Challenges to Comprehension Implied by the Logo
of Laetus in Praesens
Laetus in Praesens Alternative view of segmented documents via Kairos

5 August 2019 | Draft

Coping Capacity of Governance as Dangerously Questionable

Recognizing assumptions and unasked questions when facing crisis

-- / --

Exploring the unsaid
Indicators of coping inability of governance
Distinguishing between "being unable to cope" and "collapse"?
Defensive postures of "governance-as-usual"
Factors inhibiting collective recognition of the incapacity of governance
Recognizing the "underside": paradoxical challenge to achieving sustainable governance
Mystery of (re)production as a destabilizing challenge to governance
Imagining appropriate engagement with the coping incapacity of governance
Subtle dynamics of the Tao of governance: enhancing the binary?
Governance beyond the logical focus on true vs false?
Engaging opposition: cognitive "collapse" heralding a wider collapse?
Deprecation of potential correspondences: 16-fold patterns?
Reframing the pattern of logical choices through polyhedra
From disorderly "collapse" to orderly "renaissance"


Few have difficulty in recognizing that governance at the global, regional, national and local levels is variously stretched -- if not in a state of semi-permanent crisis. This can be reframed by some as an opportunity, whether for the advancement of particular interests -- or as presaging a necessary reformation, transformation, or revolution, as variously understood. The situation for many individuals in this context is especially problematic -- most obviously the young -- given the levels of insecurity and uncertainty, and the predictions of collapse.

The question here is whether the institutions of governance, and those attaching credibility to them, are capable of recognizing that there is every possibility that they are unable to cope. It could be argued that this has long been the case. Or it could be argued that this would only be the case in the event of a major crisis of crises in the future. The concern here is rather whether this is now the case and how this condition might be recognized.

Clearly those with a commitment to existing processes of governance have the strongest reasons to believe that they are "fit for purpose" and have every reason to make that claim -- even to the point of censuring those who argue the contrary, or marginalizing them in more radical ways. Such responses are characteristic of defensive responses by which other factors and factions can be framed as blameworthy. What are the hidden assumptions, and the questions that are kept "off the table" or under it, as considered previously (Global Strategic Implications of the "Unsaid", 2003)?

However, whether or not governance capacity is questionable, how can the possibility be addressed in a fruitful manner -- and with what expectation of outcome? Simply adopting a posture of determining inadequacy is itself inadequate to the challenge. It is difficult to claim that there are proven alternatives, despite many efforts to do so. Experiments to that end do not invite high orders of confidence.

The title has an appropriate degree of ambiguity in that the incapacity of governance to cope can now be considered ever more dangerous -- but raising any such question is also increasingly dangerous given the defensive reactions it evokes. Succinctly expressed: Can governments cope at this time -- and are they simply in denial with regard to their incapacity? More provocatively in that regard, and ironically so, is governance being "put to the question" by rising sea levels -- a "water cure" of global proportions?

A vital distinction can be made between "being unable to cope" and the "collapse" on which many commentators now focus. More attention is required to the intermediate condition, namely to the reality in which so many are obliged to live -- however surreal it is experienced to be. It may that be the case that its challenge to rationality offers insights of a necessarily unexpected and paradoxical nature, but susceptible to appreciation by intuition rather than deprecated as purely irrational.

In distinguishing the rational, on which so many socio-economic processes of production are based, from the irrationality associated with their problematic consequences, the concern is how such contradictions are embodied in the simplest forms of negligence which call for recognition in new ways.

Exploring the unsaid

There is no way -- "constitutionally" -- that any institution can call into question its own viability, or the appropriateness of its expertise. The difficulty is compounded by a need to respond appropriately to perspectives with a vested competitive interest in any such critique. There is therefore a case for attentive framing of any such assessment, variously including the following.

Undeclared assumptions: How can undeclared assumptions be highlighted? Typically strategic initiatives rely on the assertion of strategic goals, as exemplified by the United Nations Sustainable Development Goals, as successor to its Millennium Development Goals, and to Agenda 21. Such patterns of assertion provide no framework for clarification of the assumptions on which they have been elaborated -- especially when their emergence as strategies is a matter of political comprise which does not invite commentary, if not deliberately precluding it. The less said the better?

Is any checklist of such assumptions to be found? Or are any efforts at such articulation subject to early suppression in defence of the viability of strategies which have proven to be a major challenge to elaborate? Typically any effort to do so would be immediately framed as dysfunctionally "negative", especially when there is an increasingly desperate need to be "positive" (Barbara Ehrenreich, Smile Or Die: how positive thinking fooled America and the world, 2010). There is no place for what may be construed as implied criticism.

Curiously it may only be history which offers the perspective to detect the undeclared assumptions -- in the case of the above examples, the transition from the implied failures of Agenda 21 through those of the Millennium Development Goals -- possibly enabled by articulation of the 16-point Earth Charter. The unexamined assumptions of the Sustainable Development Goals have yet to acquire salience.

How do undeclared assumptions frame and determine, and to what degree, the strategies framed in terms of declared assumptions? If the declared assumptions are more explicitly based on acknowledged values, what values are ignored in establishing that framing?

Unasked questions: Any undeclared assumptions imply the existence of unasked questions, namely questions which are unacceptable in any formal setting, most obviously institutions of governance, the think tanks associated with academia, or the media (Strategic Implications of 12 Unasked Questions in Response to Disaster, 2013). The point can be argued in more detail (Tank Warfare Challenges for Global Governance: extending the "think tank" metaphor to include other cognitive modalities, 2019).

Of interest is then the contextual influence which inhibits the articulation of such questions -- effectively as being "a bad career move". Why is it left to bodies outside those associated with governance to ask "awkward" questions -- even "nasty questions"? Can the intelligence agencies afford to cultivate such a culture, thereby inhibiting their detection of weak signals -- purportedly cultivating the groupthink which inhibited anticipation of 9/11?

What might then be considered to be the unasked questions and how do they relate to the difficulty of engaging effectively with wicked problems? Again it might be asked how sidelined questions implicitly influence those that are "on the table".

Unsaid ("Non dit"): Underlying the unexplored assumptions and sidelined questions is the more general issue of the unsaid and the culture sustaining it. How many forms does this take, and who can be recognized as concerned with it (Global Strategic Implications of the "Unsaid", 2003). It could be said to be that which a culture or a civilization chooses to ignore -- possibly at its eventual peril. What can be said to have been ignored over the pas century in reaching a condition in which civilization is challenged for resources and a high percentage of species have been rendered extinct as a consequence of human activity?

Patterns of obfuscation: Clearly any attempt to recognize the above is subject to patterns of obfuscation. This is increasingly framed in terms of "fake news" (Varieties of Fake News and Misrepresentation, 2019). However there is every possibility that much of what is recognized as "fake news" is narrowly framed to exclude recognition of subtler forms.

Arguably, for example, there is every possibility that many of the claims of advertising, political manifestos and religion could be understood as constituting "patterns of obfuscation" -- if not "fake news".

Effectively excluded perspectives: The above all imply the exclusion of some perspectives through ignoring them or marginalizing them in some way. Thus science has a marked tendency to deprecate "pseudoscience" and religion. Religion has a marked tendency to deprecate many arguments and assumptions of science. The pattern is evident in business and the military. The alienated in society may deprecate any such perspectives.

The excluded perspectives may implicitly suppress recognition of dimensions of significance to many and to viable governance. The process of exclusion may well inhibit creativity, innovation and new thinking. Institutions of governance are not assiduous in recognizing new thinking, especially to the extent that it may respond to its inadequate coping capacity.

Vested interests and exploitation of the status quo: There is a strange sense in which strategies advocated as part of the governance process tend simply to ignore the capacity of vested interests, especially those of criminal intent, to exploit and undermine those strategies through detection of their loopholes. As a specialist in feedback loops, the management cybernetician Stafford Beer has succinctly made this point his adaptation of Le Chatelier's Principle:

Reformers, critics of institutions, consultants in innovation, people in short who "want to get something done", often fail to see this point. They cannot understand why their strictures, advice or demands do not result in effective change. They expect either to achieve a measure of success in their own terms or to be flung off the premises. But an ultra-stable system (like a social institution)... has no need to react in either of these ways. It specializes in equilibrial readjustment, which is to the observer a secret form of change requiring no actual alteration in the macro-systemic characteristics that he is trying to do something about. (Stafford Beer on Le Chatelier's Principle as applied to social systems: The Cybernetic Cytoblast - management itself. Chairman's Address to the International Cybernetic Congress, September 1969)

All these are suggestive of the possibilty that future historians will recognize the complicity of governments and their supporters of cultivating an unexplored and undiscussable "Big Lie" (Existential Challenge of Detecting Today's Big Lie: mysterious black hole conditioning global civilization? 2016).

Indicators of coping inability of governance

Coping capacity is most readily indicated through performance indicators. These focus on what has been achieved with the institutions and strategies in place. Any indication of less than desirable response can then be excused by other factors, such as lack of resources, the economic context, political will, etc. It is readily denied that these appropriately call into question the viability of those institutions or strategies -- provided corrective measures can be put in place.

More relevant however is that performance indicators offer no indication of the remedial capacity to address a strategic problem -- namely the effective capacity to alleviate the problem, and the time it is expected to take to do so (Remedial Capacity Indicators Versus Performance Indicators, 1981). Typically remedial capacity is framed by political promises and optimistic reporting, neither of which address the reality of the situation. Furthermore such optimism typically fails to take into account processes which are likely to undermine such achievement (Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009). In that sense performance indicators can be considered unrealistic, if not strategically naive.

The challenge to coping by governance can then be considered as variously indicated by such as the following:

Curiously the policy challenge is recognized to a degree by reference to the so-called wicked problems with which governance is faced, notably migration, climate change and terrorism (Counter-terror chief says policing alone cannot beat extremism. The Guardian, 6 August 2019). With the focus of governance on the ever-shorter term, there is ever-diminishing capacity to focus on the longer-term issues vital to the viability of society (Ungovernability of Sustainable Global Democracy? Towards engaging appropriately with time, 2011).

Distinguishing between " being unable to cope" and "collapse"?

The present time is witness to many informed predictions of financial collapse, ecological collapse, societal collapse, and civilizational collapse. Such predictions aside, there is an extensive investment in doom-mongering of various forms by opponents of current policies -- rendered widely credible to a degree by dystopian movies,

Most recently the threat of disaster has been framed in terms of the very high level of current risk of global nuclear conflict (Ernest J. Moniz and Sam Nunn, The Return of Doomsday: the new nuclear arms race -- and how Washington and Moscow can stop it, Foreign Affairs, 6 August 2019). The authors focus on "Getting Back to Jaw Jaw", namely achieving new dialogue on strategic stability. This could be considered extremely naive, given the remarkable lack of capacity for fruitful dialogue. It is appropriate to compare the investment in the progressive sophistication of weaponry with that in the development of potentially relevant methods of dialogue. The investment in the former is many orders of magnitude greater than that in the latter -- itself bedevilled by the questionable claims and behaviour of those proposing their skills in that arena.

There is a strong case for avoiding the conflation of "collapse" with "not being able to cope" -- a conflation which may well serve some interests in engendering a culture of fear and forms of collective blackmail. The question here is the nature of the domain between those two conditions. The distinction is far more clearly evident in the case of an individual faced with increasingly high orders of stress. For a person, "not being able to cope" is quite distinct from "collapse" -- although it may well precede it in time. The intermediary condition of "being susceptible to instability" may also be more clearly recognized in the case of an individual.

Failure of capacity? With respect to collectives, the condition of "not being able to cope" is framed by labels such as:

Self-destructive failure? Such distinctions may be qualified in terms

Questionable efforts may be made to deprecate any such condition in comparison with forms of governance upheld by some as orderly and appropriate, using such labels as "basket cases" and "shit hole countries". Is the controversial judgment of Donald Trump regarding "shithole countries" then to be welcomed for that reason (Ibram Kendi, The Day 'Shithole' Entered the Presidential Lexicon, The Atlantic, 13 January 2019)? Missing of course is his failure to acknowledge the primary source of planetary pollution (Earth as a Shithole Planet -- from a Universal Perspective? Understanding why there are no extraterrestrial visitors, 2018).

Although governance is upheld as appropriate and competent, the argument here is that there is a case for distinguishing the incapacity of forms of governance from overly simplistic anticipation, whether in the light of performance indicators or given the existence of some form of anarchic, gang or mob rule.

Disabling trends: between "not coping" and "collapse"? A set of 30 trends can together be usefully compared metaphorically to the spiral dynamic system typical of a cyclone, a hurricane or a tornado -- the latter being especially associated with natural disasters (Convergence of 30 Disabling Global Trends: mapping the social climate change engendering a perfect storm, 2012). Hence the sense in which "climate change" suggests reflection on a change of "social climate" -- and the "hurricanes" which may prove more destructive than the "winds of change" (cf. Climate Change as a Metaphor of Social Change: systemic implications of emissions, ozone, sunlight, greenhouse and overheating, 2008).

"Hurricane" has been frequently used by commentators of various persuasions as a metaphor to describe recent crises (Obama Compares Economic Crisis to a Hurricane, The Blaze, 10 July 2012; The European crisis: a hurricane for South Africa, Amandla! 22 July 2012; Avinash Dixit, The Cone of Uncertainty of the 21st Century's Economic Hurricane, 2012; Raymond Lotta, Financial Hurricane Batters World Capitalism: system failure and the need for revolution, Voice of the Revolutionary Communist Party, 19 October 2008).

Alternatively, switching metaphors, there is a sense in which humanity is being sucked into a form of black hole -- of which the global financial deficits are appropriately indicative as a public "confidence deficit". In information terms, this "black hole" would be such as to ensure a very high degree of disruption to the communication on which a global knowledge-based society depends. The situation might be compared to a "memetic singularity" as discussed separately (Emerging Memetic Singularity in the Global Knowledge Society, 2009). One effort to display the set of trends in this form is presented below. The trends are articulated separately in greater detail (Checklist of 30 disabling trends, 2012)

Representation of mutual reinforcement of a system of 30 disabling global trends
engendering together a hurricane-like vortex into which society is drawn
Mapping of 30 disabling global trends to form a vortex
Reproduced from Convergence of 30 Disabling Global Trends (2012)

These trends could be usefully compared to the barriers to remedial capacity previously discussed (Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009).

Defensive postures of "governance-as-usual"

The forms of governance that can be recognized as currently lacking the capacity to implement remedial strategies with any realistic degree of efficacy typically defend themselves with variants of the TINA slogan articulated by Margaret Thatcher: There Is No Alternative. The focus is therefore on heavy investment in the defensive pretence of coping adequately, despite indications to the contrary. Despite the vast resources deployed against what has been deprecated as a mob, the efforts of the international coalition in the War in Afghanistan against the Taliban are an indication of the current incapacity of governance. In optimistically implementing a new strategy, each new military commander has seemingly exhibited a total lack of capacity to learn from past experience (Transforming the Unsustainable Cost of General Education: strategic insights from Afghanistan, 2009).

Unfortunately those proposing alternatives are typically characterized by a total inability to agree on any alternative -- cultivating widespread consensus only with regard to being "against TINA" (however that is expressed). Echoes of this are to be found within the World Social Forum in its reaction to the World Economic Forum, or as is evident in left-wing criticism of right-wing strategies in countries such as the USA and the UK. This inability is also apparent in the limited capacity to demonstrate the viability, replicability and scalability of the alternatives proposed -- the focus being on uncritical optimisim.

More problematic still is the inability to analyze this condition -- other than through blaming external factors rather than allowing and encouraging any criticism of the dynamics between the alternatives so enthusiastically proposed (Collective Mea Culpa? You Must be Joking! Them is to blame, Not us! 2015). The motto: Physician, heal thyself comes to mind.

There is the further paradoxical difficulty that any "analysis", whatever the model or the group undertaking it, is necessarily suspect in terms of the bias it may be perceived to represent. Any assumption of neutrality and independence would itself be called into question and be vulnerable to criticism -- whether by the informed, the variously biased, or the inadequately informed. This paradoxical issue of methodology merits careful consideration. It could be argued that those who do not understand how they are part of the current problem of governance are fundamentally unable to comprehend the nature of the solution required. Aspects of this argument are forcefully articulated by Nassim Nicholas Taleb (Skin in the Game: hidden asymmetries in daily life, 2018).

The pre-collapse situation lends itself to the question: what is the methodological framework capable of containing the psychosocial dynamics able to call that methodology into question? How can governance itself be appropriately "put to the question" -- recalling a term from the Inquisition?

Factors inhibiting collective recognition of the incapacity of governance

A previous exercise (Mapping paralyzing factors, 2011) endeavoured to configure factors such as the above in systemic terms as follows (Mapping Paralysis and Tokenism in the Face of Potential Global Disaster: why nobody is about to do anything effective and what one might do about it, 2011).

Mapping paralyzing factors [see enlarged version]
Mapping paralyzing factors in the Face of Potential Global Disaster

The factors in the above map suggested recognition of the following clusters (articulated into sub-categories in the previous exercise).

Summary of clustering of paralyzing factors
1. ineffectual injunction
(consensus delusion)
4. unconsciously awaiting disaster
(non-decision making)

7. complicit indifference
withholding assistance

10. blame game
(fault of another)
2. assumption of authority
by the ineffectual
5. beyond human control
(crisis victim mentality)
8. inadequate attention time
(too busy)
11. palliative initiatives
3. ineffectual asystemic dialogue
6. cognitive benumbing
(never saw it coming)
9. indulgence in distraction displacement activity 12. opportunistic exploitation of hubris (manipulative divide and rule)

Such factors can be reframed and explored otherwise in terms of:

Exploration of global configurations of global collapse

If collapse is to be recognized as a global phenomenon, there is every case for configuring the features of it through appropriately "global" representations. How indeed can people be expected to get their heads "around it" otherwise? Or is its global nature to be rejected according to some "Flat Earth" arguments, as some prefer to argue? This is most obvious in the case of Thomas L. Friedman (The World Is Flat, 2005) -- as separately reviewed (Irresponsible Dependence on a Flat Earth Mentality -- in response to global governance challenges, 2008). As with the traditional fear of the unnown at the edge of the map, is it indeed a case of marking the boundary with "here be dragons" -- especially given the cyclic challenge of the Ouroboros (Complementary visual patterns: Ouroboros, Möbius strip, Klein bottle, 2017).

Flat Earth perpective: Here Be Dragons over the edge ?
Flat Earth surrounded by Ouroboros United Nations Emblem

Such criticism aside, there is a case for recognizing that very few in the world have the skills to prove that the Earth is indeed round, and it is indeed the case that most can happily assume that it is flat -- rendering comprehensible the renewed enthusiasm for a Flat Earth perspective. This is presumably reinforced by the skillful demonstration of behavioural scientist Nick Chater, drawing on new research in neuroscience, behavioural psychology and perception (The Mind is Flat, 2018).

If a global representation of collapse merits exploration, then a remarkable range of options can be considered, as discussed previously (Mind Map of Global Civilizational Collapse: why nothing is happening in response to global challenges, 2011). This distinguished:

Two-D projection: Exemplifying the nature of cognitive flatland
Three-D projection: Global configuration of incompatible uprightness
Three-D projection: Embodying disintegrative dynamics as fundamental to integrative design
Enabling comprehensible global configuration of concept maps
Global configuration of insights from "flat-pack" conventional system mapping

The following are thumbnail (screen shots) from that exploration. The first image being typical of efforts at circular configuration -- prior to enhancement by a spiral presentation (as indicated above). The remainder are exercises in the mapping of collapsing trends onto polyhedra in 3D (in virtual reality displays), with others considering the projection of 4D displays into 3D. They raise the question of how complex can such a display usefully be -- in order to evoke interest in the configuration of collapse. Do such images avoid the challenge to comprehension in some fundamental way -- as explored further below?

Screen shots of experimental mappings in 3D of a global configuration of collapse
Mind map of global civilizational collapse Polyhedral map of civilizational collapse 1 Polyhedral map of civilizational collapse 2 Polyhedral map of civilizational collapse 3
Polyhedral map of civilizational collapse 4 Polyhedral map of civilizational collapse 5 Polyhedral map of civilizational collapse 6 Polyhedral map of civilizational collapse 7
Polyhedral map of civilizational collapse 8 Polyhedral map of civilizational collapse 9 Polyhedral map of civilizational collapse 10  
Prepared using Stella Polyhedron Navigator

Recognizing the "underside": paradoxical challenge to achieving sustainable governance

To whatever degree a Flat Earth invites credibility, as suggested above, of potential interest is its "underside". This is also evident in issues with regard to the "other side" of the world -- considered as a globe. Especially significant is that factual assertions vigorously made at the same time as to whether it is "daytime" or it is "night" are then challenged from the perspective of each.

This paradox, deriving from inhabiting the surface of a global form, can be understood as highly symbolic of assertions vigorously made as to what is "right" and what is "wrong". Do those on a political spectrum have any concept of the global form which may effectively distribute their contrasting perspectives as to what is "right"? If not a globe or flat, what is the "shape of society" imagined to be by many of its members, even by the most enlightened?

Such issues and others justify a degree of recognition of some form of collective unconsciousness, necessarily elusive in the light of any "Flat Earth" assumption (John Ralston Saul, The Unconscious Civilization, 1995; Carl Jung, Archetypes and the Collective Unconscious, 1959). This may be readily dismissed as myth, as argued by Nick Chater (The Mind is Flat : the remarkable shallowness of the improvising brain, 2018). As the realm of the irrational, its distinction from the rationality of flatness can also be argued, as by Justin Smith (Irrationality: a history of the dark side of reason, 2019).

Mapping irrationality: Previous exercises in visually acknowledging this "a-rational" and problematic dimension were argued in the following (corresponding images below):

Global Underground Map Nine Remedial Capacity Boundaries Interrelating problematique,
resolutique, "imaginatique" and "irresolutique"
Nine Remedial Capacity Boundaries Problematique / Resolutique / Imaginatique / Irresolutique

Number-based cognitive constraints: It could seem strange to use "numbers" to frame the challenge of global civilization. The obvious arguments for doing so may no longer have adequate traction. Little can be said about the consequences of increasing population numbers that has not already been said. Much the same could be said for most of the quantitative criteria of the UN's Sustainable Development Goals. Such numbers, however seemingly critical to the survival of many, no longer carry real meaning on a global scale. This is becoming increasingly apparent with respect to resource use, emissions, environmental degradation, and waste disposal. Clarification of this is presented separately (Comprehension of Numbers Challenging Global Civilization, 2014), with respect to the following:

Enabling disaster through basic mathematical operations
Numbers in play in psychosocial organization
Conceptual clustering and cognitive constraints
Pattern memorability between symbolic mystification and "stretching"
Imaginative depiction of the cognitive challenge
Requisite complexification of imagery to embody greater significance
Creative pretence dissociating numbers from sexuality
Significance of "encompassing" the numbers required for meaningful governance

Root cause detection: It is curious to note the degree of avoidance in governance with regard to the identification of the root cause of any challenging issue -- however eminent the authorities investigating the matter, and whatever the requirement to do so. The focus is typically on secondary or derivative issues (Vigorous Application of Derivative Thinking to Derivative Problems, 2013). By contrast, in science and engineering, root cause analysis (RCA) is a method of problem solving used for identifying the root causes of faults or problems. As argued separately, this methodology is seemingly not employed with respect to the more challenging preoccupations of governance (Radical quest: getting to the root of a problem?; Radical identification of the root cause of terrorism; Failure of radical analysis of root causes, 2015).

This phenomenon can be explored in terms of question avoidance (Question Avoidance, Evasion, Aversion and Phobia -- why we are unable to escape from traps, 2006). A focus to this phenomenon can be considered in various domains:

Opposition and anti-otherness: In the light of ongoing sociopolitical controversies, a questionable argument can be made for Elaborating a Declaration on Combating Anti-otherness, (2018). This was explored in relation to:

Anti-otherness, anti-alterity, anti-diversity and anti-consensus?
Disputatious otherness and negative capability?
Oppositional logic?
Requirement for a paradoxical "anti-language"?
Hyperreality and anti-otherness?
Transformable architecture of future cognitive pantheons?
Confusion of otherness through cognitive bias
Periodic engendering of distinctive otherness

The logic of opposition is the subject of extensive studies, as indicated below and separately (Oppositional Logic as Comprehensible Key to Sustainable Democracy: configuring patterns of anti-otherness, 2018). Curiously the relevance of those studies to governance has seemingly yet to be explored -- despite the dramatically divisive effects of "opposition" and disagreement.

Political "hot potatoes": There are a number of issues which are so sensitive that it is virtually impossible to ensure rational discussion of them, despite their importance for global governance.

These include issues of divinely mandated right (as in the case of the initiatives of the government of Israel in relation to Palestine) and that of unconstrained population growth, most notably with respect to resources and the future implications for migration (Overpopulation Debate as a Psychosocial Hazard: development of safety guidelines from handling other hazardous materials, 2009; Global Compact Enabling Complicity in the Ultimate Crime against Humanity: institutionalizing global myopia in anticipation of excessive population growth, 2018).

Fundamental contradictions regarding the value of human life: Following from the previous point, it is extraordinary to note the level of controversy with regard to euthanasia, capital punishment, abortion, and the like -- in comparison with the casual attitude to the death of hundreds, if not thousands, through natural disasters and deliberate killing (with its associated collateral damage). The latter is given a degree of spurious legitimacy through just war theory -- now effectively extended to "just torture theory". In the first case the value of human life is held to be inestimable (and beyond dispute), in the latter case it is held to be negligible -- in comparison with other priorities (whether economic or political). The situation could be compared to the earlier role of the "gold standard" -- with the manner of its abandonment now to be foreseen.

Irrationality: According to Justin Smith (Irrationality: a history of the dark side of reason, 2019):

Irrationality is not, generally, simple ignorance. If you do not have the relevant information, then you cannot rightly be faulted for not making the correct inferences. Irrationality must rather be, some sort of failure to process in the best way information one does already have. It is, however, difficult to say, often, whether a given failure results from innocently not knowing, or rather from culpable failure to being into play what one does know (p. 265)

Irrationality, we have seen, is often inadequately treated as if it were merely an intellectual failure: a failure to frame the right inferences from known facts. If this were all it is, it would not be terribly interesting. People would make inferential mistakes, and if they were to verbalize these mistakes, others would kindly correct them, and that would be that. Things get more complicated when we consider irrationality as a complex of judgment and action. In fact, when we turn our attention to action, we see that much of what is commonly deemed irrational is not based on incorrect inferences at all, is not so much a failure to know what we know, as it is on a failure to want what we want. (p. 273)

Irrationality is ineliminable.... The problem is a serious one. It is not just that we are not doing things quite right. Rather, we sense that if we were exclusively to do things that are good for us, his would in itself not be good for us.... The thesis of this book -- that irrationality is as potentially harmful as it is humanly ineradicable, and that efforts to eradicate it are themselves supremely irrational -- if far from new... The dual case, however, against mythologizing the past, and against delusions about our ability to impose a rational order on our future, always benefits from being made afresh, as evidently what has been perfectly obvious for a few millennia nonetheless keeps slipping back into the vast category of things we know but do not now. (p. 287).

Cognitive "glass ceiling"? As discussed separately (Cognitive glass ceiling, 2008), The metaphor of the "glass ceiling" has been widely used with regard to the barrier to women (or those of other races) acceding to executive positions of responsibility. It may be fruitful to explore such a metaphor with respect to the barrier to effective action on scenarios, namely as the cognitive barrier to shifting from intellectual consideration of scenarios into the alternative behaviours for which the preferred scenario calls, namely the cognitive barrier to behaviour change -- notably amongst those who call for it.

Whether ceiling, window or glasshouse, the question is how one pattern of behaviour is contained by it such as to inhibit effective engagement with an external pattern considered desirable. How does "cognitive glazing" work so effectively? The metaphor might even be pushed further to inquire about the effectiveness of "cognitive double-glazing", or even "triple-glazing" and "security" glass -- and the possible insulation they offer against unwelcome effects on any "double bottom line" and "triple bottom line".

Mystery of (re)production as a destabilizing challenge to governance

It could be said that insufficient is known about what drives humanity to produce or reproduce -- whenever and however possible -- given the cumulative destabilizing consequences for governance. Presumably there is still scope for the future to make discoveries in this respect -- rather than assuming that reality could be fully defined by classical mechanics, as was the assumption that prevailed in academia just over a century ago -- prior to publication of the seminal paper by Albert Einstein on the theory of relativity. Civilization and its governance now await appropriate consideration of the seminal work by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015).

Production? The paradox framed above can be explored in terms of "production" variously understood, and the associated implications regarding "consumption".

In that light, are there other ways to imagine the "gross domestic product" which societies strive so desperately to increase -- as can be speculatively discussed (Evaluating the Grossness of Gross Domestic Product: Refugees Per Kiloton (RPK) as a missing indicator? 2016).

It is strange that "intercourse" is used to describe both the process of social interaction and that which results in children. There is also a more extended understanding in relation to the environment ("Human Intercourse": "Intercourse with Nature" and "Intercourse with the Other", 2007). This extended sense -- in including intercourse with the other -- is clearly problematic in the face of the variety of forms of mutual hostility which are a challenge to governance, a discussed separately (Elaborating a Declaration on Combating Anti-otherness, 2018).

From the perspective of governance, can it be said in the most general terms that civilization is faced with a challenge of "overproduction" -- whilst at the same time being variously dependent and addicted to that production? Using rabbits as a metaphor, can this unconstrained impulse to produce be compared to what is called into question by the phrase "breeding like rabbits"? Is there an unexplored desperation to doing so -- a form of panic?

From a manufacturing perspective, this focus would be framed and evaluated as the production of "units". The evaluation is evident in attentive concern with impact assessment, citations, patents, goals, and the like. Emphasis on "impact" can be understood in terms of "making a mark" -- even one to be appreciated by history. A comparison might be made between the "bullets" produced by the arms industry and the "bullet points" characteristic of any presentation. Given their relation to "scoring" as a metaphor, this could include production of semen. Is the gesture in discarding cigarette butts (and the like) then to be compared with casting seeds on stony ground (Parable of the Sower) ?

Reproduction? More curious is reference to "re-production" in contrast with "production". What is it that may need to be reproduced -- and even desperately so? Is there a mysterious generic commonality to such as the following:

There is clearly a sense in which people have considerable commitment to reproducing their own particular qualities through their children -- ensuring a legacy, possibly interpreted in terms of a bloodline. This commitment may be understood as a desire to be "remembered" -- mysteriously "reconstituted" (if not reproduced) by subsequent generations. Aspects of this understanding are evident in the process of seeing oneself mirrored in some way by one's children.

The underlying psychology of these processes clearly merits a higher degree of attention than its manifestation in the current preoccupation of governance with "productivity" and "growth". With respect to any incapacity to cope in the governance process, these dimensions -- and the identification with them -- contribute to any inability to change and to the sense of paralysis. How is "governance" then to be related to any comprehension of "self-governance"?

The question might then be asked as to who is effectively paralyzed? What is the self-reproducing identity which is unable to change? How are the dynamics of that self-reproduction so mistakenly projected into what then takes the form of problematic conditions?

Is the situation indeed to be compared to that of rabbits frozen in the headlights of an oncoming vehicle on a highway at night, as discussed separately (Learning from the anthropomorphisation of rabbits in children's tales, 2019)? What is the oncoming vehicle of that metaphor -- the sense of imminent collapse?

Imagining appropriate engagement with the coping incapacity of governance

Patterns of interference: The representation above of cyclone of spiralling trends towards collapse raises the question as to whether there is a corresponding means of configuring the trends to facilitate the quest for a remedial dynamic -- especially given the sense in which they would appear to be dysfunctionally "divergent", rather than "convergent" as those above. The spiral could be "reversed" to suggest an "anti-cyclone" -- or possibly even a "white hole" (cf. Peter Russell, The White Hole in Time: our future evolution and the meaning of Now, 1993). This would then reflect the sense of both a "negative" ("black") hole to be escaped as problematic and a "positive" ("white) hole as a desirable goal -- the resolution of humanity's challenges. The reversed image might then be presented as follows with the trend labels suggestively reframed to reflect this (as reproduced from Spiraling trends: cyclones in a climate of change? 2012).

Representation of mutual reinforcement of a system of 30 enabling global trends
engendering together an escape from the problematic convergence of the image above
Mapping of 30 global trends to escape from a vortex

Simply confronting converging and diverging spirals is clearly inadequate in terms of any recognition of the psychosocial implication in the associated processes. As discussed with respect to Interweaving "cyclones" and "anti-cyclones" in a global system (2012), another representation could exploit the interference patterns when the two spiral patterns are superimposed -- whether as in wave propagation or in Moiré patterns. These then offer insights into both the perceptual/cognitive challenges and their potential strategic implications. As cyclones this relates to the natural phenomenon whereby two hurricanes may combine in some way (Two Hurricanes Colliding: can hurricanes merge and become one big hurricane?).

Animations highlighting interference patterns in the encounter between two spirals
"Black hole" superimposing on "White hole"
(spirals in same direction)
"White hole" superimposing on "Black hole"
(spirals in opposite directions)
Animation: Black hole superimposing on White hole Animation: White hole superimposing on Black hole

Other interference patterns are evident from the following, suggesting the value of distinguishing the  ways in which sets of "disruptive" and "remedial" trends may interact -- or be perceived to interact -- in the light of systemic insights from global weather patterns across both hemispheres.

Interference patterns between co-centric rotating spirals
("white" superimposed on "black")
Interference patterns between one spiral orbiting another
(reminiscent of the Fujiwara interaction between cyclones)
Interference patterns between co-centric rotating spirals Interference patterns between one spiral orbiting another

Other experimental animations of the two alternative spirals were included in the earlier discussion as a trigger to more imaginative reflection -- as would be offered by their representation in 3D.

From a 2D "round table" to a 3D "global table": The spirals above could be understood as reflective of the dynamics of conventional round tables -- perhaps 12-fold rather than 30-fold -- with their convergent and divergent processes. Such dynamics can be imagined as holding forms of implosion and collapse, or the contrary process of explosive divergence -- both being reflective of processes on a global and a cosmic scale (Psychosocial Learnings from the Spiral Form of Hurricanes: implications of the triple helix and the 3-fold triskelion as "cognitive cyclones"? 2017).

Missing from such arguments, reflective of higher dimensionality, is the nature of the engagement of participants -- as embodied rather than as attributed to external "personifications" (archetypes, deities, etc). As discussed separately (Global table: enabling comprehension, credibility, communicability and memorability, 2019), the nature of this engagement is clarified by:

The engagement between those at a 12-fold "global table" could be understood in terms of the proprioceptive dialogue deriving from the work of David Bohm and cultivated by Steven Rosen. This implies a degree of radical honesty most apparent between participants with "skin in the game" -- namely dialoguing under conditions of risk rather than from within a comfort zone.

From engagement to implication: The challenge would then appear to be how to represent the nature of cognitive implication in the paradoxical conditions in which humanity finds itself. It is unfortunately noteworthy that, despite the widely appreciated originality of the study by Alexander Wendt (2015) that it contains no visual clues to the comprehension characteristic of quantum mind and the issues it raises for comprehension. Those concern with quantum reality and any higher order of dimensionality consider themselves totally unconstrained by the challenges of communication -- other than through the mathematical expressions they consider to be totally adequate -- a framing which it is the responsibility of others to find credible.

The same could be said of the innovative framing offered with respect to autopoiesis by Humberto Maturana and Francisco Varela (1980). Autopoiesis and Cognition: The Realization of the Living (2nd ed.). Understood as self-creation (or production), this refers to a system capable of reproducing and maintaining itself -- a concept since applied in the fields of cognition, systems theory and sociology. Specifically:.

"Cognitive twist"? Despite the relevance to associated preoccupations with the insights of social constructionism and enactivism, the essential cognitive paradox (or "cognitive twist") is lost or set aside through the manner in which it autopoiesis is explained.

The question could then be understood as finding a means of expressing any such paradoxical "cognitive twist" in visual terms to enable comprehension by those who think otherwise than through mathematical equations -- with mathematicians seemingly indifferent to how such matters might be more widely understood. Valuable indicators in this regard are provided with respect to the Möbius strip and the Klein bottle by Steven Rosen (Science, Paradox, and the Moebius Principle: the evolution of a "transcultural" approach to wholeness, 1994; How Can We Signify Being? Semiotics and Topological Self-Signification, Cosmos and History: Journal of Natural and Social Philosophy, 10, 2014).

In strategic terms, the challenge of navigating the adaptive cycle may be fruitfully considered in the light of the Mobius strip. The following animations offer further clues, as discussed separately (Visualization in 3D of Dynamics of Toroidal Helical Coils: in quest of optimum designs for a Concordian Mandala, 2016).

Torus-to-Sphere transformation Animation of Lissajous curve
on horn torus
Tesseract animation
simulating requisite 4-dimensionality?
Animation of Lissajous curve  on horn torus Tesseract animation
Made by User:Kieff Reproduced, with permission, from Wolfgang Daeumler (Horn Torus) by Jason Hise [CC0], via Wikimedia Commons

The spirals presented above may indeed be reframed in terms of spiralling helical coils. Intriguing as been the receptivity in the recent period of the need to "go down the rabbit hole" (What the Bleep! Down the Rabbit Hole,). This has implications for recognition of an underworld or an underside to be understood in quite different terms. The animations above are indicative of the kinds of cognitive transformation that may be called for. That in the centre is especially valuable in indicating a pathway "down the rabbit hole". That metaphor also recalls imaginative reflection on traversing the black holes of astrophysics. a metaphor which has been curiously given credibility (as with hurricane) in relation to financial collapse (Mark Hendrickson, The Black Hole Of Debt, Forbes, 12 February 2016; John Ainger, The Black Hole Engulfing the World's Bond Markets, Bloomberg, 13 July 2019). How is governance to be imagined as navigating a black hole -- given the radical distortion of parameters associated with that metaphor?

The animations on the right and left above are suggestive of forms of inversion of potential significance. They are indicative of ways of reflecting on the transition between binary extremes, whether in politics, between rationality and irrationality, or between inside and outside.

The 4D tesseract is currently of fundamental relevance in consideration of logical geometry -- but with little consideration (if any) of its cognitive implications, as otherwise understood. That on the right, with its transformation between a conventional "global" form and a toroidal form calls for careful consideration in relation to how global ciilization might be imagined -- perhaps as alternating between such forms. If it is appropriate to recall that one hypothesis for the shape of the universe is a torus, might the "shape of society" be other than "global"? However it is the phases of the inversion which are a fundamental challenge, as in visualization of the seemingly improbble process of inversion of a sphere or inversion of a cube ***.

Subtle dynamics of the Tao of governance: enhancing the binary?

Given the coherence purportedly associated with the symbol of the Tao, and the symbolic meaning variously attatched to it, one exercise to be considered is how any process of collapse (and emergence) might be related to it -- and how that might be understood with respect to coherent governance in circmstnaces susceptble to catastrophe of some form.

Interrelating collapse and remedial emergence: In the following animations the spirals above are "mapped" as dynamic, cyclone-like processes onto that form -- assuming that they travel across that form, as typically represented in 2D. The "eyes" of the form are understood as the focus of a "black hole" and a "white hole", as indicated above, namely implying a shift into a different dimensionality. The remedial spiral (from above) is presented in white, but the problematic spiral remains in black.

Several options can be chosen (as assumptions) for the exercise, primarily in terms of the handedness of the spirals and the direction of the arrows. Two animations are presented for discussion below. They invite criticism of what may be inappropriate ("wrong") with one or both.

Alternative animations of cyclones on the Tao symbol (for discussion)

For purposes of discussion, it could be concluded that the movement of the black spiral in the animation on the left is appropriate, but that of the white spiral is more questionable. In the case of the animation on the right, it is the handedness of the white spiral which could be considered questionable.

Tao symbol in 3D: provocatively framed? Given the importance of the Tao symbol as an indication of the possibility of transcending binary (yin-yang) thinking, the argument merits further development in the light of a previous exercise with respect to 3D representation -- on the assumption that the symbol calls for consideation in terms of higher dimensionality (Exploring Representation of the Tao in 3D: virtual reality clues to reconciling radical differences, global and otherwise? 2019). The latter includes a varety of images and animations in that respect.

With regard to the argument above, one provocative approach is to consider how the polyhedral forms employed in the extensively developed litrature on logical geometry might be presented in relation to a 3D representation of the Tao symbol. An important key to the significance for governance of hyperdimensionality is that work on logical geometry. This notably featured in the presentations at the IV International Congress on: The Square of Opposition -- Vatican City, 2014, compiled by Jean-Yves Béziau and Gianfranco Basti (The Square of Opposition: a cornerstone of thought, 2017):. This constitutes a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition), ranging from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.

Of particular relevance, beyond the Aristotelian square of opposition is its relationship to the rhombic dodecahedron featuring in Hasse diagrams -- both involving discussion of the hypercube, as featured in the work of Lorenz Demey and Hans Smessaert (The Relationship between Aristotelian and Hasse Diagrams, 2014; Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation, Symmetry, 9, 2017, 204; Geometric and Cognitive Differences between Logical Diagrams for the Boolean Algebra B4) and by Hans Smessaert (On the 3D Visualisation of Logical Relations, Logica Universalis, 3, 2009, 2).

Arguably if there is one characteristic of psychosocial reality which is a fundamental challenge to governance it is that of "oppositon" and the framework within which it can be appropriately integrated. The argument for doing so is that literature is particularly focused on the geometrical representation of opposition as articulated in truth tables through the set of Boolean connectives. A key polyhedron used to map the 16 (-2) Boolean logical connectives in that approach is the rhombic dodecahedron of 14 vertices and 12 faces.

16 logical connectives ordered in a Hasse diagram
Nodes on the right are connected like vertices of a 4 dimensional cube
with light blue edges forming a rhombic dodecahedron 
"Framing" 3D Tao symbol with logical connectives
Animation of framing with a
rhombic dodecahedron (experimental)
Contingent bitstrings Equivalent Venn diagrams Circular orientation Vertical orientation
Rhombic dodecahedron with contingent bitstrings Logical formulas and equivalent Venn diagrams
Adapted from Lorenz Demey and Hans Smessaert (2017) Reproduced from Wikipedia
Logical connectives Hasse diagram
Adaptation of 3D Tao model by Sergey Bederov at Cortona3D, as discussed in
Exploring Representation of the Tao in 3D (2019)

A case for consideration of Daoist thinking is made in the compilation of papers from the above-mentioned Vatican conference through the valuable commentary from a structural perspective by Fabien Schang (An Arithmetization of Logical Oppositions, 2017):

... just as Descartes made a connection between geometry and arithmetic through analytic geometry, the present paper relies upon the fact that there are blatant analogies between the abstract areas of geometry, logic, and arithmetic. There also exists a form of serendipity in this paper, since the final result is derived from a completely different domain area of discourse – the Chinese Book of Changes (or Yiking). There is, fairly obviously, no causal or logical connection between the latter and logical oppositions, however, a comparison of both domains leads to a fruitful explanation thanks to an analogy between elements of their common structure. [emphasis added]

Framing the Tao (or yin-yang) symbol within a framework of logical connectives is not completely unreasonable in the light of the role of Taijitu in Chinese thinking, as it might be understood from a corresponding perspective. This is clarified to some degree by the following insert and its reference to the 5-fold Wu Xing pattern, discussed further below and separately (Five-fold cognitive dynamics of relevance to governance? 2015; Memorable dynamics of living and dying: Hygeia and Wu Xing, 2014; Beyond dispute in 5-dimensional space: Pentagramma Mirificum? 2015; Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012).

(Reproduced from Wikipedia)
Ming-era Daoist Taijitu

The taijitu consists of five parts. Strictly speaking, the "yin and yang symbol", itself popularly called taijitu, represents the second of these five parts of the diagram.

  • At the top, an empty circle depicts the absolute (Wuji)
  • A second circle represents the Taiji as harboring Dualism, yin and yang, represented by filling the circle in a black-and-white pattern. In some diagrams, there is a smaller empty circle at the center of this, representing Emptiness as the foundation of duality.
  • Below this second circle is a five-part diagram representing the Five Agents (Wu Xing), representing a further stage in the differentiation of Unity into Multiplicity. The Five Agents are connected by lines indicating their proper sequence:
    Wood ? Fire ? Earth ? Metal ? Water.
  • The circle below the Five Agents represents the conjunction of Heaven and Earth, which in turn gives rise to the "ten thousand things". This stage is also represented by the Eight Trigrams (Bagua).
  • The final circle represents the state of multiplicity, glossed "The ten thousand things are born by transformation"

Governance beyond the logical focus on true vs false?

As implied above, there is a curious sense in which the intellectual commitement to the dramatic implications of opposition is unfortunately limited to clarification of the relatively complex patterns of true and false as evident in truth tables and logical connectives. In the "post-truth" condition of a surreal society, there is a case for exploring the form "post-truth tables" might take (Surreal nature of current global governance as experienced, 2016;  Towards articulation of a "post-truth table"? 2016).

Given the clue offered by "fake news", there is therefore a case for exploring whether the clarification offered by the logical pattern of truth tables does not apply equally to synonyms of truth which may be held to correspond to a greater degree to the reality of opposition and disagreement as experienced.

  Synonyms By extension?
true accuracy, authenticity, axiomatic, certainty, fact, legitimacy, principle, truthfulness, validity, veracity agree, good, like, relevant, guilty
false bogus. deceitful, dishonest, distorted, erroneous, fake, fanciful, faulty, fictitious, fraudulent, improper, inaccurate, incorrect, invalid, misleading, mistaken phony specious spurious unfounded, unreal, wrong absurd, bad, disagree, dislike, irrelevant, ridiculous, not-guilty

What additional clarity to "like"-vs-"dislike", or to "agree"-vs-"disagree", might then be achieved by adaptation of the Hasse diagram (above) and the configuration on the rhombic dodecahedron?

Confusion of insights from logic: It is extraordinary to discover the rich set of insights which are the proccupations of logic, and its implications for the operation of computer search engines and artificial intelligence. It could easily be asserted that there is a fundamental disconnect from daily language, itself both more fluid and more ambiguously confused. There is little wonder that society has edged into deep immersion in fake news with little capacity of logic to facilitate greater collective comprehension -- and with little expectation that strategic discourse in policy-making arenas will call for greater clarity. To the extent that a written record is kept, there is little motivation that arguments should be reviewed in the light of such insights -- as by discourse analysis.

Whilst it is indeed the case that there is formal recognition from a logical perspective of 16 logical connectives, it is remarkable to discover that this set of 16 is variously reduced in the light of arguments indicating that this or that set of connectives is unnecessary in practice -- as being trivial or redundant. Arguments for reduction of the 16 include:

The argument leads to the conclusion that 5 connectives would be adequate, and even one of those is superfluous (see Selection of Logical Connectives, Philosophy Stack Exchange; Maarten van Wijk, Logical Connectives in Natural Language -- a cultural-evolutionary approach, 2006; Rowan Patricia Garnier, Understanding Logical Connectives: a comparative study of language influence, 1992) . Further argument can reduce the connectives to two -- and even to one, understood as the Sheffer Stroke. The argument for five is to achieve a "balance between efficiency and parsimony" -- as may be convenient under certain circumstances, or a matter of personal preference.

The confusion is all the greater as a consequence of alternative terminology for the 16 distinctions, including distinctive notations. Greater clarity is evident from the binary notation with which the 16 can be associated, as indicated in the following table. Also confusing is the tendency of papers to avoid offering examples of what each distinction implies in terms of natural language. Hence the following composite table:

Connective Symbol Binary form Logical gate Typical words
negation "¬"   NOT it is false that it is not the case that / not, not that
material nonimplication "?"   NIMPLY but not
contradiction   0 0 0 0   FALSE
conjunction "?" 0 0 0 1 AND although / and / and then / and then within / but / even though / furthermore / however
nonimplication   0 0 1 0    
left projection   0 0 1 1    
converse nonimplication "?" 0 1 0 0   not...but
right projection   0 1 0 1    
exclusive disjunction "?" 0 1 1 0 XOR either, but not both / either...or
inclusive disjunction "?" 0 1 1 1 OR or
joint denial / nondisjunction "?" 1 0 0 0 NOR neither...nor
biconditional / equivalence "?" 1 0 0 1 XNOR if and only if / just in case / that is to say
right complementation   1 0 1 0    
converse implication "?" 1 0 1 1   ...if / is implied by / without...there is no
left complementation   1 1 0 0    
material implication "?" 1 1 0 1 IMPLY if...then / implies / no...without / so / therefore
alternative denial / nonconjunction "?" 1 1 1 0 NAND not both
affirmation   1 1 1 1   TRUE

The mapping onto the rhombic dodecahedron (RDH), as indicated above, can then be extended as indicated (tentatively) below. Of some interest is the manner in which the reduction of 16 to 14 is achieved for the purpose of this mapping, since this tends to be described in language that is less than obvious to the uninitiated. This is notably framed in terms of tautology and antilogy -- but potentially to be challenged as a "fudge", even if appropriate under the circumstances. That polyhedron can be used both as a Hasse diagram and as as Aristotelian diagram:

... there exists a deep connection between these two types of diagrams. On a visual-cognitive level, we argue that their dissimilarities can perfectly be explained in terms of general principles of diagram design and information visualization. Next, on a more abstract geometrical level, we show that if we restrict ourselves to Boolean closed diagrams, Aristotelian and Hasse diagrams can be seen as different vertex-first projections of one and the same hypercube (whether the resulting diagram is Aristotelian or Hasse depends on the projection axis). (Demey and Smessaert, The Relationship between Aristotelian nd Hasse Diagrams)

...both can be seen as vertex-first parallel projections of a 4D hypercube, but along different projection axes. The Hasse RDH results from using the axis defined by the hypercube's vertices for the bitstrings 1001 and 0110, whereas the Aristotelian RDH results from using the axis defined by the vertices for 0000 and 1111. As a consequence, the 2 non-contingent bitstrings 0000 and 1111 coincide in the centre of the Aristotelian RDH... whereas the 14 contingent bitstrings end up at its vertices.... This is the geometric motivation for the diagrammatic convention that Aristotelian diagrams only represent contingent bitstrings. (Demey and Smessaert, Geometric and Cognitive Differences between Logical Diagrams)

...the rhombic dodecahedron... can be seen as the vertex-first parallel projection of a tesseract along the projection axis defined by (the vertices corresponding to) the bitstrings 1001 and 0110, because those are precisely the two bitstrings that end up in the center of polyhedron, rather than on its exterior surface. Actually, in order to avoid that 1001 and 0110 entirely coincide with each other in the center of the polyhedron, a slight distortion in the projection axis has been introduced; this procedure is standard... and the Hasse rhombic dodecahedron can therefore be said to be a 'quasi-vertex-first projection' of a tesseract (Demey and Smessaert, Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation)

The 3D mapping of the Hasse variant on the left below was (painfully) derived by adptation of the different representations of Demey and Smessaert. Note that the negation is visualized by means of central symmetry, namely the diagonals link similarly colour coded vertices which are the negation of each other; the logical ordering of levels goes from bottom (0000) to top (1111). In the animation on the right the mapping is applied to the dual, namely onto the faces of a cuboctahedron.

Animation of 3D visualization of propositional connectives
(combining printed images by Demey and Smessaert)
Mapped onto rhombic dodecahedron
Mapped onto cuboctahedron
Animation of 3D visualization of logical connectives on rhombic dodecahedron Animation of 3D visualization of logical connectives on cuboctahedron
Animation prepared using Stella Polyhedron Navigator

Engaging opposition: cognitive "collapse" heralding a wider collapse?

Disconnect and collapse? The remarkably insightful explorations of the geometrical representation of oppositional logic (as discussed above) offer a valuable metaphor of the disconnect heralding wider social collapse through the erosion of the coping capacity of governance. Not only are those insights relatively incomprehensible and irrelevant to most, discussion of them (by its professionals) makes clear how the subtlety of 16-fold complexity is variously reduced -- purportedly for reasons of "efficiency and parsimony" -- to the binary thinking by which society is remarkably bedevilled. The latter is only too evident in the pattern of public discourse and in pariamentary assemblies.

This occurs in a period in which global governance in the face of multiple crises is purportedly:

The consequences of the latter, from an international relations perspective, are only implicit in the arguments of Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015).

There is therefore a sense in which discourse is significantly characterized by a form of cognitive collapse -- readily understood as both heralding and enabling erosion of the capacity of governance. Ironically this is matched by the subtlety, comprehensible only to the very few, of the operation of artificial intelligence and quantum computing -- to which effective responsibility for governance of complexity and crisis is being progressively transferred.

Disconnected insight -- despite oppositional logic: The tragedy of the times is evident is the polarization of strategic and tactical decision-making whereby:

It is remarkable that:

Perhaps more remarkable still, those developing further insight into the logic of opposition seem to have no detectable interest in the relevance of their understanding for the dramatic conditions n which opposition divides society -- often violently.

Deprecation of potential correspondences: 16-fold patterns?

As noted above, Fabien Schang (An Arithmetization of Logical Oppositions, 2017) makes reference to "blatant analogies" between the pattern of logical connectives and classical Chinese thinking. The history of the mathematical discovery of the so-called "monster group" arose from recognition of its unexpected connection to modular functions -- a correspondence recognized as monstrous moonshine. Arguably there is a case for seeking such improbable connections in domains of relevance to governance (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007). Recognition of correspondences is readily framed as suspicious by many disciplines, although variously valued (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007).

There is therefore a case for "confronting" the full pattern of 16 Boolean connectives with other 16-fold patterns -- however disparate -- which have acquired fundamental significance to the manner in which the world is ordered. One argument in support of this is provided by cognitive psychology (George Lakoff and Rafael E. Núñez, Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000).

The question is why 16? Especially with respect to systemic understanding of the challenges of governance, why:

Speculatively, are there 16 types of such distinctions to be fruitfully recognized? Why the absence of governmental plans articulated in this way at this time -- with some rare (if not strange) exceptions:

Suitably provocative candidates for confrontation are the 16-fold standard model of particle physics (minus the Higgs boson) and the set of 16 UN Sustainable Development Goals (minus the coordinating 17th). In systemic terms there is in an interesting comparison to be made between the 17th SDG and the Higgs boson. The Higgs boson and the ambition of goal coordination could be understood as equally elusive. It is strange to note that no attempt appears to have been made to configure either the set of goals or the set of particles in a three-dimensional visualization to facilitate wider comprehenion. Nor does any attempt seem to have been made to seek correspondences with the pattern of logical connectives. Of relevance to the "problematic" relationship between 16-fold and 17-fold is recognition of 17 ways to arrange a motif regularly in a plane (The 17 Plane-symmetries).

In the following exercise the first two images are reproduced from Confrontation of alternative mappings in Metaphorical Insights from the Patterns of Academic Disciplines (2012). The image on the right derives from a separate exercise (Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful, 2017).

Juxtaposition of 16-fold patterns potentially implying correspondencs (experimental)
Standard model of particle physics
(minus Higgs Boson)
Chinese pattern of tetragrams Sustainable Development Goals
(minus 17th coordination goal)
16-fold Standard model of particle physics (minus Higgs Boson) 16-fold Chinese pattern of tetragrams 16-fold Sustainable Development Goals (minus 17th coordination goal)
Reproduced from Wikipedia   Adapted from Wikipedia

Some justification for the approach is provided by the following (Solomon W. Golomb, Rubik's Cube and Quarks: twists on the eight corner cells of Rubik's Cube provide a model for many aspects of quark behavior, American Scientist, 70, 1982, 3; T. Csörgö, Qbe: Quark Matter on Rubik's Cube, 2017). The latter provides a detailed illustrated description of development of the technique for educational purposes:

Quarks can be represented on the faces of the 3x3 Rubik's cube with the help of a symbolic representation of quarks and anti-quarks, that was delevoped originally for a deck of elementary particle cards, called Quark Matter Card Game. Cubing the cards leads to a model of the nearly per-fect fluid of Quark Matter on Rubik's cube, or Qbe, which can be utilized to provide hands-on experience with the high entropy density, overall colorn eutrality and net baryon free, nearly perfect fluid nature of Quark Matter.

Reframing the pattern of logical choices through polyhedra

Cognitive continuity in "shifting cognitive gears": The work on oppositional logic and its geometric representation (as indicated above) would seem to offer a possibility which has as yet been inadequately explored. That work focuses on representation of contrasting propositions on a limited range of polyhedra. From a geometrical perspective it effectively ignores a very extensive range of related polyhedra of potential relevance. Ironcally, given the learning potential of artificial intelligence (as recently demonstrated by its capacity with respect to chess, go and poker), there is every reason to suspect that AI will "discover" such polyhedral patterns in extending the range of options it considers viable.

Of particular interest is the sense in which cognitive collapse can be understood as the transformation from a more complex polyhedral mapping, as on the rhombic dodecahedron, to a simpler mapping -- such as the cube, the octahedron, or the tetrahedron. Those polyhedra in 3D are variously discussed in the literature on the logic of opposition -- as evident in further reduction to the classical Aristotelian square of opposition represented in 2D.

Missing, or buried in the complex formalism of logic, is the consideration of more complex polyhedra. However of greater relevance is the nature and significance of the transformation from one polyhedral mapping to another -- understood in dynamic terms, usefully compared to shifting "cognitive gears". This metaphor helps to reframe the sense in which the exploitation of the set of 16 logical connectives is reduced from 16 to 10, to 5, to 4, to 2, or to 1. Missing however (beyond the 16) is the challenge of the 256 ternary connectives -- no doubt to be explored and exploited by artificial intelligence -- and how such complexity can be rendered comprehensible to the human mind, especially if there is need for artful shifting between patterns of different size.

It is in this respect that the transformation between polyhedra of different degrees of complexity merits attention -- given that the visualization of such forms (as indicated above) enables greater comprehension for many than the abstractions of professional logicians and information scientists.

Ironically with respect to the latter argument is the acknowledged complementarity between the rhombic dodecahedron and the cuboctahedron -- its geometric dual. The latter was central to extenssive discussion by Buckminster Fuller (Synergetics: explorations in the geometry of thinking, 1975/1979) -- despite his apparent failure to apply it as claimed by the subtitle of that magnum opus (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009).

Of particular relevance in the case of the cuboctahedron is that it can be transformed dynamically through a much-studied "jitterbug" motion into other configurations, most notably the icosahedron (Robert W. Gray, Jitterbug Defined Polyhedra: the shape and dynamics of space, 2001; H. F. Verheyen, The Complete Set of Jitterbug Transformers and the Analysis of their Motion, Computers and Mathematics with Applications, 17, 1989, 1-3; Joe Clinton, R. Buckminster Fuller's Jitterbug: its fascination and some challengesSynergetics Collab, 2011). Many videos of that movement have been produced (Buckminster Fuller's Jitterbug, 2007). Such transformation are suggestive of a degree of cognitive continuity between various coherent N-fold patterns of insights, as discussed separately (Time for Provocative Mnemonic Aids to Systemic Connectivity? 2018).

Has any effort been made to associate logical connectives with the jitterbug cycle? If not, why not? It suggests a means of justifying comprehensibly both the the conflation of the 16 and the complexification of simpler patterns from 2D forms (Vector Equilibrium and its Transformation Pathways, 1980; 12 Degrees of Freedom: vector equilibrium).

Polyhedral complexification: If the challenge to the coping capacity of governance can be reframed in terms of more comprehensible articulations of diversity (with its oppositional implications), then the challenge to representation lies beyond the relative simplicity of the rhombic dodecahedron or its dual -- whatever their immediate advantages. What degrees of diversity merit distinctive articulation on a map given the tendency to oversimplification in the face of information overload? The challenge of 256 ternary connectives is one example

Given the suggestion by some logicians that only 5 connectives are really necessary, it is intriguing to ask in what sense these relate to the classical Chinese 2D pattern of the 5-fold Wu Xing, discussed separately (Coherence of a cognitive nexus comprehended dynamically, 2019). More intriguing is the clarification in mathematical terms of the relation of that pattern to the more complex 64-fold pattern of the I Ching (Shu Shengyu, The Relations Between Ancient China's Taoism and Modern Mathematics and Physics, The Zhong Language Computing Technology Research and Development Alliance, 2015).

Somewhat ironically, one illustration of a more complex mapping is provided by the encoding which originally inspired Gottfried Leibniz in elaborating the binary coding system fundamental to computer operation -- namely the I Ching with its combination of two trigrams of 8 types forming 64 hexagrams. The classical 8-fold organizations of trigrams (as BaGua) suggests one mapping of 8 logical connectives. The more complex set, and the interrelationship of its parts, is suggested by the circular pattern on the left below.

Those on the right derive from one exercise in mapping a set of 64 complementary elements onto a polyhedral form -- the drilled truncated cube, unique in having 64 edges (and recalling 3D representations of the hypercube of interest to logicians). The images are discussed separately with other animations (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015). Noteworthy is the historical importance of those patterns to the governance of China -- and to the education of its civil servants.

Circular configuration of I Ching hexagrams Drilled truncated cube of 64 edges (with random mapping attributions)
  Hexagram names (selected faces transparent) Genetic codons (all faces transparent)
Logo of Laetus in Praesens Drilled truncated cube of 64 edges with hexagram names Drilled truncated cube of 64 edges with codons
Reproduced from Laetus in Praesens Prepared using Stella Polyhedron Navigator

Fractal organization? Comprehension of the 16-fold organization of interest here has long been explored in relation to the 4-dimensional hypercube or tesseract, as previously indicated with animations (Fractal comprehension of coherence requiring an 8-fold uncertainty principle? 2019). That included indications regarding the relevance of iterations of the  Menger sponge and the associated Sierpinski-Menger snowflake (related to the Mosely snowflake and to the Jerusalem cube).

Of particular relevance to comprehension of the 16-fold is the use of patterns of colour as described by Paul St. Denis and Patrick Grim (Fractal Images of Formal Systems, Journal of Philosophical Logic, 26, 1997, included as a chapter in The Philosophical Computer: exploratory essays in philosophical computer modeling, 1998). As argued there:

Familiar formal systems include propositional calculus, predicate calculus, higher-order logic and systems of number theory and arithmetic. As standardly envisaged, these consist of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists or series of formulae each of which is either an axiom or is generated from earlier items by means of the rules of the system, and the theorems of a formal system are simply those formulae for which there are derivations.

Given this standard approach to formal systems, however, attempts to envisage formal systems as a whole seem of necessity remotely abstract and incomplete. As a psychological matter, if one is asked to envisage the theorems of predicate calculus as a whole, one seems at best able to conjure up an image of the axioms and an empty category of 'all that follows from them'. The incompleteness of such a psychological picture accords perfectly with constructivist approaches to formal systems, and may even seem to confirm them.

In what follows we want to outline some importantly different and immediately visual ways of envisaging formal systems, including a modelling of systems in terms of fractals. The progressively deeper dimensions of fractal images can be used to map increasingly complex wffs [well-formed formula] or what we will term 'value spaces', which correspond quite directly to columns of traditional truth tables. Within such an image, tautologies, contradictions, and various forms of contingency can be coded in terms of color or shading, resulting in a visually immediate and geometrically suggestive representation of systems as an infinite whole. One promise of such an approach, it is hoped, is the possibility of asking and answering questions about formal systems in terms of fractal geometry. As a psychological matter, it is interesting to note, complete fractal images of formal systems seem to correspond to a realist and non-constructivist approach to formal systems. [emphasis added]

The image on the left illustrates the use of 16 colours to distinguish values of tautologies, contradictions, and all possible shades of contingency, corresponding to the sixteen possible conditions indicated by truth tables. Complete color shade patterns -- employing a complete palette of contingencies -- are shown in the images on the right (from Rug' Enumeration images). The central image is from discussion of the Sierpinski Tautology Map. Further implications are discussed with respect to Value Solids and Multi-Valued Logics and to Cellular Automata in Value Space

Colour coded 4-digit distinctions Sierpinski Tautology Map "Rug" style presentations of logical patterns
Colour coded 4-digit distinctions Colour coded Sierpinski Tautology Map Rug style presentations of logical patterns
Images from Paul St. Denis and Patrick Grim (Fractal Images of Formal Systems, (1997)

Reference to a "rug" metaphor is of further relevance in the light of the work of Christopher Alexander and the manner in which it was partially inspired by carpet design (A Foreshadowing of 21st Century Art: the color and geometry of very early Turkish carpets, 1993). This was the focus of an earlier discussion (Magic Carpets as Psychoactive System Diagrams, 2010) which noted 15 transformations identified by Alexander in carpet geometry, as he discusses elsewhere (Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole. International Journal for Unconventional Computing, 5, 2009).

The carpet metaphor is also valuable in recalling use of conversation threading in internet fora, as well as references in other contexts to the "social fabric", readily understood to be "torn" and "frayed" at this time, notably from a cognitive perspective (Interweaving Thematic Threads and Learning Pathways: Noonautics, Magic carpets and Wizdomes, 2010). Also of relevance to the images above are arguments relating to magic squares, as presented separately (Salvation Enabled by Systemic Comprehension: via aesthetics of magic squares? 2015). This notes their interest to Benjamin Franklin (Magic square integrity and implications for the US Constitution, 2015).

From disorderly "collapse" to orderly "renaissance"

Nesting, packing and transforming polyhedra: Collapse, most notably in cognitive terms, can be understood and represented through the transformation of more complex polyhedra into simpler polyhedra, as illustrated by the "jitterbug" dynamics mentioned above -- which include the reverse ("recovery") cycle from simplicity to complexity. As yet to be clarified is the manner in which the transformations "carry" the significance which may be associated with the logical connectives mapped onto the distinctive polyhedra in such a cycle.

Various approaches to "shifting down" using any "cognitive gearbox" are discussed and illustrated separately (Psychosocial Implication in Polyhedral Animations in 3D: patterns of change suggested by nesting, packing, and transforming symmetrical polyhedra, 2015; Embodying Global Hegemony through a Sustaining Pattern of Discourse: cognitive challenge of dominion over all one surveys, 2015). This is also indicative of "shifting up", namely an increase of complexification from the oversimplification by which current governance is characterized -- and which is clearly "not fit for purpose" (except in the binary choice of nuclear and other military strikes).

Certain polyhedra can then be understood as nested within other polyhedral frameworks -- leading to recognition of a process of cognitive "packing" and "unpacking". Here "packing" suggests that subtlety is implied -- implicit -- rather than articulated -- explicit. The dynamics recall the argument of David Bohm with regard to a holomovement. The dynamics are best understood through visualization, as indicated by the following -- in particular the "pumping" variant on the right..

Nesting 5 Platonic polyhedra:
octahedron, icosahedron, dodecahedron, tetrahedron, cube
Polyhedral model of solar system of Johannes Kepler
on Mysterium Cosmographicum (1596)
Rhombic Triacontahedron (green) as a nesting framework
videos: "pumping" mp4; "rotation" mp4)
(virtual reality variants static: vrml or x3d;
mutual rotation: vrml or x3d; "pumping": vrml or x3d)
Kepler solar systemnested polyhedra Rhombic triacontahedron as a framework for nesting dynamics of 5 polyhhedra
Reproduced from Wikipedia entry Developed with X3D Edit and Stella Polyhedron Navigator

Recognizing the range of polyhedral possibilities of relevance to governance: The highly selective list of polyhedra which are the focus of the literature on the logical geometry of opposition raises the question as to why discussion is limited to such a restricted set, and to what extent this is arbitrary, or overly influenced by tradition and convenience -- effectively an academic comfort zone almost completely unrelated to the challenges of governance. Rather than framing the question as to whether a given polyhedron is of relevance to insight into particular forms of opposition and disagreement, it might be framed as the degree to which it is of relevance and how to recognize its relevance. This is reminiscent of the current preoccupation in particle physics with "beyond the standard model".

There are many hundreds of polyhedra of greater or lesser relevance, possibly in the light of their degree of symmetry -- with visualizations and animations accessible through widely available software packages. Given the strategic importance of governance over time, such geometry also invites consideration of their four-dimensional (and higher) analogues, as discussed separately (Comprehending the shapes of time through four-dimensional uniform polychora, 2015; From space-ship design to time-ship embodiment as a requisite metaphor of governance, 2015).

Complexification in contrast with simplification? Given the options offered for complexification of a polyhedron in Stella Polyhedron Navigator, it is of interest to note their application to the rhombic dodecahedron. These include various geometrical transformations through morphing, stellation, augmentation, zonohedrification, subdivision of faces, and other transformations (into a geodesic sphere torus or spring model). Especially intriguing are the creation of 4D projections into 3D models.

Current relevance of the "simplest torus"? From the perspective of logical geometry, as noted above, the 16 Boolean connectives are reduced to 14 -- enabling them to be configured on the vertices of a rhombic dodecahedron. Given the apparently fundamental significance of 16-fold patterns, whether in that respect, or in the standard model of particle physics, there is a case for exploring what polyhedra might be suitable (if only for mnemonic purposes) to display such a pattern -- rather than as a checklist, a matrix or in tabular format. Potentially this is of relevance to the 16 (+1) Sustainable Development Goals by which global governance is purportedly framed at this time.

It is therefore of interest to note what has been termed the "simplest torus", together with its dual -- as shown in the following animations. Of particular interest is the less than obvious notion of "face" in each case, since some faces have two seemingly separate components when passing from inside the model to outside, or being contiguous (but not separate as appears). This is most evident from the colouring of the faces in both models. Each "double" face exhibiting such characteristics is coloured the same -- although parallel faces across the model may use the same colour. This confusing characteristic is clearest in the case of the simplest torus, rather than its dual.

Rotation of simplest torus (faces visible and transparent)
(16 vertices and 12 faces: 4 hexagonal, 8 square)
Rotation of dual of simplest torus (faces visible and transparent)
(12 vertices and 16 faces: 8 triangular, 8 square)
Animations prepared with Stella Polyhedron Navigator

These unusual forms then raise the question as to how they may be used to map 16-fold patterns, rather than the 14-fold discussed above. Most obviously, in the absence of any mapping worthy of the challenge to governance in the case of the 16 Sustainable Development Goals, what valuable counter-intuitive meaning is derived from the use of mapping surfaces which have an "inside" and an "outside" -- with such faces being continuous within the model (despite appearances). An initial attempt to apply the standard thumbnails for each of the 16 Goals to the relevant surfaces in the dual model proved problematic with the application package. Appropriately perhaps, the image was reversed when slid across the face from "outside" to "inside", for example.

A further clarification, using the thumbnail images of the 16 Goals, suggested the mapping in the following animations. Here it is to be noted that 2 opposing clusters of points (of the 4) are each used for 8 such mappings. The 2 intermediary clusters of points have faces which are extensions of those on the other 2 (as indicated by the similar colouring of the faces). As before, parallel faces are of the same colour. The thumbnails images are arbitrarily oriented. The inner surfaces of the torus do not seemingly have any images on them -- since those faces are an extension of those visible on the outside. These various subtleties invite recognition of the subler relationships between the Goals and altenative mapping conventions -- perhaps with the images shifting between positions of the surface.

Experimental mapping of 16 UN Sustainable Development Goals
onto 16 faces of dual of "Simplest Torus" (with 12 vertices)
"Vertical" rotation "Horizontal" rotation
Mapping of 16 UN Sustainable Development Goals onto dual of Simplest Torus Mapping of 16 UN Sustainable Development Goals onto dual of Simplest Torus
Animations prepared with Stella Polyhedron Navigator

For ease of mapping and colouring the surfaces using the software, use was made of the first stellation of the variant indicated above with 12 vertices, of potential significance previously explored (Eliciting a 12-fold Pattern of Generic Operational Insights: recognition of memory constraints on collective strategic comprehension, 2011). Of some interest for further investigtion is that the stellation has an additional 8 vertices, making 20. This recalls the separate visualization issue of potential relevance to governance (Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights, 2018; Memetic Analogue to the 20 Amino Acids as vital to Psychosocial Life? 2015). The coherent interrelation of 8, 12, 16 and 20 merits further investigation, as discussed in an annex (Global Coherence by Interrelating Disparate Strategic Patterns Dynamically: topological interweaving of 4-fold, 8-fold, 12-fold, 16-fold and 20-fold in 3D, 2019).

The possibility of mapping the 16-fold standard model of particle physics onto such forms is intriguing in the light of the integrity it would then exemplify to a higher degree than in its tabular form. Of further interest is the extent to which the relationship between the elements are then understood dynamically rather than statically -- forming some some analogue to a resonance hybrid.

Of further interest with respect to governance is the reconciliation on two related forms of the 16-fold pattern with the 12-fold -- so enthusiastically adopted with respect to round tables and strategic principles, as discussed separately (Clarifying the Unexplored Dynamics of 12-fold Round tables: visualization of patterns of sustainable discourse between 12 systemic archetypes, 2019).


Christopher Alexander:

Linda V. Berens and Dario Nardi. The Sixteen Personality Types: descriptions for self-discovery. Telos Publications, 1999

Jean-Yves Béziau and Gianfranco Basti (Eds). The Square of Opposition: a cornerstone of thought. Birkhauser, 2017 [contents]

Jean-Yves Béziau and Dale Jacquette (Eds). Around and Beyond the Square of Opposition. Birkhauser, 2012 [contents]

Nick Chater. The Mind is Flat: the remarkable shallowness of the improvising brain. Yale University Press, 2018

Yehezkel Dror:

Barbara Ehrenreich:

Melvin Fitting and Ewa Orlowska. Beyond Two: Theory and Applications of Multiple-Valued Logic. Springer, 2003

Karen L. French. Gateway to the Heavens: how geometric shapes, patterns and symbols form our reality. Duncan Baird Publishers, 2014

R. Buckminster Fuller with E. J. Applewhite:

Patrick Grim, Gary Mar and Paul St. Denis. The Philosophical Computer: exploratory essays in philosophical computer modeling. MIT Press, 1998 [contents]

Carl Jung. Archetypes and the Collective Unconscious. Princeton University Press, 1959

George Lakoff and Rafael E. Núñez. Where Mathematics Comes From: how the embodied mind brings mathematics into being. Basic Books, 2000

Kelly McKinney. Moment of Truth: the nature of catastrophes and how to prepare for them. Savio Republic, 2018

Mayan Moudgill, Keshav Pingali and Stamatis Vassiliadis. The 16-fold Way: a microparallel taxonomy. Proceedings of the 26th Annual International Symposium on Microarchitecture, 1993 [abstract]

Nicholas Rescher:

Steven M. Rosen:

Elisabet Sahtouris and James E. Lovelock. EarthDance: Living Systems in Evolution, iUniverse 2000

John Ralston Saul. The Unconscious Civilization. Anansi, 1995

Fabien Schang:

Izchak M. Schlesinger, Tamar Keren-Portnoy and Tamar Parush. The Structure of Arguments. John Benjamins Publishing, 2001

Shu Shengyu. The Relations Between Ancient China's Taoism and Modern Mathematics and Physics. The Zhong Language Computing Technology Research and Development Alliance, 2015 [text]

Justin E. H. Smith. Irrationality: a history of the dark side of reason. Prineton University Press, 2019

Nassim Nicholas Taleb:

George Trevelyan and Edward Matchett. Twelve Seats at the Round Table. Neville Spearman, 1976

Alexander Wendt. Quantum Mind and Social Science: unifying physical and social ontology. Cambridge University Press, 2015

Arthur M. Young. The Geometry of Meaning. Delacorte Press, 1976

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

For further updates on this site, subscribe here