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29 July 2024 | Draft

Reframing "Two-state" Possibilities

Beyond the constraints of disciplinary frameworks in a two-state civilization

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Introduction
Range of applications of the two-state concept
Two-state geopolitical proposals
Research on geopolitical two-state possibilities
Blurring the relation between states beyond the "two-state" model
Multi-state solutions beyond the "two-state" -- 3, 4, 5, 6, 7, 8, 9, 10, 12?
Extraterritorial enclaves, special jurisdictions and "special relationships"
Challenge to "statehood" of indigenous cultures and alternative worlds
Diasporas, reservations and micronations as challenges to traditional statehood
Two-state focus as an exemplification of constrained "binary thinking"
Deprecation of otherness as an instance of "binary thinking"
Neglected dynamic of alternation in two-state modelling
Dramatic reframing eliciting cognitive engagement
Linguistic and cultural implications of "two-state"
Questionable role of religion in reinforcing unfruitful two-state frameworks
Potential reframing of two-state by mathematical theology and mathematical epistemology
Recognition of dynamics of 64 two-state pattern with AI?
Mythological reframing of two-state dynamics by the humanities?
Collective consciousness and unconsciousness -- a psychosocial two-state dynamic?
Challenge avoidance through "dialogue" and "interdisciplinary research"?
Psychosocial inertia and procrastination in response to the two-state challenge
References


Introduction

There is no lack of references over an extensive period to "the" Israel-Palestine "two-state" solution. This has been brought dramatically into global focus through the unprecedented level of violence and destruction in Gaza -- now upheld internationally and controversially as an instance of genocide. Examples include:

Various bodies provide a forum for discussion of the possibility, as with the Geneva Accord Coalition for a Two-State Solution (2021). Less evident is the comprehension of those who claim to support it in some manner, as with the government of Australia, as noted by Matthew Doran:

At its base level, the idea of "a two-state solution" is to formalise those territorial claims and some of the sticking points in the relationship between the two sides here — things like controversial Jewish settlements in Palestinian territory and control over the holy city of Jerusalem. (What does the government mean when it says it supports a two-state solution? ABC News, 10 April 2024)

The level of widely publicized violence in Gaza frames the question explored here, namely whether there is any more fruitful way of approaching a "two-state" solution, as evoked by the following, for example:

On the other hand there are many reference to the "death" and impossibility of the "two-state" solution -- or its catastrophic consequences and miraculous revival -- as for example:

In such a context it is appropriate to ask how "two state" is understood and evoked -- and especially by whom and through what disciplinary lens. Given the apparent incapacity of those disciplines claiming unique relevance to reframing the challenge to civilization of "Israel-Palestine" -- in a manner which evokes "new thinking" -- it could be asked how "discipline" is then to be understood. Does a discipline simply provide the justification for what its practioners are entitled to ignore in the execution of their profession? Given the specificity through which they define themselves, can disciplines even "think" in "global" terms -- when faced with global crises? Do the disciplines claiming such relevance engage in any root cause analysis of their apparent ineptitude?

Given the frequency with which "two-state" is cited, such considerations evoke the question as to where research on the matter is actively funded and studied -- and by what disciplines, with what agendas. What disciplines are ignored by some in the process as being unable to furnish insights of relevance? How is any dialogue on the possibility thereby undermined?

Where is such presumably vital research assembled for critical evaluation and inspiration? In the Bulletin of Peace Proposals? Given its apparent importance as a strategic opportunity, is there any indication that the situation has been the focus of sophisticated simulation to evoke previously unrecognized possibilities -- other than the current use of AI for targetting purposes in Gaza? If not, why not? (Simulating the Israel-Palestine Conflict as a Strategy Game, 2023; Envisaging a Game of Subtlety Enabling New Global Dynamics, 2024).

The following exercise in interaction with two AIs (ChatGPT and Claude) is an effort to reframe the understanding of "two-state" from a variety of perspectives beyond those conventionally favoured in the literature -- in the quest for insights that may otherwise have been systematically ignored.

The focus follows from earlier consideration of the challenge from the neglected perspective of mathematics (And When the Bombing Stops? Territorial conflict as a challenge to mathematicians, Technological Forecasting and Social Change, 61, 1999). This was subsequently followed by consideration, with the aid of ChatGPT, of conventional dependence on "flat earth" thinking -- ignoring insights of mathematics and physics (Neglect of Higher Dimensional Solutions to Territorial Conflicts, 2024).

Given the apparent inability of "Western" inspired disciplines to inform mediation of the Gaza situation, it is intriguing to note the current initiative from an "Eastern" perspective (Laurie Chen and Nidal Al-Mughrabi, China brokers Palestinian unity deal, but doubts persist , Reuters, 24 July 2024; Mohamad Zreik, China Mediates a New Era of Palestinian Unity, The Diplomat, 25 July 2024 ). This could be considered consistent with Coherent Reconciliation of Eastern and Western Patterns of Logic (2023) -- a study facilitated by AI commentary. Ironically it is of course the case that China is faced with its own "two-state" challenge, as with the Koreas.

The wider perspective on "two-state"evoked in the following, frames the curious question as to whether humanity effectively dwells in a "two-state civilization" -- which it has engendered and assiduously cultivates. This would reframe any assertions regarding the "death" of the "two-state solution" and its implications.

As in the previous experiments, the responses of ChatGPT are distinctively presented below in grayed areas, in parallel with those of Claude 3. Given the length of the document to which the exchange gives rise, the form of presentation has itself been treated as an experiment -- in anticipation of the future implication of AI into research documents. Web technology now enables the whole document to be held as a single "page" with only the "questions" to AI rendered immediately visible -- a facility developed in this case with the assistance of both ChatGPT and Claude 3 (but not operational in PDF variants of the page, in contrast with the original).

Reservations regarding this method of interaction with AI have been previously highlighted (Eliciting a Pattern that Connects with AI? 2024). These noted questionable styles of response readily characterized as "algorithmic enthusiasm" (or "synthetic appreciation"), together with presumptions of an anthropomorphized relationship by which the questioner is repeatedly flattered. These can be understood as a marketing technique to encourage engagement in the process or as formulaic courtesy deemed appropriate in some cultures. Whilst these could be edited out, as a feature of the experiment they have not been removed; responses have been minimally edited for format alone. The approach allows readers to repeat the questions at a later stage or to other AIs -- possibly at a future time when their capacities have been further developed.

Of greater potential concern regarding the use of AI in this context is the questionable role of leading questions in eliciting responses deemed of value -- in a period in which the undoubted capacity of AI to aggregate relevant information is now called into question by science and otherwise (Joe Slater, et al, ChatGPT Isn’t ‘Hallucinating’ -- It’s Bullshitting! Scientific American, 17 July 2024; Edisa Lozic and Benjamin Stular, Fluent but Not Factual: a comparative analysis of ChatGPT and other AI chatbots' proficiency and originality in scientific writing for humanities, Future Internet, 2023). Somewhat ironically such assertions occur in a period in which unprecedented numbers of academic papers are being retracted.. In a period in which there is seemingly limited capacity to address global issues effectively, the proactive responses of AI contrast strangely with the dismissive style of academia (Richard Phelps, Dismissive literature reviews reduce understanding – so why do academics keep making them? LSE, 17 June 2024).


Range of applications of the two-state concept

As evoked in the following questions to the AIs, the concept of "two-state" is understood in a far wider range of instances than that of Israel-Palestine. For example:

Question: Other than Israel-Palestine, and with respect to other territories, I note that the concept of "two-state" is a focus of particular attention in thermodynamics, chemistry, protein folding, as well as those exemplified at the molecular level by Richard Feynman under the heading "other two-systems" in the famed (The Feynman Lectures on Physics). Could you clarify this wider understanding of "two-state" -- and potentially in the psychosocial sciences

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The challenge of two-state psychosocial relationships can be explored in terms of the "us and them" framework, highlighted as a basic principle of US foreign policy (You are either with us or against us) -- and the declaration to that effect by Hillary Clinton (2001) as US Secretary of State. (Jerry Z. Muller, Us and Them: the enduring power of ethnic nationalism,Foreign Affairs, March/April 2008; Us and Them: Relating to Challenging Others: patterns in the shadow dance between "good" and "evil", 2009; Iman Kurdi, Splitting the World Into Us and Them, Arab News, 4 August 2005).

Of relevance is how that two-state framing might be transcended (Dimitri Schuurman and Peter Mechant, Beyond Us and Them: a mixed method approach supporting a virtual scientific interdisciplinary organization, Interfaces, 2009; Karina Korostelina, Redefining "Us" and "Them": Gülen's approach to transformation of perceptions between Muslims and Non-Muslim, November 2008)

Question: In considering the psychosocial applications of the two-state model, reference can appropriately be made to the fundamental challenge of "us" and them", exemplified by being "in" or "out". Could you comment on this

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Two-state geopolitical proposals

The simplest quantum systems that are of interest to mathematic are two-state quantum systems, since the dynamics of a one-state system is trivial (as there are no other states the system can exist in). The mathematical framework required for the analysis of two-state systems is that of linear differential equations and linear algebra of two-dimensional spaces. Seemingly use of "quantum" in relation to Israel-Palestine has been limited to passing references to the necessary "quantum leap" in understanding (Joel Singer, Developing the Concept of Palestinian Autonomy, The Cairo Review of Global Affairs, Winter 2019). Curiously it is suggested that a Palestinian understanding of their existential context is best framed by the insights of quantum mechnaics (Mark LeVine, The Quantum Mechanics of Israeli Totalitarianism, State Crime Journal, 5, 2016, 1)

Question: The concept of a two-state solution to territorial dispute seems to be primarily focused on Israel-Palestine. Is there a more general approach and how are its possibilities researched, notably in the light of more complex mathematical solutions to a complex problem

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Question: Could you provide a list of the territorial disputes in which a "two-state" solution has been evoked as a possible response

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Question: In previously identifying two state solutions like condominiums, I am surprised that reference was not made to territorial curiosities like Andorra, Monaco, the Vatican and perhaps regions defined as "autonomous" to some degree, as with Corsica. Then there is also the question of enclaves and exclaves which offer another sense of two state. Could you clarify these options

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Research on geopolitical two-state posibilities

Question: Do you have any trace of new research regarding two-state geopolitical possibilities especially of a mathematical nature

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Question: I understand the possibilities but I am seeking to locate research applied specifically and not just in theory. One example is the condominium solution, used in the past

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Question: The lack of specifics contrasts to a remarkable degree with the amount of two-state research in quantum mechanics

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The resulctance to consider cross-fertilization of ideas between disciplinary domains is exemplified by the widely recognized challenge of silo information, which seemingly has yet to be explored mathematically -- or from an AI perspective on balancing integration and identity in the face of civilization's strategic complexity (Mathematical Modelling of Silo Thinking in Interdisciplinary Contexts, 2024)

Question: It is appropriate to cite quantum mechanics because of the innovation it represents, most obviously with the notion of superposition which suggests a framework for consideration of the territorial case. Time sharing is another. I am concerned that the two-state solution research has become a victim of silo thinking with the legal approach deprecating the mathematical approach and vice versa

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Question: The implication of that response is that such research is possible but it is not currently undertaken in an integrated manner by any institution, and if undertaken at all it is a victim of silo thinking ironically itself an unfruitful "two-state" model

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Blurring the relation between states beyond the "two-state" model

There is increasing recognition of surrogates and proxies in international relations -- a particular form of "two-state" relationship (Andreas Krieg and Jean-Marc Rickli, Surrogate Warfare: the art of war in the 21st century? Defence Studies, 18, 2018, 2; Michael A. Innes, Making Sense of Proxy Wars: States, surrogates and the use of force, Potomac Books, 2012; Michael Kagan, The UN Surrogate State and the Foundation of Refugee Policy in the Middle East, U.C. Davis Journl of International Law and Policy, 18, 2012),

Question: Reference to superposition in quantum mechanics and implications regarding degrees of sexual arousal suggest the value of considering "two-state" from another perspective. Any distinction between "states" may well be blurred by the degree to which one state is effectively independent rather than dominated or influenced in some manner (and to some degree) by the other. Thus in geopolitical terms, one "independent" state may be recognized as the surrogate of another -- with a degree of independence in the "two-state" formula which may only be symbolic or tokenistic, even cynically so. Cases like the Vatican or Monte Carlo merit consideration in that light. Is there any recognition of "surrogate states"

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Multi-state solutions beyond the "two-state" -- 3, 4, 5, 6, 7, 8, 9, 10, 12?

The concept of "multi-state" invites misunderstanding in that in geopolitical terms it may indicate either subdivision of a state or a multiplicity of states. Other disciplines offer other conotations (2010). Multi-state Systems in Nature and in Engineering. Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers, 2010; Bent Natvig, Multi-state Coherent Systems, Encyclopedia of Statistical Sciences, 1985)

Question: Beyond the "two-state" solution, could you comment on references to 3, 4, 5, 6, 7, 8, 9, 10 and 12-state solutions with respect to Israel-Palestine

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Question: Could you comment on any "multi-state" solutions especially highlighted by the sciences, but independent of the references to the Israel-Palestine situation,, especially to the extent that they might offer insights into a multi-state geopolitical challenge

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Extraterritorial enclaves, special jurisdictions and "special relationships"

A notable degree of attention has been devoted to the "special relationship" between two countries, most notably that of UK-USA, but variously citeed with respect to other countries (John Dumbrell, The US–UK Special Relationship: Taking the 21st-Century Temperature, The British Journal of Politics and International Relations, 11, 2009, 1).
Current focus is given to such a relationship between the USA and Israel, especially in the light of the unprecedented US support for military operations in Gaza, as justified in an historical presentation by the Prime Minister of Israel to the US Congress (Jon Hoffman, It’s Time to Rethink the U.S.-Israel ‘Special Relationship’, Time, 24 July 2024; Fayez Hammad, A brief history of the US-Israel "special relationship" shows how connections have shifted since long before the 1948 founding of the Jewish state, The Conversation, November 30, 2023; Dahlia Scheindlin, Can America’s Special Relationship With Israel Survive? How Gaza Has Accelerated the Social and Political Forces Driving the Countries Apart, Foreign Affairs, 23 May 2024; Yaacov Bar-Simon-Tov, The United States and Israel since 1948: A "Special Relationship"? Diplomatic History, 22, 1998, 2).

The vital importance of such a relationship is variously explored (Chuck Freilich, Israel’s Dependence on the United States is Existential, Belfer Center for Science and International Affairs, 7 February 2017; Jon Hoffman, Israel Is a Strategic Liability for the United States The special relationship does not benefit Washington and is endangering U.S. interests across the globe, CATO Institute, 22 March 2024). The reason for US support of Israel -- for the special relationship -- remains a matter of controversy (Stephen Zunes, Why the U.S Supports Israel, Foreign Policy In Focus,1 May 2002). Conspiracy theorists continue to suggest the probability of Israeli intelligence possessing kompromat on U.S. politicians (Joe Lauria, Netanyahu Commands, US Obeys, Consortium News, .24 July 2024).

Question: From a "two-state" perspective, what is especially exemplified by the following cases: settlements, colonies, research bases (Antarctica), military bases, extraterrestrial bases (Moon, Mars), embassies, free trade zones, and "special relationships" (USA-UK)

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Challenge to "statehood" of indigenous cultures and alternative worlds

Question: In seemingly contrasting ways both traditional indigenous cultures and virtual worlds call into question the conventional reality of "statehood". Could you comment on the ironical ability of some individuals to be associated with such worlds (as "states" in their own right) and to shift from them into a conventional state-governed reality -- thereby offering a quite distinctive understanding of "two-state".

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Diasporas, reservations and micronations as challenges to traditional statehood

With the massive migration of populations between countries, the connection of people sharing a culture is exemplified by the role of diasporas and the extent to which they are recognized by states. They invite a reimagination of possibilities of engaging with place and time (Affinity, Diaspora, Identity, Reunification, Return, 2013).

The heading was suggested by Claude, as appropriate to encompassing diasporas, reservations and micronations -- while capturing their shared qualities, thereby encapsulating several key aspects:

The suggestion was associated with an indication of the following themes as relevant for discussion:

Question: Could you comment on how disasporas might merit consideration in reflection on the two-state territorial model, especially given the possibility of diasporas to vote in their "home country" in some cases -- and the related possibility (irrespective of voting rights) of expat and migrant recognition of a "home country" with which they identify

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Question: Necessarily marginalized from many perspectives, the emergence of micronations -- and the freedom to create them -- offers an extreme perspective. Despite its deprecation from a conventional perspective, what implications does this have for the two-state territorial model as formally understood.

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The complexity of the matter with respect to "reservations" is highlighted by a decision of the Supreme Court of Canada regarding a 174-year old treaty concluded with a group of Anishinaabe nations (Leyland Cecco, Canada owes First Nations billions after making ‘mockery’ of treaty deal, top court rules, The Guardian, 27 July 2024).

Question: Given the challenges to the conventions of "statehood" by diasporas and micronations, could you comment on the perception of indigenous peoples obliged to live in "reservations"

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Two-state focus as an exemplification of constrained "binary thinking"

The possibility of alternatives to to binary decision-making is explored separately -- notably in contrast to "2-stroke democracy", as suggested by 4-sided ball games (Destabilizing Multipolar Society through Binary Decision-making, 2016).

Question: As an exemplification of "binary thinking", it is appropriate to reframe the "territorial" challenge as an instance of other binary situations with which many are more familiar and to which creative responses have been variously sought. Many examples relate to interpersonal relationships of which divorce is the most widely recognized "two-state" solution. However there is considerable effort to explore compromises, notably in terms of housing and children.

Collectives, notably intentional communities, may develop formula for resource sharing irrespective of their assertion of independent identities. A complex historical example is offered by the manner in which the spaces of the Holy Sepulcher in Jerusalem are shared, notably through a form of time-sharing [Dionigi Albera, et al, Sharing Sacred Spaces in the Mediterranean: Christians, Muslims, and Jews at Shrines and Sanctuaries, 2012; Elazar Barkan, et al, Choreographies of Shared Sacred Sites: Religion, Politics, and Conflict Resolution, 2015]. Especially intriguing for individuals are issues of gender identity to which the term "binary" is applied. Potentially most challenging is the binary nature of bipolar behaviour and how it is managed. These would appear to call for a systematic framing and study, given that each instance may offer insights for the others.

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Question: Curiously obvious is binary thinking in governance with the distinction systematically cultivated between "government" and "opposition" and the occasional contrast with "bipartisanship". As indicative of distinct ideologically-driven policies, the pattern is evident in the problematic instances of religious vs secular, science versus humanities, abstraction versus action, and the like. Is there any methodology which addresses these dynamics systematically

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Deprecation of otherness as an instance of "binary thinking"

As with the "us and them" characterization, noted above, there is a curious sense in which recognition of any "other" is a "two-state" framing, inviting its deprecation (Avoiding Dialogue with Alternative Worldviews at any Cost, 2005). This may evoke consideration of how it could be addressed otherwise (Elaborating a Declaration on Combating Anti-otherness, 2018; Post-Apocalyptic Renaissance of Global Civilization: Engaging with otherness otherwise? 2018; Reframing the Dynamics of Engaging with Otherness, 2011).

To the extent that ignorance is an aspect of the recognition of otherness, this frames the potentially more fundamental question of how to enage with ignorance, as notably discussed by Nicholas Rescher (Ignorance: on the wider implications of deficient knowledge, 2009; The Strife of Systems: an essay on the grounds and implications of philosophical diversity, 1985). The "knowledge-ignorance" dynamic can be explored as an instance of binary thinking (Engaging with the Inexplicable, the Incomprehensible and the Unexpected, 2010; Incomprehension and ignorance within systems of belief, 2012)

Question: In contrast to the insights of mathematicians of religious faith, those of secular persuasion typically condemn the religious dimension with the greatest severity as with the more general attitude of science with respect to ignorance. Ironically this dynamic, as with that associated with various articulations of "anti-otherness", would seem to frame a modality with which mathematics and science are unable to engage in a manner consistent with their disciplines. It frames the question as to why they are unable to frame "ignorance" mathematically (or through simulation) from a self-referential perspective, given the learning to which such disciplines are committed.

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Neglected dynamic of alternation in two-state modelling

Although the possibility of alternation between states is framed as fundamental to viable democracy, the dynamics of the process is not explored in the light of the patterned elegance of dance (Embodying Values Dynamically through Alternation, 2008; Warp and Weft: Governance through Alternation, 2002; Alternation between complementary policy conditions, 1995).

Question: There is a curious aspect to the conventional focus on "two-state" in many domains, in addition to resolution of territorial disputes, in that the "static" is emphasized in contrast to any "dynamic" with which the two states may be associated -- especially where the concept is used in domains other than the geopolitical. There is particular irony to recognition of the dynamic between indifference and arousal in the sexual experience familiar to many -- readily described in two-state terms. Could you comment on that dynamic in general terms in the light of the use of the term beyond the territorial process -- and consequently with unconsidered insights that might be offered to the territorial challenge

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Curiously it is the process of walking which offers special insight into how the constraints of duality are transcended, as noted in a congress on transdisciplinarity (Learning to walk as a metaphor for transcending duality, 1994). The metaphor has been explored otherwise in terms of enactive cognition (Francisco J. Varela, Evan Thompson, Eleanor Rosch, Laying Down a Path in Walking, 2017).

Question: Given the emphasis on the necessity of an interdisciplinary approach to the "two-state" challenge, could you comment on the relevance of the most familiar two-state dynamic, namely the alternation in human leg movement in walking

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Question: That response could be adapted further to apply to a fundamental characteristic of democratic government by its framing of the ability to derive its healthy appropriateness by alternation of control between distinctive political parties -- with the "opposition" as a source of vital feedback. Such adaptation could offer further insights into a "two-state" solution

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Dramatic reframing eliciting cognitive engagement

Question: Any such framing from an especially engaging dramatic perspective then evokes the question of what makes a drama interesting potentially in contrast to the boredom engendered by the conventional dynamics between political parties, for example. How many "plots" can then be usefully recognized and labelled in the light of Polti's Thirty-Six Dramatic Situations. These also frame the question of what roles are brought into play and which roles are mysteriously missing to render the drama meaningful in an aesthetic sense, with potential implications in practice

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Question: In the light of those responses, the value ascribed to the drama characteristic of major works of art (opera, cultural epics, etc) frames the question as to why binary dynamics are not regularly "translated" into those frameworks as is becoming ever more feasible with AI thereby offering a new language (and criteria) in terms of which they can be discussed and appreciated.

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Question: As the primary drama for many, what could the development of relational diversity in practice (LGBT) imply by analogy (or as a metaphor) to "two-state" geopolitical relations between "states" -- heterosexual, homosexual, bisexual, pansexual, asexual, demisexual, queer -- given the dynamics between states and the frequent use of sexual jargon to describe them

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Question: Given the drama and the tragedy of sexual violence, the metaphorical framework offered above as a lens for the exploration of "two-state" possibilities merits further exploration in the light of the sexual jargon frequently used behind the scenes to frame the relation of a dominant partner to a weaker partner in any geopolitical relationship

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Linguistic and cultural implications of "two-state"

Question: The term "two-state" is a very particular grammatical construct in English. Given the importance of the concept in countries with languages very distinct from English (Arabic, Hebrew, Chinese, Korean, etc ), is there any trace of the implications of the translation of the term in those languages, potentially even due to problematic associations with dualism -- as with "nongovernmental"

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Question: Given that "two-state" features widely in the scientific literature unrelated to the Israeli-Palestine territorial issue, does this result in the evocation of other nuances. Is it the case that in Korean and Chinese that this would be especially affected by their "two-state" territorial disputes

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Question: In contrast to the potentially problematic impacts of the geopolitical usage of "two-state" in some languages, is there any trace of subtler understanding of two-state relational dynamics in cultures other than English -- and especially in Chinese in attaching fundamental significance to the yin-yang relation

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Questionable role of religion in reinforcing unfruitful two-state frameworks

Over centuries religions have cultivated two-state thinking in their articulation of "good" versus "evil". This framing has extended to their complicity in the violent exemplification of that relationship by their adherents -- as most recently evident in Gaza. Despite the fundamentlal value they associate with transcendental unity, interfaith discourse has never been of a nature to address their dissociation -- matter appropriately framed by Stephen Prothero (God is Not One: the eight rival religions that run the world and why their differences matter, 2010).

Question: Religions have strong commitments to framing binary dynamics in terms of archetypal engagements between the forces of light and those of darkness. The particular irony is that each religion tends to frame itself as identical with the "forces of light", with other religions then necessarily "forces of darkness". Given the considerable investment by their respective theologians in the transcendental unity characteristic of deity as they comprehend it, how is it that they are so inadequate in reframing binary dynamics more fruitfully.

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Potential reframing of two-state by mathematical theology and mathematical epistemology

Especially intriguing is the seeming fundamental "two-state contrast" between religion and theology, although both attach fndamental importance to the implications and symbolism of number -- especially 1, 2, and 3. The relationship is variously explored (Philip J. Davis A Brief Look at Mathematics and Theology Humanistic Mathematics Network Journal, 27, 2004, 14; Mathematical Theology: Future Science of Confidence in Belief, 2011; Sarah Voss, What Number is God? Metaphors, Metaphysics, Metamathematics, and the Nature of Things, 1995; T. M. Nishad, Mathematical Theology: A New Approach, International Journal of Mathematics Trends and Technology (IJMTT), 67, 2021, 8).

Question: Whilst the constraining role of theologians may indeed be evident, more curious is the role of the many iconic mathematicians with deep religious convictions. This frames the question of their ability as mathematicians to reframe binary dynamics more fruitfully especially the relation between "good" and "evil". The discipline of mathematical theology would seem to merit particular attention as a contribution to the quest for elusive "common ground" and effective transdisciplinarity beyond tokenism

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Question: Given that "two-state" can be associated with "binary", is there a possibility of exploring patterns of "two-states" instead of assuming it is a "singular" condition. There are several well-recognized binary patterns, most obviously that which was at the origin of binary computing, namely the set of 64 hexagrams of the I Ching. Reference is made to "binary" in relation to the periodic tale of chemical elements -- as in binary compounds, binary nomenclature, and binary decomposition of elements. Could elements themselves be considered to be binary in nature, especially given the particular importance of the relationship between electrons and protons. Would this then suggest that the periodic table is effectively a table of two-states -- or is it the set of binary compounds which could be more readily understood in that light.

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Question: Should "two-state" be considered a particular instance of a larger set of binary patterns. Of relevance would then be the study of local binary patterns, as a type of visual descriptor used for classification in computer vision. Of related interest would be the Morphological segmentation of binary patterns (Pattern Recognition Letters, 30, 2009, 4). Do relationships more generally invite morphological exploration as binary patterns.

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If a fundamental challenge to a binary "two-state civilization" is one of elaborating a "pattern of two-states", a valuable point of departure is the traditional Chinese Shao Yung circle associated with the origin of binary computing. Efforts have also been made -- controversially -- to relate the pattern of 64 hexagrams to that of 64 genetic codons as indicated in the image below (Fernando Castro-Chavez, Defragged Binary I Ching Genetic Code Chromosomes Compared to Nirenberg’s and Transformed into Rotating 2D Circles and Squares and into a 3D 100% Symmetrical Tetrahedron, Journal of Proteome Research, 1, 2012, 3; Martin Schonberger, I Ching and the Genetic Code, 1992; J.F. Yan, Biomathematics Derived from the I Ching, Advances in Human Factors/Ergonomics, 20, 1995)

With each triplet understood as a "state", the double triplet of the hexagram offers an indication of one distinct two-state condition of which there are then 64. Especially intriguing with respect to the triplet and the hexagram is the various ways in which the line coding may be read and interpreted in relation to any number system. Thus the hexagram may be read with the "top" facing inward, or facing outward -- the outer ring of trigrams may then represent the lower trigram of each hexagram, with the inner ring representing the upper trigram (or the reverse).

With respect to the numbers which may be associated with the line coding, there is a choice to be made between a pure binary representation or the traditional I Ching numbering system.

Such a choice implies that any effort to associate numbers with the circular arrangement of hexagrams can offer several variants each with their implications.

Circle of hexagrams surrounded by a circle of codons
Circle of hexagrams surrounded by a circle of codons

The prevalence of 8-fold patterns, together with their cognitive and strategic coherence, has been discussed separately (Clarification of 8-fold strategic patterns with ChatGPT, 2014; Comprehensible Configuration of 8-fold Psychosocial Patterns in 3D, 2024). The use of metaphor in alluding to the subtle connotations of 8 distinctive states has also been highlighted (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching), 1997) That exercise was applied tor sustainable dialogue, vision, conferencing, policy, network, community and lifestyle.

Question: Using the 8 trigrams to distinguish 8 conditions or "states" then calls for a set of distinctions between the 8 ways a state might participate in a two-state geopolitical arrangement -- with the second state having 8 corresponding modalities. What is required is the most general formulation of those 8 distinctions -- as they may apply in other domains. Can you comment on how that 8-fold pattern might be described -- especially given the Chinese use of metaphor to that end.

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Question: Whilst this describes the octants, in two-state terms each of those conditions would be modified by the other seven and reinforced by one. This then distinguishes the 64

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Recognition of dynamics of 64 two-state pattern with AI?

It could be considered curious that whilst there is a periodic table of chemical elements, there is as yet no clarification of any potential psychosocial analogue by which the pattern of "two-states" might be reframed (Periodic Pattern of Human Knowing, 2009).

Question: Given the history of the development of the periodic system which has only gradually been completed, that response suggests that there may be some conditions in the 64 which have not been recognized in geopolitical terms (or in other two-state relationships for that matter)

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As a complement to the circular configuration, the four classical tabular arrangements of the hexagrams are presented separately (Strategic Patterns in terms of Knowing, Feeling and Action, 2008) and combined in an experimental animation (Metaphorical frame offered by 8x8 encoding patterns in Chinese tradition, 2008).

Question: A further challenge to understanding the 64-fold pattern is the tabular format which accompanied the Shao Yung circle communicated to Leibnitz. There are in fact four such tabular "arrangements" (King Wen, Fu Xi, Jing Fang, Mawangdui) suggestive of other ways of thinking about two-state patterning

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Question: How indeed might these contrasting arrangements offer particular insights into two-state relationships or systems

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Of further interest are the 81 insights of the influential Tao Te Ching and the 9x9 pattern constituted by the 81 tetragrams (or quadgrams) of the T'ai Hsüan Ching (Tai Xuan Jing) -- inspired by the 8x8 pattern of the 64 hexagrams .(Sustainability through Magically Dancing Patterns 8x8, 9x9, 19x19 -- I Ching, Tao Te Ching / T'ai Hsüan Ching, Wéiqí (Go), 2008; 9-fold Magic Square Pattern of Tao Te Ching Insights experimentally associated with the 81 insights of the T'ai Hsüan Ching, 2006).

Question: Traditional Chinese thinking offers a further patterning system (Taixuanjing) through use of the ternary arrangement giving rise to 81 ternary tetragrams -- characters composed of four lines, with each line either unbroken, broken once, or broken twice. It is intriguing that the 8x8 system and the 9x9 system are consistent with George Miller's The Magical Number Seven, Plus or Minus Two -- but there does not appear to be any corresponding 7x7, 6x6, or 5x5 system.

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Question: Whilst there have been studies of mathematical theology, seemingly relevant to these points is a focus on mathematical epistemology. However whilst the epistemology of mathematics is considered fundamental to mathematics education [Epistemology of Mathematics, ncatlab, 2022], there seems to be little reference to mathematical epistemology [George Lakoff and Rafael Núñez, Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000]. Can you confirm the need for such a focus

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Question: With respect to your recognition of how the 64-fold pattern might apply to geopolitical two-state arrangements, could you suggest instances of that pattern with specific examples [The examples produced were so interesting, a complete set of 64 was generated as a speculative exercise -- appending a "confidence level" of High, Medium or Low]

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Question: You generated pairs of names for two-state conditions for which Chinese has metaphors in the case of hexagrams. What is the expression that allusively refer to a concept that t defines set of terms that cannot be adequately defined. Memetic nexus, semantic field?

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The descriptors are necessarily to be considered as indicative and calling for debate in relation to traditional labelling and systems terminology. The issue has been separately addressed with respect to an extensive set of value polarities. The examples necessarily call for extensive discussion. No effort was made to engage in iterative refinement of the initial list of examples, nor to challenge the selection in any way -- as is an obvious future possibility. Of particular interest is the use of gerunds rather than nouns in labelling the "states" -- given the "dynamic" that they then imply. If a two-state relationship is primarily a dynamic -- in which the shift between states maybe slow or fast -- this suggests that the pattern might be usefully explored through the metaphor of dance.

Question: In the version of the Shao Yung circle I shared with you, the hexagrams are linked by lines indicative of the transformations traditionally recognized between hexagram conditions as a consequence of changing a single hexagram line (from yin to yang, or the reverse). Rather than a static pattern, this offers the implication that any "two-state" may variously transform into another -- with some transformations being of greater probability than others. As yet to be explored is how the semantic connotations then shift, as is somewhat implied by the array of 16 topological types of René Thom (Structural Stability and Morphogenesis, 1972) -- perhaps collapsible into an 8-fold array corresponding to the trigrams

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Question: Understanding the Shao Yung circle as representing 64 conditions or "voices", with transitions between them as indicated by my variant shared with you, frames the question how could the dynamics of those potential transitions be best recognized in audio visual terms. Additionally, clustered as they are into8 octants inviting comparison with octaves or sets of instruments, there would seem to be scope for composing melodies as recognizable audio visual / symbolic patterns. Definitely a nice challenge for AI

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In the discussion by Peter Joly (A Logical Way of Ordering the Trigrams and Hexagrams of the Yijing, The Oracle: the Journal of Yijing studies, . 2, 2002, 12) reference is made to the Gray code forming a Hamiltonian cycle on a hypercube, where each bit is seen as one dimension. The code is an ordering of the binary numeral system such that two successive values differ in only binary digit -- as with the hexagrams.

Question: With respect to your response concerning an audio visual presentation of the dynamics implied by the Shao Yung circle of hexagrams, a related question would concern how best to present a Hamiltonian cycle through all 64 conditions. This of course recalls the old problem of a knight's move through 64 positions on a chess board. How might that challenge relate to the transformation between the conditions in the circle

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Question: I question the implication of your statements that: In the Shao Yong arrangement, adjacent hexagrams differ by only one line; This creates a natural "neighborhood" structure that could be used to define allowable moves in a Hamiltonian cycle. As in the diagram I shared with you transformations of one line can be to distant hexagrams -- not just those which are adjacent

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Question: What is involved in determining the Hamiltonian cycle

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Question: There is some implication in the literature that the ordering of the hexagrams could be understood as forming a Hamiltonian cycle on a hypercube -- when understood through the Gray code. How might hexagrams be ordered on a hypercube such as to constitute a Hamiltonian cycle

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Question: If indeed a 6D hypercube is required to represent the Hamiltonian cycle linking 64 "two-states", how might the cognitive distortion of that 6D structure be understood through its projection into the 3D configuration of 64 edges of the drilled truncated cube -- which echoes the hypercube configuration to a degree

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Question: Having previously produced mappings of the 64 hexagrams onto the edges of drilled truncated hypercube, in the absence of further insight this could only be done arbitrarily. Does a projection of hexagrams ordered in 6D into such a 3D structure offer any indication of how the mapping in 3D could be best ordered -- possibly with use of alternation in the visualization

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Question: Given the constraints of representing a Hamiltonian cycle of 64 "two-states" on a 6D hypercube, rather than a 3D projection, the possibility of a 2D projection merits consideration in the light of the Knight's Tour. Given the similarity to a 8x8 chess board of the tabular representations of the hexagrams (as noted above), is there any trace of whether the placement of hexagrams in any of those arrays allows for a "Knight's Tour" progression through the conditions -- thereby corresponding to the 6D cycle.

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The AI indicated that the number of closed Knight's Tours on a standard 8x8 chessboard is 26,534,728,821,064 (approximately 26.5 trillion) -- namely where the knight can move from the last square back to the first square. Such tours bear a degree of relationship to diophantine equations and to Ising Hamiltonian models used in the study of phase transitions (Steven A. Abel, et al, Ising Machines for Diophantine Problems in Physics, Fortschritte der Physik, 70, 2022). Where the tours are visually symmetric, the numbers are as follows:

Of potential interest are the visualizations presented by Dan Thomasson, especially in the light of their symbolic connotations (Symmetrical Knght's Tours). It could then be asked whether various traditional tabular arrangements of the hexagrams correspond in any way to a Knight's Tour. As an indicative experiment each of those tabular arrays (from Classical Chinese arrangements of 64 hexagrams in squares, 2008) was used as an overlay on one widely featured animation of an open Knight's Tour, as reproduced from Wikipedia -- as shown below. It is presumably closed tours which are of far greater relevance to the argument with respect to hexagrams, as discussed separately (***)

Experimental use of Knight's Tour with 4 traditional tabular configurations of hexagrams
Fu Xi pattern King Wen pattern Jing Fang pattern Mawangdui pattern
Knight's Tour animation related experimentally to Fu Xi  pattern of hexagrams Knight's Tour animation related experimentally to King Wen   pattern of hexagrams Knight's Tour animation related experimentally to Jing Fang   pattern of hexagrams Knight's Tour animation related experimentally to Mawangdui pattern of hexagrams
Knight's Tour animation by Ilmari Karonen from Wikipedia

Question: The set of 64 "two-states" you provided is a useful basis for discussion but does not include examples involving dominance and submission, or the manner in which the framework might variously apply to Israel-Palestine, China-Taiwan, the Koreas, or Russia-Ukraine.

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Question: It is interesting in its own right that you are able to detect and suggest such examples -- and presumably many more. A complementary challenge would be whether you can detect any of the 64 for which there are no obvious examples -- and therefore might merit a particular degree of attention

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Question: The "Eastern" use of metaphor to render complex and subtle systemic abstractions communicable is seemingly far from the style of "Western" science. It is however appropriate to ask whether, in the contexts in which this "language" is especially familiar, use is made of this lens in exploring the dramatic two-state challenges involving highly problematic "dialogues" -- namely the Koreas and China-Taiwan. Do you have any trace of this

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Question: Although primarily appreciated from an "Eastern" perspective, the "languages" in question (Yi Jing, Taixuanjing, Tao Te Ching) can be recognized as "pattern languages" -- as credibly articulated from a "Western" perspective by environmental designer Christopher Alexander (A Pattern Language, 1977). It is curious that other instances of such a pattern language include both George Polti's Thirty-six Dramatic Situations (from a "Western" perspective) and the (Thirty-Six Stratagems) from an "Eastern" perspective. Do you have any trace of studies endeavouring to reconcile such languages -- if only from a cognitive perspective of the number factors involved in each of them.

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Mythological reframing of two-state dynamics by the humanities?

Question: Given that the problematic challenges of binary dynamics are readily deplored from perspectives more closely associated with the humanities (law, political science, current affairs, etc), rather than from a scientific perspective (mathematics, complexity theory, etc), is there a case for encouraging the reframing of those dynamics through those of mythological deities (war of the gods, etc). Developments of AI, otherwise deprecated as "deep fakes", could be used to reframe protagonists in divine guise and to visualize engaging stories about their complex relationships. This can be recognized as an appealing development of current techniques of political cartoons and satire. Archetypal tales could then offer a form of integrative meta-perspective contrasting with the often alienating presentations of narratives through the media and transcending binary identification

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Collective consciousness and unconsciousness -- a psychosocial two-state dynamic?

Question: Consciousness and unconsciousness are distinguished as two contrasting states. Given their potential psychosocial implications for a collective, could you comment on the relevance of that frame to any "two-state" challenge

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Question: Any comment from a psychosocial perspective must necessarily take account of the manner in which the leading schools of thought in that matter (Jungian, Freudian, Lacanian, behavioural, etc) deprecate each others insight to a significant degree. Could you comment on how each potentially offers insights of particular significance to any two-state model they distinguish

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Question: Do you have any trace of the application of psychological and psychoanlytical frameworks to major ongoing geopolitical conflicts such as that of Israel-Palestine, China-Taiwan, or the Koreas. Is there any trace of efforts to reframe them through new symbols and metaphors by the relevant disciplines -- and why might this have been avoided

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Question: Do you have any trace of psychosocial insights from the associated professions on the tragedy of Gaza -- especially given the the high proportion of Jews in those disciplines, and in the related schools of thought. Also calling for comment is the apparently extreme collective silence of Psychotherapists without Borders, Psychoanalysis without Borders, Psychologists without Borders, Psychologists without Borders, Psychology beyond Borders,  and Psychosynthesis without Borders. Curiously it is only Doctors without Borders who are effectively engaged in the problematic processes so evident in the media

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Question: With respect to Jung's insights into manifestation of the collective shadow in territorial conflict (such as Gaza), could you comment on the article by Michael Gellert (The Eruption of the Shadow in Nazi Germany, Psychological Perspectives: A Semiannual Journal of Jungian Thought, 37, 1998, 1)

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Challenge avoidance through "dialogue" and "interdisciplinary research"?

Question: It would seem that engendering concerted effort and requisite interdisciplinarity in the quest for solutions to complex problems is itself bedevilled by professional understanding of "discipline" in a context characterized by silo thinking. Could you comment on the sense in which a discipline provides an explicit frame for that to which attention should solely be devoted whilst implicitly identfying that which is irrelevant and to be avoided. That is reminiscent of the "flat Earth" framings of centuries past and the indication on maps of "there be dragons".

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Question: In response to the challenges of binary thinking and unfruitful dualism, proposals are typically made for "interdisciplinary research" and "dialogue". Given their apparent inadequacy in practice, to what extent should such proposals be recognized as questionable displacement and therefore suspect as an avoidance of any quest for more appropriate methods

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Psychosocial inertia and procrastination in response to the two-state challenge

Question: Whether "evil" or "ignorance", a peculiar aspect of any remedial response recommending what "ought" to be done, or "should" be done, is the manner in which these are associated with inertia and procrastination. Ironically it would seem that why these themselves go unresearched by disciplines which engage in those assertions is deemed to be beyond their mandates. Such inertia is treated as a matter of indifference however vigorously it may be deprecated. Even more curious are the many specific references to "evil" by leadership then failing to allocate any of the resources at their command to addressing it specifically as a root cause.

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Question: Could you comment on the sense in which humans could be said to dwell in a "two-state civilization" -- exemplified, by rich-poor, happy-sad, pleasure-pain, love-hate, like-dislike, kind-cruel, good-evil, and the like. These can be understood as calling into question any inference that the "two-state solution is dead"

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References

Christopher Alexander. A Pattern Language: towns, buildings, construction. Oxford University Press, 1977.

Ruth Gavison (Ed). The Two-State Solution: the UN Partition Resolution of Mandatory Palestine (Analysis and Sources). Bloomsbury, 2013

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

Darrell A. Posey. Cultural and Spiritual Values of Biodiversitya complementary contribution to the global biodiversity assessment. United Nations Enviroment Programme and Intermediate Technology Publications, 2000 [comments]

Nicholas Rescher:

Society for the Psychological Study of Social Issues. Psychologists' Response to the Violence in Gaza. 2024 [text]

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

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