whether an underlying motivation in bullying or sexual harassment could itself be usefully seen as "ideological" in the light of the manner in which it may be partially excused and legitimated by cultural norms and religious dogma.

The surreptitious nature of the pattern typical of sexual harassment is shared by intimidation more generally in its subtler forms, even structural violence, and especially with the variety of forms of "cheating" via transactions "under the table". However dubious, are the distinctions so carefully made between tax avoidance and tax evasion indicative of distinctions which might apply to sexual harassment -- especially given the existence of tax havens?

In extending the focus on harassment to the complexity of the dynamic system of which it is one process, the further concern here is with the controversial issue of how harassment is encouraged and enabled by the discriminatory cultivation of attraction and the quest for attentive recognition. Through its role in cultivating images, this is most notably a focus of the advertising industry -- with the complicity of consumers -- as with other forms of propaganda.

Is there a case for recognizing the extent to which many are effectively harassed, if not coerced and bullied, by unrelenting exposure to advertising extolling the singular appeal of those with attributes that are systematically enhanced by marketing and image building? Understood more generally, promoting attraction in whatever form, evokes a response -- whatever the form -- as it is designed to do. Welcome or not, both the attraction and the response can be expressed by various means -- sight, sound, odours, touch, and subtle invasion of space.

The systemic cultivation of relative attraction necessarily engenders a tension with those consequently attracted, whether far from endowed to that degree -- or seeking to possess that quality in some way. Any perceived relative advantage of this nature can be variously exploited in a complex process in which both parties are complicit -- with responsibility for any problematic consequences excused by the dubious legalities of plausible deniability and willful blindness. These may well be framed by cultural norms and preferences -- variously evolving over time -- and righteously defended from within their respective frameworks.

Mapping processes of harassment and terror systemically

Expressed otherwise, little effort is made to map the dynamics of the system in which the process of harassment emerges. There appears to be no mind map incorporating the process in experiential terms -- or any motivation for doing so. The limitations are evident in an effort with respect to employment discrimination (Alain Garrido, Employment Discrimin - Mind Map, 2009).

Sexual harassment: A rare exception is the technique for producing one such map, proposed as a feature of a HarassMap project launched in 2010, initially funded by the International Development Research Centre of Canada (Niki Wilson, Mapping Sexual Harassment in Egypt, 22 February 2017; Mind Map of Violence Against Women in Egypt, YouTube, 22 February 2017).

The exceptional incidence of sexual harassment reported in Egypt has evoked a related mapping initiative by Mahtab Sharifi and colleagues (A model-based study and policy analysis of Domestic Violence and Sexual Harassment against Women and Children, Conference Proceedings. 31st International Conference of the System Dynamics Society, Cambridge, 2013). It is the relative degree of articulation of their "map" which is of significance to this argument, rather than its illegibility as presented below (larger versions can be viewed using standard browser facilities).

Domestic violence and sexual harassment against women and children
Stock-flow diagram of the base model
Domestic violence and sexual harassment against women and children
Mahtab Sharifi and colleagues (A model-based study and policy analysis of Domestic Violence and Sexual Harassment against Women and Children Conference Proceedings.
31st International Conference of the System Dynamics Society, Cambridge, 2013)

Terrorism: To illustrate the generality of the system dynamics approach, the same conference included a paper by Nancy Hayden (Innovation and Learning in Terrorist Organizations: a complex adaptive system framework, 2013). One can look in vain for any analogous paper entitled: Innovation and Learning in Sexual Harassment: a complex adaptive system framework. Why is that?

In the case of terrorism, the following is an illustration of one such possibility using a particular software package, as described separately (Mapping the Network of Terror, 2002). The map was produced as a brainstorming exercise using the software package Decision Explorer -- which also allows such networks to be analyzed and represented as conceptual models in various ways. In developing the map further, links to web resources could have been been provided from the individual concepts. The suggestion is that such a map could be adapted to encompass the terror associated with harassment in its various forms.

Mapping the network of terror -- extended to harassment?
Map of network of terror

Climate change: To the extent that a case can be made that humanity is effectively engaged in a systemic process of "harassment of the environment", it is appropriate to consider the following adaptation to climate change of a map that was skillfully articulated to encompass the challenges of terrorism in Afghanistan. The adaptation was introduced under the heading Climate change used as a fig leaf -- to conceal a more challenging issue? (2009) in reviewing the issues of the UN Climate Change Conference in Copenhagen (Insights for the Future from the Change of Climate in Copenhagen, 2009). This too avoided any systematic articulation of the issue.

It was therefore interesting to contrast this aversion to the analytical overview with the Office of the Joint Chiefs of Staff of the US of the counterinsurgency (COIN) initiative in Afghanistan, as articulated by the PA Consulting Group. This took the form of a map, notably publicized on behalf of McClatchy Newspapers by Dion Nissenbaum (The great Afghan spaghetti monster, Checkpoint Kabul, 20 December 2009; Graphic Shows Complexity of US Counterinsurgency in Afghanistan, The Huffington Post, 22 December 2009). Coincidentally this map has been publicized over the web at the end of the Copenhagen event. As indicated. the subsequent analysis of that event gave rise to no map of equivalent systemic detail.

In the absence of any such map for Copenhagen, as an experimental exercise it was therefore instructive to adapt the rich analytical framework of the Afghanistan counterinsurgency analysis to climate change. The legitimacy of such an adaptation may be argued on the basis that the viability of both strategic initiatives is dependent in cybernetic systems terms on a set of interacting functions. From the perspective of general systems theory, it is to be expected that there is a degree of isomorphism between a systems analysis of the global initiative in Afghanistan and that with respect to climate change. Whatever the inadequacies of such an exercise, it may at least serve to highlight the knowledge tools used to focus initiatives on which unprecedented global resources are being expended -- given the shameful paucity of resources devoted to representing the challenges of climate change in the light of the conflicting relations between those party to that process.

Toward a systemic analysis of harassment?
in the light of an adaptation to climate change of a representation of counterinsurgency operations in Afghanistan
(click on image for larger version)
Adaptation to climate change of a representation of counterinsurgency operations in Afghanistan
Afghanistan COIN dynamic
(clusters in original map)
Climate change COIN dynamic
(clusters in adapted map)
Population/Popular support
Infrastructure, Economy and Services
Afghanistan Security Forces (ANSF)
Crime and Narcotics
Coalition Forces and Actions
Physical Environment
Population/Popular support
Infrastructure, Economy and Services
Activist NGO Strategic Forces (ANSF)
Dissenters ("Them")
Crime and Distractions
Initiatives of Coalition of the Willful ("US")
Physical Environment

Relating understanding of harassment to Afghanistan in this way helps to emphasize another valuable point. Clearly some claim that it is the intervention of foreign forces in Afghanistan which constitutes harassment and justifies their action. Their response to those forces is in turn framed as harassment by those intervening to constrain them. In a situation involving "harassment", the question is then who is "harassing" whom where there are such contrasting perceptions in play? Do those framing themselves as victims necessarily deny any complicity in "harassment"?

The confusion is curiously exemplified in the case of a gesture of affection on the part of elderly relatives to a child, who may well experience this as unwelcome -- readily framed by the child as a form of harassment to which submission is exepected. Between adults the conventions of social kissing and hugging raise similar issues. In both cases it is a matter of the "touchy-feelies" versus the "untouchables" -- with all the problematic cross-cultural connotations of those terms.

Bullying: With respect to map adaptation, seemingly the various efforts to map bullying have not been adapted to harassment more generally, including its sexual forms:

Given the importance of interpersonal relationships, it is somewhat extraordinary that intercourse in its most general sense does not feature in widely available maps, regularly upgraded in the light of new insights and criticism (An Approach to Systematic Classification of Interpersonal Relationships, 1978). The most remarkable effort in this respect is the extensive work of Laura K. Guerrero, et al (Close Encounters: communication in relationships, 2017). Understood in a general sense, there is also the question of how this failure reflects on intercourse with nature and other species ("Human Intercourse": "Intercourse with Nature" and "Intercourse with the Other", 2007; Beyond Harassment of Reality and Grasping Future Possibilities: learnings from sexual harassment as a metaphor, 1994).

All such senses feature issues of bullying and harassment, as exemplified in the human response to other species. The questionable mindset may take forms seemingly distinct from sexual harassment. What are the tools and insights which could be brought to bear on this inadequacy -- appropriately understood as a form of impotence?

Framing a psychosocial ecosystem in terms of control factors

Without stressing the correspondences, it is useful to explore a quite different framing of an equivalent number of factors to distinguish between several forms of "positive" and "negative" such as to recognize valid concerns but to avoid collapsing valid distinctions. This is inspired by a generalization articulated by Edward Haskell with respect to a "coaction cardioid" (Full Circle: the moral force of unified science, 1972; Generalization of the structure of Mendeleev's periodic table, 1972). Its implications have been further developed by Timothy Wilken (The Relationship Continuum, 2002 ), as discussed separately (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005).

Haskell's approach, is introduced by Harold Cassidy as follows:

In the cybernetic analysis of the more complex and organized systems we recognize two distinct kinds of factors. There is the work component or components, which we shall designate X, and the governor, or controller, which we shall designate Y. Of course, the governor does work too (the strategic work), and we have simplified the relationships very greatly. There will be cases of a system made up of sub-systems, one controlling in some respects, not in others, and so on. Let us stay with the simpler case. Now, the processes that characterize X may, in the interaction with Y, be accelerated or in some way enhanced ( + ), or may be unaffected ( O ), or may be decreased ( - ). Similarly, the processes that Y undergoes. When the possibilities are cross-tabulated, it becomes evident that there are nine and only nine of these qualitatively different `coactions.' [glossary]

Haskell applies this insight to a range of systems, notably in the natural environment (as shown below) but also in the social environment. In the case of the different kinds of relations between animals in an ecosystem, the following patterns then emerge -- of which 8 of the 9 are non-neutral. Note that there are variations in the terminology of biological interaction, notably differing from Haskell's usage [more | more]. The dynamics of each of the 8 relationships might be described as a "game", however asymmetrical or predictable the outcome (as with the "cat-and-mouse" game of predation).

Possible 8-fold Positive-Negative Hybrid Conditions
. . Y = "Control component"
. . Negative Neutral Positive
X =
Positive predation
(positive negativity)
(positive neutrality)
(positive positivity)
Neutral amensalism
(neutral negativity)
(neutral neutrality)
(neutral positivity)
Negative synnecrosis
(negative negativity)
(negative neutrality)
(negative positivity)

Such an articulation, as with the Chinese BaGua pattern (discussed below), offers a means of distinguishing between conditions which are deprecated and those towards which there may be aspiration. In representing a system, the table could indeed be adapted to language employed with regard to the dynamics of harassment, dominance, bullying and terrorism. As indicated there, "predation" is an obvious example. However the scope of the table raises the question as to what degree other interpersonal relations are also identifiable.

Given Haskell's inspiration from nature, the issues of harassment could be explored in the light of humanity's primate ancestors. How indeed do chimpanzees do it? What forms do bullying and exploitation take with baboons? Have humans transcended those behaviour patterns? (Are some primates wired for sexual harassment? Science, 6 July 2017; Long-term sexual intimidation may be widespread in primate societies, Science Daily, 6 July 2017; The Science of Sexism: primate behavior and the culture of sexual coercion, Scientific American, 20 July 2011). Whether or not evolution selected for such behaviour as a means of ensuring successful reproduction, the latter offers valuable insights into the contrasting collective behaviour of the bonobos -- now faced with extinction. How does human society ensure propagation of fruitful memes (Onkar Dalal, A Study of Meme Propagation, 2009; Xuetao Wei, et al, Competing Memes Propagation on Networks, 2013).

Haskell's insights have been very usefully (and extensively) adapted by Timothy Wilken (2002) to an ordering of the spectrum of personal relationships: adversity -- neutrality -- synergy. Wilken equates "synergy" with "positive" and "adversity" with "negative". Wilken's study reframes Haskell's ordering in the following table, where "win" equates with "positive" and "lose" with "negative"

8-fold Pattern of Non-Neutral Relationships
(Timothy Wilken, The Relationship Continuum, 2002)
8-fold Pattern of Non-Neutral Relationships

Potentially relevant to this argument is the further extension of Haskell's model to the detection of what he describes as a coaction cardioid (discussed separately, as noted above). Through it he distinguishes the balance between the entropic (synnecrosis) conditions and negentropic (symbiotic) conditions of the system. Arguably systemically pervasive harassment could be recognized as an entropic condition.

Missing dimensions -- exploring the shadow and crafting the unsayable?

Impossibility of reasonable dialogue? Is "reasonable" discourse on the complex dynamics of any form of harassment -- exploitative or otherwise -- necessarily impossible through the current modalities of "linear thinking"? Or is "reasonable" to be associated with an unreasonable degree of oversimplification?

As illustrated by recent exchanges between Kim Jong-un and Donald Trump regarding nuclear weaponry, there is no question of who is "right" or who is engaged in "harassment". This renders dialogue impossible, if not meaningless. As a "hot topic" in several senses of the term, it invites consideration of possible analogues to known methods in more obvious domains, as explored separately (Overpopulation Debate as a Psychosocial Hazard: development of safety guidelines from handling other hazardous materials, 2009).

If some process of attraction is a factor in harassment, how is it to be recognized with other "shades of grey"? The editors of The Guardian admit of no such subtlety (The Guardian view on sexual harassment in Westminster: no grey areas, no excuses, 5 November 2017). In how many arenas is the absence of shades of grey to be mistakenly asserted in defence of a particular agenda?

As suggested above, clues to relevant insights into "sexual harassment" may well have been framed with respect to other domains, just as insights of relevance to those domains may be found through the challenges of sexual harassment. This possibility might be expressed by the following.

Harassment generically reframed

Inherently problematic discourse: One insightful approach is that of Frans Cilliers (A Systems Psychodynamic Description of Organisational Bullying Experiences, South African Journal of Industrial Psychology, 38, 2012, 2). He notably remarks, with extensive citations:

Organisational bullying experiences manifest themselves as an intense unconscious systemic dynamic involving the bully, the victim and the organisational culture. The relatedness between the objects is characterised by valences and mutual defence mechanisms such as splitting, projection and projective identification.... The systems psychodynamic perspective... studies the extraordinary and sometimes seemingly odd and out-of-place behaviour in the organisation, and also its meaning and deep motives, wherein anxiety leads to the blurring of boundaries between the rational and irrational...

The bully's dynamics manifest themselves as masochism, sadism, narcissism, rivalry and envy... Although bullies exhibit psychopathic tendencies, they are not classified as such....

On the one hand, victims experience being filled up with the bully's projected feelings of worthlessness, incompetence, self-doubt, powerlessness, despair and even that they need to be treated badly as evidence of a form of inner madness.... On the other hand, victims experience their own and more real feelings of rage, anger, bewilderment, shock and disbelief about what is happening to them, followed by self blame...

The bully and the victim are psychically intertwined as if in a frenetic and parasitic dance [of death]

Especially intriguing is the nature of the attractor, most notably when it is recognized to embody value in some strange manner -- whether associated with beauty, wealth, or otherwise (Human Values as Strange Attractors, 1993). As a strange attractor, any engagement with it should call for more complex exploration.

As indicated above, the process of discussing the patterns of dominance and exploitation is readily challenged and called into question -- even reactively. Assumptions regarding objective definitions are increasingly suspect as serving a particular agenda in the process rather than offering a perspective fruitfully disassociated from the process. This could be recognized as to be expected.

The challenges of discussion of sexual harassment can be highlighted by the more obvious challenges of "terror" -- potentially a feature of such harassment. It is intriguing to note how phenomena which engender terror are carefully framed in media and legal terms to distinguish them from "terrorism". Might the same be said of gender-related interactions, with some lending themselves to interpretation as "harassment", but crafted such as to avoid being condemned as "sexual harassment"? The case of terror offers further insight in that it may be deliberately sought and cultivated for recreational purposes -- reframed as thrills and described as "terrific". There is also the fact that there is increasingly little contrast between media depiction of shootings and entertainment featuring such terrifying experiences -- possibly on the same media "channel".

It is of course highly controversial -- to the point of being framed as ridiculous if not seditious -- to argue that those framed as terrorists may well have some kind of case through which they justify their action. The point may be made less controversially by noting the variety of national leaders who were previously labelled formally as terrorists -- prior to the achievement of the independence of their country. They would of course include: Nelson Mandela, Robert Mugabe, Gerry Adams, Yasser Arafat, George Washington, and Jomo Kenyatta (cf. 10 Former Terrorists Who Became Politicians, When Terrorists Become State Leaders, Israeli Prime Ministers who were Terrorists and War Criminals). The question has even been raised as to whether Jesus would now be framed as a terrorist, according to current definitions. The response to any such ridiculous claims is that those subsequently held in the highest of honour were campaigning against a situation which was inherently unjust, whether or not it involved (violent) repression.

The even more obvious challenge of terrorism raises the question as to whether there is a systemic lack of capacity to approach the matter otherwise -- a combination of lack of imagination, confirmation bias and group think, as argued separately (30 Questions for the Counter-terrorism Experts of the World -- raising the question as to why they are not effectively addressed, 2017). What might be the analogous questions with respect to sexual harassment?

Complicity of celebrities: One feature of the dilemma is currently highlighted by the political issues arising from circulation of a list of UK Members of Parliament variously accused of sexual harassment. As noted in that respect in a comment by Katy Balls:

It's the distinction between what constitutes sexual harassment and assault and what constitutes an unsuccessful - if ill-judged - pass that government and Commons officials need to work out how to deal with as they address the unfolding scandal (The Michael Fallon story distracts from more serious allegations of Westminster sleaze, The Spectator, 31 October 2017)

Should all failed and mis-judged passes, as claimed by the "victim", now be criminalized and potentially making of the law an ass -- exploiting an appropriate intercultural play on words?

The complexity of the issue has long been made evident in the case of the sexual proclivities and dalliances of leaders of nations, notably including those most prominent in the international community -- for which there are many checklists (List of federal political sex scandals in the United States, Wikipedia; Priscillia Charles, Eight other sex scandals that rocked French politics, The Local, 11 May 2016). Examples include the well-documented cases of: John Fitzgerald Kennedy, Bill Clinton, Francois Hollande, Silvio Berlusconi, Francois Mitterand. At what stage these processes slide into non-consensual exploitation of dominance is naturally controversial. More complex are the issues raised by institutional complicity in such processes, as highlighted in the case of the IMF (Pre-Judging an Institution's Implicit Strategy by the Director's Private Behaviour: remarkable parallels in the case of the IMF and Dominique Strauss-Kahn, 2011).

Far more obvious, but kept carefully beneath a "cloak of silence", is the extent of institutional complicity in arranging entertainment for clients in which the possibility of sexual relations (in whatever combination) is considered appropriate to creating an environment favourable to decision-making and the signature of contracts. Those providing such services may be variously complicit and variously rewarded -- as in the case of escort services and enabling career advancement. With respect to any deprecation of dominance by clients, simplistic conclusions are called into question by bondage and enthusiasm for sadomasochism.

With every pronouncement on such matters evoking defensive responses -- possibly strongly backed by forms of greater condemnation and further intimidation -- the challenge may perhaps be explored otherwise, as exemplified by the process of "anti-anything" (Guidelines for Critical Dialogue between Worldviews -- as exemplified by the need for non-antisemitic dialogue with Israelis? 2006). As discussed in the latter with respect to isomorphs of the case of Israel, other examples are offered by discourse between religions (Christianity/Islam), academic disciplines (science/humanities), political ideologies (liberalism/socialism), and nationalism / cultures (anti-Americanism, etc), aesthetical preferences (classical/modern), physically characterized social groups, social status and behavioural skills, and lifestyle preferences. The primitive quality of discourse in each such case has long been only too evident.

Ostentatious inequality: Rather than a focus on "difference" and demonstrably vain appeals for tolerance, there is a case for focusing more critically on "inequality" -- currently obscured by a related process (Cultivating the Myth of Human Equality: ignoring complicity in the contradictions thereby engendered, 2016). The challenge might be better understood through recognition of the extent to which inequality is ostentatiously cultivated systematically. This is exemplified in the desperate quest for higher relative status, with whatever this may be associated. The greater the disparity however, the greater the tension engendered between the unequal -- despite obscure references to "equality" of which there are few comparable manifestations in practice.

Exploring the critical argument against the practices of "Israel" could well prove significantly emblematic and useful in offering a systemic parallel to the case against the dominating behaviour of "men". In practice such criticism of Israel is reactively reframed as "anti-semitic". Israel does not offer any frame by which appropriate criticism can be made against its practices without inviting such a reaction. Similarly "men" do not voluntarily offer any frame by which appropriate criticism could be made against particular behaviours. Any criticism is framed by men as ridiculously "anti-male". Is the reverse potentially true of women -- if not of feminists?

Mutual perceptions and boundaries -- recognizing the experiential challenge

The argument in the exploration of Guidelines for Critical Dialogue between Worldviews (2006) was that it would be appropriate for any of the systemic isomorphs of "Israel" -- with analogous proclivities -- to articulate their understanding of the scope for legitimate criticism by others, as systemic feedback. This would provide guidance to avoid the reactive "anti-semitism" response. Making further use of the Israel model, the approach could be extended to the complementary perspective of the isomorphs of "Palestinians". The charged nature of the exercise is evident in recognizing the degree to which feminists would recognize the extent to which women are systemically positioned in a manner analogous to the Palestinians. (There is of course the further complexity to any such comparison in that both Judaism and Islam have rather particular approaches to framing women in relation to men -- also a focus of criticism).

Insights from "anti-feminism"? The commentary on the proposal in those "Guidelines", included the following argument in terms of "anti-feminism".

Given the more widespread familiarity with discourse concerning abuse in the form of sexual harassment and rape, the map of this terrain could offer methodological pointers to experiences associated with "anti-semitism" (including "non-anti-semitism" and "anti-anti-semitism"). The relationship has notably been explored by Eishiro Ito (Anti-Semitism/Anti-feminism in Giacomo Joyce. Journal of Policy Studies, 2006). But, as noted by Peter Zohrab (Sex, Lies and Feminism, 2002):

A central problem within feminist discourse has been our inability to either arrive at a consensus of opinion about what feminism is or accept definition(s) that could serve as points of unification. Without agreed upon definition(s), we lack a sound foundation on which to construct theory or engage in overall meaningful praxis

This raises the possibility that "anti-feminism", like "anti-semitism" may not be a single definable concept but rather a dynamic of concepts whose coherence may be multi-dimensional -- rather than as might be expected in any theory tending to focus on possibilities of simplistic remedial "road maps" over conventional terrain. Tools such as concept mapping may be fruitfully employed (cf Rebecca Campbell and Deborah A. Salem, Concept mapping as a feminist research method: examining the community response to rape. In: Ellen B. Kimmel and Mary Crawford, Innovations in Feminist Psychological Research, 2000; Marie-Nathalie Beaudoin Agency and Choice in the Face of Trauma: a narrative therapy map Journal of Systemic Therapies, 2005; Cheryl Tatano Beck Pentadic Cartography: Mapping Birth Trauma Narratives Qualitative Health Research, 2006)

Distinct from approaches such as that of Inger Skjelsbaek (Sexual Violence and War: mapping out a complex relationship, European Journal of International Relations, 7, 2001), there is the possibility that the so-called "vicious cycles of violence", whether physical or structural, might be mappable onto complex mathematical objects. These could offer more integrative approaches to sustainable relationships between seemingly opposed positions -- rather than depending (yet again) on negotiating techniques of Getting to Yes (1981) or Getting Past No (1993) in the hope of simplistic "win-win" reconciliation. Such a dynamic context could offer more legitimacy to the various understandings of "anti-semitism" ("anti-feminism", etc) and the various critical perspectives on it that now sustain a complex dysfunctional system.

Application to sexual harassment: A form of the proposed Guidelines is suggested by the following table -- reverting to the specifics of sexual harassment. However the exercise could as well be applied to the marketing of any product or service to consumers -- variously perceived as "targets" or "marks" to be exploited for purposes of profit, as with use of the "scoring" metaphor. If challenged, the active participant in any such process would necessarily, and perhaps innocently, seek a position of plausible deniability and willful ignorance.

Juxtaposition of contrasting perceptions of harassment
    When might a "woman" feel harassed
-- and framed as a victim ?
When might a "man" feel harassed
-- and framed as a victim ?
When might a "minor" feel harassed?
-- and framed as a victim ?
Mode Behaviours Perspective of
Perspective of
Perspective of
Perspective of
Perspective of
Perspective of
Verbal degrees of intimidation            
degrees of humiliation            
degrees of insinuation            
Sight degrees of exposure            
-- undress            
-- nudity            
degrees of voyeurism            
-- invasion of privacy            
Spatial degrees of proximity            
-- invasion of space            
Touch degrees of fondling            
-- non-genital            
-- genitalia            
Odour exposure to perfumes            
exposure to pheromomes            
exposure to (bad) breath            

The issues are of course exemplified by how much of the body, or portions of it, should be (un)covered to be acceptably attractive rather than a deliberate (even indecent) provocation -- held by some to invite any response, however purportedly unacceptable. Contrasts are evident in modern degrees of cleavage and skirt length in comparison with coverage to the ankles a century ago -- in some cultures. Or emphasis on the cod piece in high society's past -- now restricted to a subculture and otherwise framed as ridiculous. Clearly variants of the table could be usefully made by culture and period -- perhaps using interactive web facilities.

It is appropriate to note that some classic methodologies to measure sexual harassment create the impression of themselves suffering from gender bias in avoiding consideration of harassment of men, for example (Louise F. Fitzgerald, et al, Measuring Sexual Harassment: theoretical and psychometric advances, Basic and Applied Social Psychology, 1995; Simon A. Turmanis, et al, The Stalking and Harassment Behaviour Scale: measuring the incidence, nature, and severity of stalking and relational harassment and their psychological effects, Psychology and Psychotherapy, 2006; Sexual Harassment Scale, US National Center for PTSD).

References to "measurement" and "scale" do not seemingly include any consideration of a quantitative measure, as might be readily recognized in other contexts as dress codes (skirt length above the knee, breast exposure, transparency, etc) or specific forms of touching -- and what may be perceived as a violation of norms in what context, given the very strong views of some cultures on such matters (The Cleavage Conundrum, The New York Times, 28 July 2007; Is dressing sexily a provocation to men? Quora, 2016; Christian Modesty in Dress - What does the Bible Teach? Reformed Presbyterian Church, 22 February 2009; Daniel Haqiqatjou, Dress Codes are Sexist, Apparently, The Muslim Sceptic, 16 August 2016).

Attraction as provocation? The table abouve endeavours to frame the question as to when is attraction experienced as provocation -- whether the attraction is consciously cultivated or not, and whether the provocation is consciously intended or not. Rather than the attractor being of a sexual nature, the question may be asked with regard to the deployment of any asset of value -- monetary or otherwise. In deploying what may be appreciated by others, is it appropriate to assume that this may not be experienced as a provocation? Is the message "admire but do not touch" realistic in a complex system where inequalities are so deliberately cultivated -- as a right?

Exploitation of the term "harassment" is now framing a situation in which both "women" and "men" invest heavily in being "attractive", some more than others, however:

Whether for a "woman" or a "man", the challenge is the interpretation of signals and the intention behind them -- whether conscious or unconscious. Thus for a man in the archetypal interview situation, how to respond to the length of the mini-skirt and all it may unconsciously or deliberately reveal. For a woman, how many buttons on a blouse should be done up or undone to enhance attraction and memorability? Should a bra be worn or not? How should perfume be used -- on the hand which may be shaken? In creating an impression, what signals should be sent and received? In a formal setting it can be claimed that this dimension can of course be deliberately ignored as irrelevant by both parties -- each within their rights -- whatever the unconscious messages. And for the dominant partner, how is the "lion's den" prepared to fa ciliate encroachment -- psychoactive aids in their most general sense, etc (Varieties of Encroachmen,t 2004)?

As with the earlier 4-fold diagram, the complexity associated with attributing significance and making distinctions is usefully highlighted by relating the 4-factor Venn diagram on the left below with the logico-mathematical argument of Tony Phillips (Topology of Venn Diagrams, AMS) -- usefully compared with a tesseract.

Possible framings of harassment and attraction
4-factor Venn diagram 4-dimensional implications?
(from Tony Phillips)
(reproduced from Wikipedia)
Harassment: 4-factor Venn diagram Harassment: 4-dimensional implications? Harassment understood in terms of a tesseract

As Phillips indicates with respect to the image on the right above, in a topologically faithful Venn diagram for the 4 statements A, B, C, D, the dual graph will have 16 vertices, labelled from not A and not B and not C and not D up to A and B and C and D. Each region must share an edge with exactly four other regions, since there are 4 places where "not" can be inserted or eliminated. Correspondingly, the dual graph would have to show 4 possible directions at each vertex; this gives the graph of edges of a 4-dimensional cube. That 4-cube is drawn as projected into 3-space; edges going off in the 4th dimension are shown in green.

Why would it be appropriate to assume that the challenges of attraction and harassment could be effectively addressed through arguments and depictions in 2 or 3 dimensions, when time is a significant factor in the dynamic of attraction and response? There is a challenge to conventional logic to be recognized -- exemplified by the subtle dynamics of flirtation and courtship and the manner in which these are expressed and appreciated both in different cultures and at different periods (as discussed below).

If harassment and perceptions of harassment involve problems of perception, there is a case for recognizing the relation between the Phillips depiction above, a tesseract, and the Necker cube through which issues of ambiguity are studied. Careful distinctions are made between their implications and that of the Klein bottle by Steven Rosen (Science, Paradox, and the Moebius Principle, 1994, p. 197). For Rosen it is the Klein bottle which embodies the "nondual duality" which calls for new understanding. Do these different forms offer contrasting insights into how harassment might be variously framed?

Extending the exercise to other "transactions": The table above could be extended as a metaphorical template -- especially since very extensive use is made of metaphors associated with processes of sexual intercourse. In common jargon, for example, concern is widely expressed with the problematic possibility of "being screwed" in any transaction. Negotiations may be explicitly preceded by presentations and processes defined as "foreplay" (and explicitly conceived as "seductive") . These may then be followed by frank use of "are you fucking with us" and warnings "not to fuck with us". Other example relating to international relations are presented separately (The Coalition of the Willy: musings on the global challenge of penile servitude, 2004).

Some such template could serve to articulate the dimensions of current exchanges of global significance, as with the childish reference to Kim Jong-un by Donald Trump as "Little Rocket Man", in the light of some sense that North Korea was "fucking with the USA" -- namely with a leader necessarily to be understood as the global "Big Rocket Man"? The provocative sexual insinuations of the exchange have presumably been deliberate. That said, for each the harassment-attraction dynamic is effectively the "only game in town".

One of the most controversial features of the current focus on celebrities, now being singled out as exemplars of sexual harassment, is the extent to which the context of that behaviour has typically been one in which it could readily be understood as a commercial transaction -- an exchange of "favours". This interpretation can of course be highly contested when the victim claims total innocence, surprise and unfair exploitation by the perpetrator -- a person of renown. How this claim is to be compared with a consumer being misled in a street market by a sales person merits consideration -- namely the sense of "having been screwed".

Why would it be appropriate to assume such contexts were free of any problematic process when calls for vigilance have been widely formulated in modern society? Don't talk to strangers. Beware of whom you trust. Snake oil salespeople indeed have many wiles. Vigilance is a necessity in some contexts -- as when being "streetwise" is vital for survival. Is there a questionable relationship between innocence and righteousness framed otherwise by the legal principle to the effect that ignorance is not a plea before the law? What "law" is that, however? Is a reasonable protest to be made against the "law of the jungle" and the wilderness? What reaction is to be expected when entering a lion's cage -- especially in that the powerful may well be characterized by such a metaphor?

Such an example helps to extend further the value of a template of the above kind. As is increasingly widely documented, many transactions at the highest level are facilitated by an exchange of "favours" -- taking many forms. The most euphemistic of these is a "commission" -- possibly offered "under the table". How are such transactions "under the table" to be understood as differing in systemic terms from the fondling which some may experience when enjoying the privilege of dining next to a person of distinction -- allegedly including a famed Nobel Peace Prize laureate, as yet to be outed? Why might a "commission" in some cultures be reframed as "gracing the occasion" -- whilst being framed as completely unethical elsewhere?

Far more questionable is the assumption of the right to innocence when entering such an arena -- and the right to protest any abuse of it from the perspective of a particular time and culture, framed as universally appropriate. This would not be appropriate in a jungle -- and readily defined as stupid. What responsibility have parents naively avoided in assuming that the behaviour of authorities in educational and religious institutions does not call for similar vigilance? The dimensions of the challenge are evident otherwise in those areas of the world where women are obliged to walk long distances through the bush each day to get water -- and may well get raped in both directions.

Framing the system of harassment in a memorable schematic? Systems diagrams and maps, such as those indicated above, are not conceived with any concern for memorability. There is therefore a case for rendering the dynamic they articulate into more succinctly memorable schematics of which the following is an example. Their features would then offer a focus for discussion -- leading to their improvement.

Schematizing the representation of harassment?
Schematizing the representation of harassment?

What complex dimensions and processes need to be held by such schematics -- including the critiques of any such formulation or interpretation, as most commonly articulated by feminists? What forms of flirtation, if any, are acceptable from that perspective? When is marital intercourse to be understood as involving a degree of unwelcome harassment -- by either partner?

To be adequate to the challenge to comprehension, does such a schematic need to be represented dynamically, as argued separately (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity, 2017)?

Promoting ostentatious inequality: dubious complicity in an unmentionable game of unquestionable dimensions?

Many intractable issues in society would still appear to involve the "unsayable" in some form (Varieties of the "unsaid" in sustaining psycho-social community, 2003). In the case of sexual harassment, this has been partially remedied by the current process of claims against authorities and celebrities. Is the systematic cultivation of relative attraction a factor yet to be recognized in a society characterized by ever increasing inequality? What is engendered in the underprivileged -- whatever form that may take -- when they are encouraged by the media to admire that which they are unable to acquire, except according to the most dubious theories?

Irresponsible advertising of beauty products? It is perhaps extraordinary to recognize the role of the advertising industry in promoting inequality and encouraging some to distinguish themselves significantly from others -- through acquisition of goods explicitly claimed to establish discrepancy in status. This is most evident in the case of products designed to increase allure, a sense of beauty, and of self-esteem, relative to others. It extends to a wide range of products and services effectively marketed for this purpose. Ratcheting up inequality in this way is undertaken with the pretence that the intentions are entirely innocent and that any unfortunate consequences should be seen as incidental and beyond the responsibility of the producers and advertisers.

There is a strange similarity between such arguments and those used in the USA by the powerful lobby of the National Rifle Association in relation to gun control. Acquisition of ever more powerful weaponry is framed as a means of ensuring advantage over others held to be a potential threat. There is an acclaimed innocence to the supply and acquisition of such arms -- with any unfortunate consequences carefully framed as incidental and beyond the responsibility of the suppliers. There is an entitlement appeal to the 2nd Amendment of the US Constitution regarding the right to keep and bear arms. This claim then bears a strange relationship to appeals to various Declarations of Human Rights through which people are explicitly free to enhance their personal Right to Life, Lberty and the Pursuit of Happiness -- irrespective of the impact on others through their manner of doing so.

With respect to "weaponry" and its display, there is also a strange naivety to the denial that "strutting one's stuff" constitutes a provocation rather than a fundamental right -- as with undertaking "military exercises" off the coast of Korea. How indeed to distinguish between language justifying the display of one's wares to intimidate and harass and the enjoyment of their use to sustain and enhance self-esteem? In both cases it can be righteously argued that any provocation is in the eyes of the beholder -- readily to be managed with maturity. However both evoke extensive analysis of the legitimacy of any such perception in their respective domains. In the case of sexual harassment this is especially the case for both men and women, with the argument of men readily called into question (The Defence of Provocation, National Association of Women and the Law; Provocation: what does it mean to women? Salient, 3 August 2009). Whether in military terms or otherwise, exhibitionism in its various forms merits further clarification as provocative harassment.

It has long been noted that the specification of individual rights in the Universal Declaration comes with all the questionable ambiguities of its precautionary Article 30:

Nothing in this Declaration may be interpreted as implying for any State, group or person any right to engage in any activity or to perform any act aimed at the destruction of any of the rights and freedoms set forth herein.

Despite proposals, no necessary provision has yet been approved for any complementary Universal Declaration of Human Responsibilities, or its possible extensions (Universal Declaration of Responsibilities of Human Intercourse, 2007; Universal Declaration of Patent Responsibilities, 2007). What of the right to the assumption of innocence until guilt is proven?

Perfuming an encounter? Readily recognized as "women's weapons", the improbable relationship between cosmetics and weaponry has been explored otherwise (Marlen Komar, In the Cold War, Makeup Was a Weapon, Racked, 28 August 2017). For Abuczki ágnes:

In the ads of perfumes, women are often represented as tempting, attractive food for men. For example, consider the slogans of Macy's perfumes: "feast your senses", "make them [men] melt", "ripe [the woman herself] for romance", "spice things up",.... All these ads present food, therefore, cosmetics - such as perfumes as weapons - if we talk about sexual desire in terms of hunting or warfare in the hands of women in order to attract men. (The Use of Metaphors in Advertising, Argumentum, 5, 2009, pp. 18-24)

Irrespective of men, Michelle M. Lazar argues that women's own bodies are the enemies they are urged to battle, using the weapons and strategies offered by various beautification businesses. There is a nod to feminist sensibilities with talk of women's "rights", yet at the same time it is also assumed that women will enlist as dutiful foot soldiers in the beauty "wars", deferring to the industry's "experts" to set their goals and map out tactics for achieving them. (Entitled to consume: postfeminist femininity and a culture of post-critique, Discourse and Communication, 3, 2009, 4, pp. 371-400)

For Fern Johnson:

In the cosmetics business, there is also this underlying image of women as helpless against the enemy of facial degradation unless saved by the latest cosmetic product, in short, saved by the weapons and strategies used to combat the enemy in an all-out war. The tropes used to advertise face-fixing cosmetics for (mainly) White women arc becoming so common, almost universal, that they are coming to be first-order "reality". (Imaging in Advertising: verbal and visual codes of commerce, 2012)

Aside from the deliberately alluring images of women through which beauty products are so widely sold unchallenged, especially intriguing are the names of perfumes held to enhance the attractive process (Marisol Velasco-Sacristán and Pedro Fuertes Olivera Olfactory and Olfactory-mixed Metaphors in Print Ads of Perfume , Annual Review of Cognitive Linguistics 4, 2006, pp. 217-252). Curiously the preoccupation with "odour" extends to its metaphorical use by public relations consultants to provide image "deodorants" for individuals and institutions.

Harassing by allure? Under what conditions can this omnipresent marketing of attraction be seen as "bullying with beauty", or "harassment by allure", in which all are somehow complicit? Should bling-bling, as notably cultivated by Silvio Berlusconi, be recognized as a form of harassment? As a form of weaponry, does it not have consequences in terms of response evoked from the less endowed (Sarkozy's 'Bling-Bling' Presidency, Time, 20 December 2007)?

Given the manner in which use of make-up can be framed with military metaphors -- even as camouflage -- how is arming oneself cosmetically and competitively then to be understood given the widely announced investment of the new President of France (Emmanuel Macron has spent €26,000 on makeup in his first three months as French president, The Telegraph, 24 August 2017; Macron keeps up appearances with €26,000 makeup bill since May, The Guardian, 25 August 2017; Emmanuel Macron's $30,000 makeup scandal hides a much bigger blemish, The Washington Post, 25 August 2017). In modern society should everyone be enabled to increase their relative allure in this way?

Harassing by upgrade of "features"? Given the extent of increasing dependence on computer-related devices, the manner in which they are promoted offers a valuable lens through which to view sexual harassment -- and one which is somewhat less charged. As with promotion of beauty products and the allure they offer, marketing of new devices in a highly competitive industry can be seen in terms of the highlighting of alluring features of new products and of the upgrades to existing products. Users are deliberately perceived as "targets" for the presentation of what is commonly deprecated as "feature bloat" (or software bloat). There are few means of avoiding such exposure -- claimed by those promoting them to be vital to the increased performance and pleasurable experience of their users.

As with the sexual parallel, and on behalf of the producers, advertisers cultivate the innocent pretence that their initiatives can only be seen as in the best interests of users. The fact that every possible means is sought to capture the attention of users is in no way seen as detracting from that claim -- however much that invasion is experienced as unwelcome harassment. Major issues as a consequence of misleading advertising are readily set aside as incidental (or legitimate puffery), with their provocative nature framed as primarily a challenge for the discerning user.

Understanding the dynamics of the game: The complex dynamics of the relationship between men and women has long been framed as a game. There are many articulations of that relationship in those terms. Many metaphors descriptive of processes in that relationship have been borrowed from sport -- "foreplay" could be understood as an anticipation of "scoring", for example. Use of "offside", in relation to an unwelcome "pass" (as with "crossing the line"), would be immediately understandable in relation to harassment. "Marking" an opponent can be seen as "stalking".

The difficulty is that selective use of metaphors in this way does not give a sense of the game as a whole, or the rules of the game -- in relation to what is acclaimed as the "spirit of the game" in both cases. It is unfortunate to note, for example, that transactional analysis seemingly has little to say about harassment and especially sexual harassment -- despite its seminal framing such dynamics (Eric Berne, Games People Play, 1964).

Just as the game has borrowed insights from sport, it has also borrowed insights from strategic warfare -- even cyberwarfare, now that harassment has become significantly evident in that medium as cyberharassment, cyberbullying and cyberstalking. Seemingly as yet unexplored is the possibility of reframing the game in the light of the martial arts and its philosophy, as most notably and subtly framed by The Book of Five Rings: a classic text on the Japanese way of the sword. Is there an interpretation of aikido of relevance to the dynamics of interpersonal relations and response to abuse (List of Aikido Katas with Videos and Instructions)?

The further possibility, mentioned above, is the identification of a set of complementary games fundamental to relationship (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005). Potentially of far greater relevance is the understanding of "infinite games" in contrast to "finite games" by which so many interactions are characterized -- winning or losing (as with sexual harassment). In making the distinction, James Carse clarifies the differences between finite games that are played for the purpose of winning and infinite games played for the purpose of continuing the play (Finite and Infinite Games: a vision of life as play and possibility, 1986). This has given rise to the Infinite Game Project initiated by Niki Harré (The Infinite Game: how to live well together, 2018). Are the processes of flirtation already understood as an infinite game in some cultures?

Whilst the dynamics of interpersonal relationships could be compared to the simple game of noughts and crosses, such a comparison might be fruitfully extended to the far more complex game of go. However with the consideration given to the recent advances in artificial intelligence in surpassing human capacities exemplified in playing that game, especially significant has proven to be the ability to discover "moves" previously unrecognized by the experts in the game (AlphaGo Zero: Google DeepMind supercomputer learns 3,000 years of human knowledge in 40 days, The Telegraph, 18 October 2017). Might neural learning networks offer new ways of understanding both the subtlety of human relationships and the variety of forms of abuse?

Cultural distinctions and contradictions regarding harassment

Clash of righteousnesses? The point has been frequently made that the incidence and acceptance of harassment varies widely, both between cultures and over time. The evolution of attitudes is evident within living memory in western cultures. Distinctive norms are evident as a consequence of tourism and immigration, whether or not these are recognized in terms of a " clash of civilizations".

With respect to the theme of this argument, could the contrasting perception be better seen as a "clash of rightousnesses" -- given the defensiveness of all parties and the assumption that each should conform to the norms and expectations of the other? The recent emergence of feminist criticism in the west can be seen as the emergence of a sense of "righteousness" calling into question any continuing belief in droit du seigneur.

As with terrorism, even within the western cultural sphere, the nature of sexual harassment is understood differently, as noted by Abigail Cope Saguy:

France and the United States are particularly strategic case studies since their definitions of sexual harassment in laws in the workplace represent two opposite extremes. The United States has adapted one of the most inclusive definitions of sexual harassment in its EEOC guidelines, which designate any "conduct of a sexual nature" that creates an "intimidating, hostile, or offensive working environment".... In contrast, French sexual harassment law adapts a more restrictive definition, which designates only situations in which a hierarchical superior "abuses his official power" using "orders, threats, force" with "the intent of obtaining sexual favors" from another. Moreover, in the United States costly sexual harassment lawsuits are common and awareness of this problem seems to be growing while in France compensatory damages are tiny and public concern in this area remains relatively low. (Defining Sexual Harassment in France and the United States: arguments of activists and public figures, Princeton University July 1997)

The issue can be framed otherwise in terms of the culture of women in comparison with that of men. For Debbie Dougherty:

It is important to rethink sexual harassment by addressing the following question: Because most men do not harass women, why do men tend to be resistant to admitting the breadth and depth of sexual harassment in organizations? The author posits that because men and women do not understand each other’s standpoints on sexual harassment, a gap exists between men’s and women’s understanding of what sexual harassment means. Specifically, men’s power over standpoint and the related fear of marginalization clash with women’s power with standpoint and the related fear of physical harm. The author concludes by suggesting that engaging in a dialogue with the goals of understanding and accepting other standpoints is necessary before sexual harassment can be approached in a humanistic manner. ( Dialogue through Standpoint: understanding women’s and men’s standpoints of sexual harassment, Management Communication Quarterly, 12, 1999, 3)

Voicing claims: A related issue is the encouragement of women to "speak out" -- framed as legitimate -- irrespective of the nature of any conclusive evidence as conventionally understood (Theresa May under pressure to explain what she knows about nearly 40 Conservative MPs accused in sexual harassment scandal, Business Insider, 30 October 2017). Multiple claims may suffice, whatever their motivation, as discussed by Andrew Rawnsley (Theresa May could be the ideal woman to lead the clean-up of Westminster, The Guardian, 5 November 2017).

In the process of trial media to go totally unchallenged -- given the immediate impact of allegations made on those accused without due process as normally understood? Is "crowdguilting" to be recognized as an appropriate process for an advanced civilization? Perhaps to be understood as pre-emptive or anticipatory justice -- consistent with increasing global indifference to collateral damage.

The current political situation invites speculation on "counter-measures" which might be employed by the accused, namely collectively to claim (using a hashtag #ToMe ?) that their accusers had (literally) exposed themselves to some degree -- inviting the response now upheld as scandalous. How would a a context of multiple claim and counter-claims be disentangled given the current modalities? Any such initiatives, and the complex consequences, would be consistent with the current "fake news" culture and the trend toward "trial by media". However this would then be readily seen as mirroring patterns of claims and counter-claims in many intractable disputes (Israel/Palestine, US/North Korea, conservative/progressive, Sunni/Shia, etc). How might counter-productive claims be framed otherwise?

Cross-cultural implications: A more global approach to cultural differences has been taken by Harsh Luthar and Vipan Luthara (Theoretical Framework Explaining Cross-Cultural Sexual Harassment: integrating Hofstede and Schwartz, Journal of Labor Research, 28, 2007, 1, pp. 169-188). The rich variety of relevant cultural biases merits attention, as well as the biases in distinguishing them (Systems of Categories Distinguishing Cultural Biases, 1993; World Health Organization, Changing Cultural and Social Norms Supportive of Violent Behaviour. 2009).

The cultural clash of righteousnesses is especially evident in international conferences, as separately discussed with respect to its problematic consequences (Reframing Discourse on Sexual Harassment in Conferences, 1994; Women and the Underside of Meetings: symptoms of denial in considering strategic options, 2009). The title of the latter follows from the provocatively insightful title of Elise Boulding (The Underside of History: a view of women through time, 1976). The current challenge of deliberately facilitated harassment of men by women is evident in such events (Fears British officials will be seduced by Chinese 'honeypot' spies at G20 summit, The Independent, 3 September 2016; UK officials warned against falling prey to G-20 'honey pots': Report, CNBC News, 3 September 2016).

Paradoxical remedies: The issues raised suggest that many encounters, whether male-female, male-male, or adult minor, will in future need to be conducted with CCTV coverage to avoid the embarrassing possibility of false claims and processes. These recall concerns previously raised with regard to the extensively documented moral panic associated with allegations of satanic ritual abuse hysteria and the incidence of false memory syndrome (Romeo Vitelli, Implanting False Memories: how reliable are memories of abuse "recovered" during psychotherapy? Psychology Today, 4, 11 2012; Edward Wasserman, Remember the Wave of Satanic Child Abuse Hysteria? You Should, Huffington Post, 20 February 2012; Aja Romano. The History of Satanic Panic in the US -- and why it's not over yet, Vox, 30 October 2016).

Curiously there is the possibility of a systematic reversion to the traditional use of chaperones, as is already the practice in many medical consultancies. With respect to male-female interaction prior to marriage, this continues to be the practice perceived as appropriate in some cultures.

If men cannot be trusted as some women would have it (in the light of their experience), should women be trusted by men, given the current pattern of claims against them -- exemplified by that against Julian Assange? Is a reversion to systematic segregation by gender to be envisaged as a remedy in certain environments -- clubs, public transport, workplaces, restaurants, recreational facilities? A case for gender apartheid (aka sexual apartheid) -- understood otherwise? This has been the case in the past and remains the practice in some cultures -- presumably for the best of reasons. Ironically this would be consistent with the segregation of toilet facilities at a time when this is challenged by transgender requests.

Any such evolution suggests the extraordinary possibility that western feminist concern with harassment may justify a reversion to the arguments and etiquette framed by the cultural precepts of Islam, Judaism and Hinduism with respect to women -- and to some principles of Christianity (more notably in the past). If avoidance of harassment is most effectively achieved by separation and coverage, as continues to be argued in terms of such precepts, how are arguments to the contrary to be formulated?

With such a prospect, the clash of righteousnesses is surprisingly evident in the nature of the controversy regarding the clothing of women, exemplified by use of the burkha and the niqab by those of Islamic faith. There are multiple ironies to this debate as discussed separately (Facism as Superficial Intercultural Extremism: burkha, toplessness, sunglasses, beards, and flu masks, 2009). These include:

Toward encompassing relationship discontinuities through phase diagrams and catastrophe theory

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
Phase diagram interrelating suggesting 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

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
Attribution of complementary "languages" as control factors of a characteristic behaviour surface of catastrophe theory Attribution of complementary "languages" as control factors of a characteristic behaviour surface of catastrophe theory

Encompassing the "attraction-harassment" dynamic with a notation of requisite ambiguity?

Ambiguity: Is it appropriate to affirm unquestionably, as many would tend to claim, that in any form of harassment the victim is to be considered totally innocent and the perpetrator totally at fault? Is this the case whether the harassment is male-on-female, male-on-male, or otherwise? This framing does not apparently admit of any nuance -- with claims of "provocation" being readily dismissed as fabrications by interested parties. There are no "shades of grey".

There is no legitimated sense of any process whatsoever whereby the victim may attract or evoke harassment in a manner to be considered risky or inappropriate. The advice to those entering a bull-ring or a lion's cage would suggest otherwise. Seemingly innocent gestures may trigger unexpected responses, just as exposure of the wealth in a purse may lead to theft. In some cultures the wealthy ensure that the front of their dwelling is modest, even unattractive, to avoid evoking unwanted attention from thieves. Ironically, at the time of writing, much is made of the manner in which the extremely wealthy hide their assets in order not to attract attention and to avoid harassment by fiscal authorities (Paradise Papers: secrets of the global elite, International Consortium of Investigative Journalists, 5 November 2017; Paradise Papers leak reveals secrets of the world elite's hidden wealth, The Guardian, 5 November 2017).

Accepting that the "attraction-harassment" dynamic is complex, any reference to it is also necessarily complex. It does not allow for simplistic definition -- or if this is attempted then this itself becomes part of the problem. In this sense the dynamic exemplifies a far more fundamental challenge of comprehension and reference for which an appropriate notation would be beneficial. This could be expressed in terms of the challenge of encompassing ambiguity -- as distinct from uncertainty. There is extensive reference to the latter in these "uncertain times" but relatively little to the former.

The nature of ambiguity could be usefully seen as fundamental to how any predilection for definition is discussed. Living with uncertainty implies living with ambiguity and "shades of grey", fruitfully explored in terms of liminality (Living as an Imaginal Bridge between Worlds: global implications of "betwixt and between" and liminality, 2011; Living with Incomprehension and Uncertainty Re-cognizing the varieties of non-comprehension and misunderstanding, 2012).

Notational ambiguity: A useful point of departure is the Chinese binary notation of the I Ching that became variously fundamental to the information sciences subsequent to the early insight of Leibniz. However this must necessarily be interpreted dynamically in contrast to the framing previously explored (Discovering Richer Patterns of Comprehension to Reframe Polarization, 1998). One of its major benefits is the inherent nuance that accompanies any interpretation.

The conventional deprecation of this Chinese insight by western science and philosophy can however be usefully seen as a feature of the "clash of righteousnesses" indicated above. The point is succinctly articulated by Bryan Van Norden (Western Philosophy is Racist, Aeon, 2017) as an excerpt from his Taking Back Philosophy: a multicultural manifesto (2017) -- which has evoked considerable controversy. The "racism", as a form of "righteousness" can be usefully associated with sexual harassment in the light of the arguments of Massimo Pigliucci (Does philosophy have a sexual harassment problem? Rationally Speaking, 19 August 2013). Methodologically, conventionally understood, are both extremes as much a part of the problem as part of the solution?

As a symptom of "another righteousness" in its own right, Van Norden argues that: Mainstream philosophy in the so-called West is narrow-minded, unimaginative, and even xenophobic. Noting Leibniz's appreciation of the I Ching, he continues:

Leibniz also said that, while the West has the advantage of having received Christian revelation, and is superior to China in the natural sciences, 'certainly they surpass us (though it is almost shameful to confess this) in practical philosophy, that is, in the precepts of ethics and politics adapted to the present life and the use of mortals'.... So the exclusion of non-European philosophy from the canon was a decision, not something that people have always believed, and it was a decision based not on a reasoned argument, but rather on polemical considerations involving the pro-Kantian faction in European philosophy, as well as views about race that are both scientifically unsound and morally heinous. Kant himself was notoriously racist....

Kant is easily one of the four or five most influential philosophers in the Western tradition. He asserted that the Chinese, Indians, Africans and the Indigenous peoples of the Americas are congenitally incapable of philosophy. And contemporary Western philosophers take it for granted that there is no Chinese, Indian, African or Native American philosophy. If this is a coincidence, it is a stunning one.

Missing is the motivation to engender a methodology to reframe the relationship between clashing righteousnesses. As a fundamental issue of binary thinking, given its appreciation in both East and West, a useful point of departure in the quest for such a methodology is the notation fundamental to the ambiguities encompassed by the I Ching. The classic point of departure there, as "2-phase comprehension", calls for dynamic representation as:

These signs can be too readily identified with "male" (yang) and "female" (yin). Somewhat provocatively, but appropriately, this depiction can be contrasted with the common sociobiological equivalent -- especially with the emerging psychoanalytical recognition of an "inner male" within any "female" and an "inner female" within any "male" (John A. Sanford, The Invisible Partners: how the male and female in each of us affects our relationships, 1979).

Animation male female  symbols Animation female male  symbols

A far more general understanding may however be more fruitful. In practice "women" may empower themselves in a "yang-mode" and frame "men" as being in a "yin-mode" -- who may welcome this dominance in some situations. Between men in prisons, some may be framed as "bitches". Either men or women, in a "yang-mode" may frame targets and marks for exploitation as being in a relatively vulnerable "yin-mode". The victims of any form of dominance may reframe themselves aggressively in a "yang-mode" -- as with jihadists. Any such attribution or framing may itself be contested in the dynamic -- given any capacity for reframing by donning or doffing a frame.

Potentially more intriguing is the contrast between "reality" and "imagination" where assumption of either can arguably imply some form of projection -- well-recognized in interpersonal relationships and courtship processes. This is most charmingly articulated in the famed butterfly dream of Chuang Tzu (aka Zhuangzi):

Once Zhuangzi dreamt he was a butterfly, a butterfly flitting and fluttering around, happy with himself and doing as he pleased. He didn't know he was Zhuangzi. Suddenly he woke up and there he was, solid and unmistakable Zhuangzi. But he didn't know if he was Zhuangzi who had dreamt he was a butterfly, or a butterfly dreaming he was Zhuangzi. Between Zhuangzi and a butterfly there must be some distinction! This is called the Transformation of Things.

The dream is held to be the most celebrated ever to be recorded in the history of Chinese philosophy (Kuang-Ming Wu, The Butterfly as Companion: meditations on the first three chapters of the Chuang Tzu, 1990). In its distinction between two fundamental cognitive conditions, this recalls ongoing academic dispute regarding the psychosocial construction of reality. It is related to distinctions between "explicit knowledge" and "tacit knowledge" -- presumably increasingly to be considered a matter of controversy in relation to sexual harassment through "touching". The dilemmas are all the greater given the importance associated with phatic communication as a much-valued bonding ritual (between world leaders) in contrast with formal substantive communication between them. The contrasting symbols are indicative of the mathematical archetypes of 1 and 0 whose mysterious relationship in the light of the Euler identity invites further speculation (Correspondences: "epi", Euler identity, and sexual dynamics? 2013).

In this light, rather than indicating statically either the "yang" or "yin" variants, these are presented above in parallel through a dynamic. Appropriately (when printed), these appear static -- however it is their dynamic alternating condition (as it may feature on a web page) which is of far greater significance. They frame the question as to which is the empowered attractor and which is the potential harasser. In a particular situation, is it the yang or yin condition which is the attractor or the harasser? To which symbol does either lay claim? With which is identification made? How does comprehension oscillate between either interpretation? Necessarily, the dynamic does not readily lend itself to formal discourse based on unambiguous (invariant) definitions. Each is a focus of a sense of righteousness.

A more complex pattern, previously indicated as "4-phase comprehension", can then be expressed using combinations of the following:

Combined dynamically this would however give the following, again with the distinctions made evident in the dynamic (on a web page) rather than in static interpretation assumed to be definitive (when printed).


The above presentation in quadrants is valuable in suggesting how the condition indicated by each quadrant may alternate with that of other quadrants -- but with any definitive allocation of significance to a particular quadrant then called into question. How might this hold the interplay between relative dominance and relative passivity -- however each may be valued or deprecated?

Provocatively again, these distinctions could be usefully contrasted with an emergent equivalent -- using four LGBT standard gender symbols. Of value to this argument, the relationships they signify are all indicative of behaviours which have long been considered highly abusive (even abhorrent, criminal or "evil"). However controversial, this continues to be the case in particular cultures and in particular segments of society. Not to be forgotten, as especially significant, is the conviction for homosexuality of Alan Turing following his unique contribution to the outcome of World War II, to the development of computer technology, and to speculation regarding processes transcending its limitations, as discussed separately (Imagining Order as Hypercomputing Operating: an information engine through meta-analogy, 2014).

The conventional inability to process such emergent distinctions is only too evident in the controversies that are evoked in contrast to the relatively "comfortable" binary modality of righteousness faced with its unreasonable challenges. Curiously tragic is evidence of such radical reversion to a particular sense of rightness, despite emergence of the subtler 4-fold insight (Brendan O'Neill, Questioning gender fluidity is the new blasphemy, The Spectator, 14 November 2017).

It is perhaps useful to see these 4-fold distinctions more generally, with the sexual connotations as only a potential specific instance in each case of: female-female bonding, male-male bonding, male-female bonding, and bonding transcending any gender focus. They might better be understood as indicative of a set of modes of self-reference of a "higher" order -- beyond that of second-order cybernetic feedback processes (third order? fourth order?).

In contrast with the abstract binary symbolism, these qualitative dimensions add to its simple "positive/negative" distinction an as yet unresolved sense of what is "right" or "wrong" ("good" or "evil") -- variously distinguished through "shades of grey", as with the problematic distinction "overt/covert". It is of course notable that women continue to be framed -- by men of some religious persuasions -- as more closely associated with "evil". The charged nature of the basic distinction continues to play out in the distinction between "right" and "left" -- especially in many political contexts. The complexity of such associations is evident with respect to "Alt-Right" and "Alt-Left" -- and the unreasonableness of the arguments of the other .

In addition to the positive/negative distinction, also implied is a complex pattern of "true/false" distinctions -- "shades of grey" understood otherwise and potentially relevant to any logical truth table appropriate to a "post-truth" era (Towards articulation of a "post-truth table"? 2016). The argument can be more appropriately complexified using "8-phase comprehension", with a pattern of distinctions as follows:

Given the confusion regarding the extended distinction of gender-orientation symbols, it is as yet unclear what such a corresponding set might usefully signify, and how they might be reduced to a coherent pattern of 8, for example. A set of 12 with associated computer codes is available (Gender Symbols Female and Male Signs, Alt-Codes). A larger set is presented by Anunnaki Ray (All the Gender Symbols), with indications of an even more comprehensive set as shown below.

Comprehensive set of gender-orientation symbols
Extended list of gender symbols
reproduced from Cari-Rez-Lobo (Gender Symbols, Deviant Art), which includes a further clarification of each

Commentary on the schema of 64 I Ching hexagrams offers an 8-fold pattern of potential significance (Organization of I Ching hexagrams in terms of traditional "houses", 1995) -- potentially implying insights into harassment. It is however tempting to see the symbols above as indicative of distinctions analogous to those made in the earliest stages of insight into the periodic table of chemical elements with its clustering into 8 groups -- held to be consonant with the musical octave. In that spirit there is a case for imagining a future articulation of "human knowing" -- as it might be of relevance to interpersonal relations (Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order, 2009). As noted there, 8-fold patterns are a feature of various distinctions of cognitive frameworks (Systems of Categories Distinguishing Cultural Biases, 1993). Can the interacting "elements" distinguished be variously understood as "harassing" one another, given the imaginative exploitation of that metaphor by Primo Levi (The Periodic Table, 1975) -- acclaimed as the best science book ever. Do the musical associations suggest that harassment could be explored in terms of discord -- especially with its diabolus in musica?

Rather than representing the BaGua set as a dynamic, a form of dynamic can be implied by any of the following configurations. Those on the left are traditional depictions, widely evident in Chinese iconography. These raise the valuable question as to how any sign they should be "read". Should it be read and interpreted "top-down" or "bottom-up"-- "top-in" or "top-out". The issue of direction of reading could be seen as fundamental to the difficulties of discourse regarding hierarchy and empowerment -- given preferences in the matter. The question can be explored more generally (Unquestioned Bias in Governance from Direction of Reading? Political implications of reading from left-to-right, right-to-left, or top-down, 2016).

It is for such reasons that the depictions on the left (with their traditional directions of reading) are also presented on the right -- suggesting an alternative direction of reading of the same trigrams.

Schematic representation of 8-fold Ba Gua (Pa Kua) Mirror
King Wen "Later Heaven" arrangement
Oriented with trigram top outward
(traditional presentation)


Oriented with trigram top inward
(non-traditional presentation)


FuXi "Earlier Heaven" arrangement
Oriented with trigram top outward
(traditional presentation)


Oriented with trigram top inward
(non-traditional presentation)


Articulation for "intercourse": The distinctions made in this overly abstract Chinese notational framework are the basis for the extensive articulation of the numerous modalities of change in the long-appreciated Chinese Book of Changes -- the I Ching. The question is whether that articulation in terms of 64 interrelated hexagrams can be fruitfully adapted to the specifics of interpersonal relationships with its challenges of attraction and harassment. One such adaptation was previously made for dialogue -- understood more generally and fundamentally as intercourse (Transformation Metaphors -- derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). Aside from the index to the complete pattern offered in that document, the dialogue thread can be explored from this point.

As a potentially instructive exercise, there is a case for extending the associated commentary on "dialogue" to "relationship" or "intercourse", especially in the light of the general implications of the latter, as noted above ("Human Intercourse": "Intercourse with Nature" and "Intercourse with the Other", 2007; Beyond Harassment of Reality and Grasping Future Possibilities: learnings from sexual harassment as a metaphor, 1994). Given that the exercise is essentially a simple matter of substitution, the question would be the choice of emphasis between "relationship" and "intercourse", and what insights either would offer -- or whether the adaptations are anyway too artificial and contrived. They could indeed clarify any need for sharper language commensurate with the experience of abuse.

Comprehensive relational map? A study by Anagarika Govinda (Inner Structure of the I Ching; the Book of Transformations, 1981) resulted in the following map of all 64 I Ching conditions projected onto a circular diagram (shown below left), as reproduced from previous discussion of it (Alternating between Complementary Conditions -- for sustainable dialogue, vision, conference, policy, network, community and lifestyle, 1983).

Arguably, as a map, it is several orders of articulation greater than has as yet been produced by the conventions of academia -- or deemed of relevance to the dynamics of righteousness in question, as simply framed in practice.

A unique feature of the focus on the "inner structure" is that this diagram results from the interplay between the 8 fundamental conditions from which the 64 are derived. As indicated above, the 8 are each denoted by a half-hexagram, namely a trigram. Depending on the order in which any given pair of trigrams is read, one of two hexagrams is thus defined. It is the condition numbers of these alternatives which are indicated on the straight lines within the circle. Each line thus represents two transformative movements. The eight conditions around the circumference represent those cases when the two trigrams are identical. Thus the straight lines denote transformations governed by the relationship between the 8 fundamental conditions denoted by each doubled trigram on the circumference.

Relational map from a Chinese cultural perspective?
Projection of all 64 I Ching relational conditions (hexagrams) onto a circle

Original version
by Anagarika Govinda (1981)

Addition of labels to version on the left
(use browser facility to view enlarged version for details)
I Ching hexagrams projected onto a  circle by Anagarika  Govinda I Ching hexagrams projected onto a circle and labelled

Reproduced with the kind permission of Anagarika Govinda, from the
Inner Structure of the I Ching; the Book of Transformations (1981)

Labels added from Transformation Metaphors -- derived experimentally from the Chinese Book of Changes (I Ching) (1997)

The labels added to the conditions in the right hand image derive from an extensive exercise in interpreting the conditions and identifying a simple phrase in English with which to associate each of the 64 conditions. There are many translations and interpretations of the I Ching and the labels chosen can necessarily be variously challenged. The commentary on each condition, as indicated above, clarifies the subtlety of the understanding of the conditions in the pattern and the network of 384 relationships between them. That commentary also includes the corresponding Chinese ideogram and the Chinese phrase associated with it.

The pattern of parallels and polygons in the schematic above invites further reflection regarding styles and modalities of sets of relationships. Colours could be used to distinguish these further. The original commentary by Govinda offers further insight in this respect.

As shown below, another version of the map on the right can be produced with Chinese elements instead of the questionable non-traditional English interpretations. This could encourage further insight from that cultural perspective. Indication of the pair of hexagrams associated with each relational line across the circle serves to clarify the pattern in the depictions above. Note that the ideograms and hexagrams are presented somewhat differently with respect to the lines for reasons of space and legibility.

Relational map as above with hexagrams and Chinese ideograms?
(use browser facility to view enlarged version for details)
I Ching Relational map with hexagrams and Chinese ideograms
Hexagrams and ideograms from Transformation Metaphors (1997)

Patterning psychosocial relationships in 3D or more?

It was argued above that there is a need for a coherent memorable schematic through which the diversity of relationship dynamics could be comprehended. One approach noted, is the projection of 64 relationships onto a circle in the light of the I Ching articulation. As a pattern depicted in 2D it raises the same questions as any 2D projection of the planetary globe. That challenge has given rise to an extensive range of techniques of projection, with each of which there is a well-recognized particular form of potentially misleading distortion (List of map projections, Wikipedia).

It is therefore to be expected that any effort to portray the complete range of human relationship dynamics would also be subject to distortion, with whatever technique is favoured. Presumably this would indeed be reduced if the depiction was in 3D, on the assumption that a more comprehensive pattern -- if not more comprehensible -- would require four dimensions or more. There is the further irony that a major issue, as highlighted above with respect to ambiguity, is the extent of "projection" apparent in relationships in which the parties each have a particular understanding of what is "right" -- indicating a challenging relation to others framed as "wrong".

The identification of an appropriate holding framework in 3D and 4D was previously discussed from a different perspective (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity, 2017). That exploration was informed by the efforts of logicians to map the 16 Boolean logical connectives onto a suitable polyhedral framework, of which the image above by Tony Phillips is one example. It is described as a tesseract, namely a cubic form in 4D. That earlier discussion presented images and animations of other related polyhedral structures which could hold the 16 connectives or the more extensive set of 64 relationships of the I Ching pattern dynamics. Most notable were the 3D projections of the 4D polychora: truncated tesseract and rectified tesseract (Dynamic relationship between polyhedra engendered by circles -- variously implying forms of unity, 2017). In the light of that terminology, from the perspective of contrasting framings of relationship -- "disagreement" -- could well be understood as appropriately resulting from "cognitive truncation" or "cognitive rectification", namely a form of reductionism with respect to complexity of higher order.

The 2D articulation of Anagarika Govinda presented above invites further consideration in the light of the 3D/4D possibilities -- given the constraints associated with any form of mapping projection. Aside from the above-mentioned variations on the tesseract as a means of mapping all 64 relationships, other projections could emphasize:

As with projections of the planetary globe, there is then a sense of the need to alternate between contrasting 2D projections to arrive at an understanding of 3D globality -- if such is adequate to the complexity of relationship dynamics. A further constraint is the desirability of the simplest degree of symmetry in the form(s) chosen in order to enhance comprehensibility and communicability.

Mapping 24 relational dynamics onto a faceted cube: Assuming that the relational dynamics between the 8 primary patterns constitute a special case, associating their 4 diagonals through the centre across the cube can be set aside leaving the focus on the 24 edges of the faceted cube as shown below, using the numbering from the Govinda schematic above. It is appropriate to note the widespread familiarity with that form through its use in jewelry. The polyhedron has two types of face: rectangles between opposite edges of the original cube, and bow-tie shaped faces using the four vertices of each original square face. Unusually, its dual has vertices at infinity.

Animations of faceted cube with attribution of 24 relational dynamics
(excluding the pattern of 4 dynamics associated with 4 diagonals through the centre)
Faces non-transparent Edges only (faces transparent)
Animation of faceted cube with attribution of 24 relational dynamics Animation of faceted cube with attribution of 24 relational dynamics
Animations prepared with the aid of Stella Polyhedron Navigator. Video version: mp4

The diagonals omitted, as may be seen from Govinda's schematic, correspond to: 11/12 (peace/stagnation); 63/64 (accomplishment/transformation threshold); 32/42 (assistance/endurance): 31/41 (influence/deficiency). Of potential further interest are the triangular and rectangular planes across the cube -- between the vertices -- corresponding to the polygons in Govinda's schematic.

Mapping 28 relational dynamics using the "simplest torus": An animated version is provided by Jerzy Mil (Simplest Torus, GeoGebra). Its relationship to the tesseract is discussed by Stan Tenen (The Alphabet That Changed the World, 2013). It has 28 edges, satisfying one requirement. The dual form of those relationships (as evident in Govinda's schematic) is evident in the labelling of the edges (left-hand image) and in its dual (central image). The labels have been arbitrarily allocated to edges (for convenience) although an alternative would be to exploit the parallelism in Govinda's depiction in order to attribute them more meaningfully. The right-hand image shows one kind of morphing between the other two forms.

Animation of "simplest torus" Animation of dual of "simplest torus" Morphing between "simplest torus" and its dual
Animation of 28 relational dynamics using simplest totus Animation of 28 relational dynamics using dual of simplest totus Morphing animation between simplest totus and its dual
Animations prepared with the aid of Stella Polyhedron Navigator

The quest for a more appropriate attribution of relational dynamics, in the light of the symmetries of Govinda's schematic, raises a number of interesting questions. There are two primary square patterns within that 2D schematic. The form of the simple torus suggests that these squares should be "drawn appart" vertically into the third dimension and rotated 45 degrees with respect to each other to a position of coincidence, in order to provide the basic framework of that form. The two sets of 4 primary hexagrams could then be usefully allocated to the vertices of those two squares, following the earlier approach with respect to the faceted cube. Hexagram pairs can then be attributed to the edges of each square.

In a preliminary approach the question of the direction of 45-degree rotation emerged, namely a question of chirality (which could be appropriate to any mapping onto the cube, as above). This gave rise to the following alternatives with attribution of primary relationships only -- leaving the question of how the other relational pairs might be appropriately distributed.

Preliminary attribution of relational dynamics to faceted cube
Rotation of primary square 45 degrees left
(faces transparent)
Rotation of primary square 45 degrees left
(image on left with faces non-transparent)
Rotation of primary square 45 degrees right
(faces transparent)
Attribution of relational dynamics to faceted cube Attribution of relational dynamics to faceted cube Attribution of relational dynamics to faceted cube
Images prepared with the aid of Stella Polyhedron Navigator

This approach raised the question of whether such contrasting polyhedral mapping forms should be understood as alternating, one with the other, especially since each pair of relational dynamics can itself be best understood as an alternation between two complementary conditions. The attribution of any set of relational pairs to such a form also clarifies the sense in which any form with fewer mapping features than required necessitates rendering some relational dynamics implicit rather than explicit (as previously evident with the cube).

This recalls the arguments regarding explicate/implicate order and holomovement of David Bohm (Wholeness and the Implicate Order, 1980) and their potential cognitive implications (Paavo Pylkkänen, Cognition, the implicate order and rainforest realism, Futura, 31, 2012 2, pp. 74-83). Of interest to any such flexibility is the sense in which, rather than being rigid, the polyhedral edges are better understood as springs or rubber bands, recalling the oscillating dynamics of tensegrity structures as articulated with respect to biological cell structures by (Donald E. Ingber, The Architecture of Life, Scientific American, January 1998).

Mapping 24 relational dynamics onto a cuboctahedron: The question of how to attribute the relational pairs to the 28 edges of the "simplest torus", together with any notion of necessary "flexibility", recalls the central role of the 24-edged cuboctahedron (or rather the rhombic dodecahedron as its dual) in mapping the Boolean logical connectives, as previously discussed (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity, 2017). Together with the faceted cube and the simplest torus, the degree of structural equivalence is striking -- anticipating the drilled truncated cube and the tesseract. The interplay of implicit and explicit features is also strikingly evident in the manner in which the cuboctahedron can be "folded" progressively into icosahedral, octahedral and tetrahedral forms by collapsing its square sides, in a process extensively documented by Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975).

It is for this reason that he describes that structure as a vector equilibrium, as separately discussed (Vector Equilibrium and its Transformation Pathways, 1980). He nicknamed the contraction/expansion process as a jitterbug -- of which many explanatory videos are accessible (Vector Equilibrium: R. Buckminster Fuller; Buckminster Fuller's Jitterbug, YouTube). The latter indicates how the transformation passes through a form which closely resembles the simplest torus discussed above.

Despite Fuller's own interest in its cognitive implications, no attempt seems to have been made to attribute patterns of relational significance to that structure, as discussed separately (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009). The possibility of "collapsing" the cuboctahedron is indicative of the manner in which relational pairs may be conflated (or confused) into smaller patterns of relational dynamics of greater generality -- namely rendered "implicate" to a higher degree.

The following depictions are the result of one mapping exercise in the light of learnings from the exercise with the simples torus. The two primary squares of Govinda's map are associated with two opposite squares on the cuboctahedron, respectively labelled with with vertices in red or yellow. This enables relational dynamic pairs from the map to be attributed to edges of each of those squares.

Alternate views of cuboctahedron with attribution of all hexagrams except those across diagonals
(labels of vertices of the 2 complementary squares in yellow or red)
faces transparent image on left with faces non-transparent
Cuboctahedron with attribution of I Ching hexagrams Cuboctahedron with attribution of I Ching hexagrams
Images prepared with the aid of Stella Polyhedron Navigator

It proved necessary to rotate the attribution of labels to the primary squares (in the light of the process with the simplest torus). This positioned those vertices so that a single relation could be attributed to the two edges linking between the two squares (with one of the pair following another instead of being doubled up). After completing the mapping in this way, the 12 unattributed relational pairs from Govinda's map could be recognized as implicit links: 8 triangulating the 6 squares and 4 passing diagonally through the centre of the form.

The distinction made between edges mapped with relational pairs and those with a single relation is potentially significant with respect to the manner in which the cuboctahedral structure can be collapsed in the jitterbug mode (mentioned above). It also recalls the alternation in the benzene molecule between a single-bonded and double-bonded condition -- basic to the stability of its existence as a resonance hybrid fundamental to organic life. Some such alternation dynamic would indeed be appropriate to any sustainable pattern of psychosocial relationships.

Benzene molecule as a resonance hybrid
(showing alternation between single and double bonds)
Animation of benzene molecule as a resonance hybrid Animation of benzene molecule as a resonance hybrid
(Animation developed from Wikipedia image)

This approach would allow the exercise with the simplest torus to be revisited in order to achieve a complete mapping.

Mapping 8 primary vertices subtending relationship dynamics using 4D hexadecachoron: In this case the emphasis, as noted above, is on the 8 relational conditions around the circumference of Govinda's circular schematic. The form -- one of the simplest in 4D, with its dual -- offers similarities to the cubic structure of the tesseract. It has 16 cells, recalling the pattern of Boolean connectives with the cells morphing to vertices in the dual. However there are only 24 edges -- short of the 28 required to hold the set of relationships as indicated above.

Morphing of 4D hexadecachoron with its dual
Morphing of 4D hexadecachoron with its dual
Animation prepared with the aid of Stella Polyhedron Navigator

Alternation between forms? The limitations of the above projections suggest that the quest for a fruitful mapping in 3D or 4D may call for other insights, including the possibility of alternation between forms which need to be understood as complementary -- in dynamic relationship to one another. The following table is a tentative effort to indicate how mapping a set of 64 (or more) relational distinctions may be "collapsed" when projected onto the edges (and vertices) of particular forms of varying degrees of complexity. An edge may then have to "hold" multiple relations -- necessarily conflating their distinctions into an implied generality which it is then difficult to articulate in a simple expression.

An interesting issue is whether and when some distinctions cannot then be held explicitly within the mapping form and have to be implied by other features, most notably what is suggested by relationships of symmetry (such as a square of edges inviting triangulation). Symmetry is then one reason for privileging simple spherically symmetrical forms, given the memorability of coherence they offer. In this connection, also of interest is how the more fundamental (hexagram) conditions may be usefully shifted to/from attribution to an edge, to attribution to a vertex. or to an axis of symmetry within the pattern.

Characteristics of polyhedra as candidates for mapping purposes
  mapping candidates


of significance
relational bonds/vertex relational
1D line     1 64 0 64 0
1D line   2 1 64=2x32 32 0 0
2D triangle 1 3 3 64-4=3x20 3 (plus 1) 20 0
3D tetrahedron 1 3 6 64-4=6x10 4 10 0
3D octahedron 4 4 8 64=8x8 0 8 0
3D cube   8 12 5x12 ? 5  
3D dodecahedron     30 64-4=2x30 ? 2  
3D icosahedron     30 64-4=2x30 ? 2  
3D cuboctahedron   8 24   8 2 or 1 8 + 4
3D faceted cube   8 24   8    
3D simplest torus     28   8    
3D drilled truncated cube     64     1  
4D hexadecachoron (3-hex, 16-cell)     24        
4D cantitruncated tesseract ("grit")     384        
3D prism-expanded rhombicosidodecahedron     384        

Implication of a central hole? Of particular interest, with increasing complexity of the pattern, is the enhanced memorability enabled by rendering explicit a central hole in the structure. This recalls the arguments of Terrence Deacon as a cognitive anthropologist regarding the role of what is missing (What's Missing from Theories of Information? 2010). The progressive hollowing of the patterns is evident in the forms indicated as potentially useful, especially when the hole is explicitly framed as in the simplest torus, the drilled truncated cube, and various toroidal polyhedra.

The point can be further emphasized through the shift to 3D representations of 4D polyhedra. This is especially the case if the argument is extended from the mapping challenge of 64 relational distinctions to the pattern of 384 associated with all the possible transformations between the 64 hexagram-encoded conditions (namely 6x64). The few polyhedral forms suitable for edge mapping of the latter could be said to be inherently interesting/memorable given their extraordinary symmetries -- worthy of any imagined (extraterrestrial) spacetime ship or habitat (Timeship: conception, technology, design, embodiment and operation, 2003). Missing, as yet, is insight into how the distinctions should be meaningfully attributed -- exploiting parallels, edge types, etc.

Animations of polyhedra especially suitable for more complex explicit mappings of binary distinctions
drilled truncated cube with relational conditions
(64 edges; non-transparent version)
prism-expanded rhombicosidodecahedron
(384 edges; non-transparent version)
cantitruncated tesseract
(384 edges)
Animation of drilled truncated cube Animation of prism-expanded rhombicosidodecahedron Animation of cantitruncated tesseract
Animations prepared with the aid of Stella Polyhedron Navigator

Use of the drilled truncated cube for mapping purposes is discussed, with multiple images, in the following:

Consistent with the above polyhedral argument, also of potential interest is an unusual related form of value to exploratory mapping of relational dynamic pairs rather than singular relations, namely a form with 192 edges rather than 384. The peculiar assymetry of the pattern enfolded by the outer structure invites reflection.

Screen shots of double drilled truncated cuboctahedron (most external faces transparent)
(90 faces of 24 types; 80 vertices of 20 types; 192 edges of 48 types; central structure has 24+8 edges)
Double drilled truncated cuboctahedron Double drilled truncated cuboctahedron Double drilled truncated cuboctahedron
Images prepared with the aid of Stella Polyhedron Navigator

Arguably it is some such "enholed" framework which would be of requisite complexity to frame the "incomprehensibility" of the violent relationships between righteous world views, exemplified by the case of the Abrahamic religions and their quarrelling denominations. The mystery of their respective insights might be more appropriately recognized in terms of holes, understood otherwise (Roberto Casati and Achille C. Varzi, Holes and Other Superficialities, 1994). Ironically, given the biological distinction between male and female, reflected in the binary notation, there is a charming poetic justice to the role of holes, as discussed separately (Is the World View of a Holy Father Necessarily Full of Holes?, 2014). Rather than being either "filled" or "white-anted", the sense in which the centre indeed needs to be "empty" (to encompass higher orders of complexity) is perhaps paradoxically anticipated by lines from The Second Coming by the poet W. B. Yeats:

The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,

The fundamental cognitive nature of the challenging reconciliation between the opposites is of course a theme of a number of schools of thought and is notably explored by Carl Jung (Mysterium Coniunctionis:s an inquiry into the separation and synthesis of psychic opposites in alchemy, 1970). Within that framework it is often symbolized by the Ouroboros, occasionally depicted in relation to the dynamics of the benzene mlecule (above). In relation to the polyhedral argument here, it is the toroidal form of that symbol which is intriguing, if indeed a central hole helps to engender and sustain relevant insights. This suggests the possibility of a more memorable depiction, taking advantage of modern visualization facilities.

Forces in play? That which can only be rendered explicit in 4D (or more), makes it impossible to render visible in polyhedral mappings in 3D. Polyhedral forms can however be used to provide an explicit encoding of binary notational ambiguity -- through highlighting the role of resonance in "encompassing" forms. It is especially intriguing to note in the commentary on the 3D perspective on the cantitruncated tesseract, as a 4D polychoron, that 8 truncated cuboctahedra that feature in that structure have to be "hidden" in order to represent it in 3D (as shown above).

The sense of resonance, and self-organization of any configuration in 3D, can be represented to a very limited degree using force-direct graph depiction (d3.js) as shown below.

Indicative screen shots of use of force-directed graphing for 3D configuration
(highlighting text associated with a single node selectively isolated by the cursor)
Drilled truncated cube configuration with 64 nodes 384 I Ching transformations between 64 hexagrams
Fore direct graph of drilled truncated cube Use of force-directed graphing for 3D configuration
source and explanations source and explanations

There is a curious sense in which the process of "collapsing" relational distinctions bears a similarity to the challenge of comprehending the compactification of "extra dimensions" in fundamental physics -- thereby effectively "curled up" in the polyhedral edges as hidden "levels" of insight, as can be variously explored according to the number thereby implied (Distinguishing Levels of Declarations of Principles, 1980; Varieties of Rebirth -- distinguishing ways of being "born again", 2004; Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? 2015).

The exceptional handling of the four primary relational categories in the mapping exercises above are then suggestive of a strange relationship to the challenge for string theory. This endeavours to reconcile the gap between the conception of the universe based on its four observable dimensions with the ten, eleven, or twenty-six dimensions by which theoretical equations suggest the universe is composed.

Understood otherwise, there is an intriguing resemblance of "enholed" polyhedral forms to many of the multitude of radiolaria, as some of the simplest forms of life -- depicted in the famed compilation by Ernst Haeckel (Radiolaria, 1862).

"Infinite game" as polyhedral Neti Neti: There is a curious sense in which encompassing meaning through mapping should preferably (if not necessarily) avoid closure. It is indeed a case of "not this, not that" (Neti Neti). It could be better understood as a play with patterns more appropriately "re-cognized" as a cognitive dance between different configurations -- whether complex or of the simplest kind, unpacked or packed. The insight of James Carse, mentioned above, suggests that this dance might itself be considered an "infinite game" (Finite and Infinite Games: a vision of life as play and possibility, 1986). Given its suggested similarities to romantic flirtation, the aesthetic role of poetry in reframing relationships through metaphor recalls the argument of Gregory Bateson:

One reason why poetry is important for finding out about the world is because in poetry a set of relationships get mapped onto a level of diversity in us that we don't ordinarily have access to. We bring it out in poetry. We can give to each other in poetry the access to a set of relationships in the other person and in the world that we are not usually conscious of in ourselves. So we need poetry as knowledge about the world and about ourselves, because of this mapping from complexity to complexity. (Cited by Mary Catherine Bateson, Our Own Metaphor, 1972, pp. 288-9)

Aside from some processes enabling morphing between proximate forms, missing is the capacity to transform between any polyhedral form through a finite number of steps -- to "translate" from one pattern of thinking to another. The possibility might even be framed by current studies of six degrees of separation -- with the implication that the seemingly "distant" ways of knowing, by which society is so divided, might be separated by no more than six transformations of some kind -- as possibly suggested by the six potential transformations of any hexagram. The process might be framed in terms of analogical steps, as could be implied by the arguments of Douglas Hofstadter and Emmanuel Sander (Surfaces and Essences: analogy as the fuel and fire of thinking, 2013), as a further development of Hofstadter's earlier work (Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995).

Whether current insights into the geometry and topology enable this, there is the emerging possibility that neural learning networks -- fed with the variety of polyhedra -- could detect transformational pathways between any two mappings, as suggested by the recent advances cited above with respect to the game of go (AlphaGo Zero: Google DeepMind supercomputer learns 3,000 years of human knowledge in 40 days, The Telegraph, 18 October 2017). This process is already envisaged for a future release of Stella4D -- but only for convex shapes (or radially convex shapes) of the same genus. The two models are placed on parallel hyperplanes in 4D, allowing a 4D convex hull to be created around both, so that sliding a slicing plane through the 4D shape makes it possible to see a morph from any convex 3D shape to another.

As noted, this might offer new ways of understanding both the subtlety of human relationships and the variety of forms of abuse.


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