Towards a geometry of systemic thinking and its symbolism

Exhortation to We the Peoples from the Club of Rome (Part #10)

[Parts: First | Prev | All] [Visuals] [Links: To-K | From-K | From-Kx | Refs ]

Geometry of thinking: An approach such as that described above necessarily derives much of its inspiration from the extensive pioneering work of Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975), as discussed separately (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009).

However, beyond the capacity to map the complexity of any complex strategic proposal lies the question of how people can engage with its meaning as an incitement to action -- in the spirit proposed by Come On! Other than through its reference to education, this dimension is neglected in the report. Arguably it is more closely associated with how people engage with a "psychoactive" symbol -- as with those of the Abrahamic religions -- as may be variously discussed (Symbolizing Collective Remembering Otherwise: encompassing the "headless hearts" and "heartless heads" through their dynamic entanglement, 2018; Reconciling Symbols of Islam, Judaism and Christianity: catalytic methodology for effective interfaith dialogue, 2017; Cognitive Implications in 3D of Triadic Symbols Valued in 2D, 2017).

The question is summarized otherwise by John Gaboury (Tetrahedral Geometry and the Psyche: Implications of Natural Geometry for Typology, the Structure of the Unconscious, and Wholeness, The Jung Page, 2004). It is of course a feature of the significance associated with mandala-type structures as psychoactive mapping devices in their own right, as may be variously discussed (***). Could, or should, the elements of the Club of Rome report be presented as a new form of mandala?

Quantum reality: Conventional considerations of the meaning to be associated with geometrical configurations can now be fruitfully challenged by speculative reflection on quantum consciousness, as notably articulated from an international relations perspective by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015; video; interview). The implications are discussed separately (Quantum consciousness implications of fundamental symbol patterns, 2017; Paradoxes of communicating fundamental insight through metaphor, 2017).

Prior to such considerations, Buckminster Fuller considered the manner in which the tetrahedron (understood as a process with implied directionality) can be configured in two forms, as depicted below. For Fuller:

Tetrahedron as Vectorial Model of Quantum: The tetrahedron as a basic vectorial model is the fundamental structural system of the Universe. The open-ended triangular spiral as action, reaction, and resultant (proton, electron, and anti-neutrino; or neutron, positron, and neutrino) becomes half quantum. An association of positive and negative half-quantum units identifies the tetrahedron as one quantum.

Tetrahedron as vectorial model of quantum (according to Buckminster Fuller)

Such thinking offers a provocative challenge to the 3-fold organization of the Club of Rome report -- especially given the absence of any systemic consideration of countervailing insight, too readily simply deplored as resisting appropriate social transformation -- even as "sin". From a psychosocial perspective, Fuller's depiction of "fundamental structure" might then be (very tentatively) labelled as follows -- inviting speculation on the analogues to the 6 quantum processes in relation to the 3 Club of Rome sections and their hypothetical "antitheses".

Tetrahedron as vectorial model of "quantum-based strategy"?

Speculative elaboration of central image above

On the assumption that the triadic organization of the Club of Rome report lacks systemic dimensions (as articulated), the suggestive cyclic approach indicated above can be speculatively applied to the integrative understanding of the central image above. The cycles may then be understood as feedback loops of some kind. A cycle can then be associated with each of the four faces of the tetrahedron. These distinctively coloured cycles then offer the suggestion of broken or incomplete portions -- with the incomplete portions indicated by dotted lines. The complete portions then relate to the three sections of the Club of Rome report. The framing of the three sections in the Club report, can clearly be challenged in systemic terms as calling for a far more fundamental indication of their distinctive roles -- and how they might relate to the metaphors offered by the quantum terminology. Of particular interest is of course the nature of the three unnamed processes and how these may be neglected, implicit or unconscious in the articulation of the report. The question relates to the arguments of John Ralston Saul (The Unconscious Civilization, 1995; Voltaire's Bastards: the dictatorship of reason in the West, 1992)

Oppositional symbolism? As noted above, the argument can be developed in terms of oppositional logic with respect to a 4-dimensional polyhedral configuration of directions (Neglected recognition of logical patterns -- especially of opposition, 2017).

In the quest for a means of engaging otherwise with the ("pathological") obsession with one pole (the "positive") of a binary, there is a case for deriving insight from the highly innovative rotational approach of Nikola Tesla to the relation between positive and negative in electromagnetic terms (Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014; Potential implications of alternation and rotation in psychosocial fields, 2014; Encycling positive and negative for future sustainability, 2014).

In the quest for higher orders of integration and comprehensibility, the image above recalls speculation with regard to the symbolism of the Star of David understood as a particular unfolding into 2D of a tetrahedron. This association has the merit of offering indications as to the nature of all six systemic processes, even if they are expressed in mystical terminology. The possibilities are all the greater in that other speculation sees the Merkabah -- a star tetrahedron (or stellated octahedron) -- as a 3D variant of the Star of David, as can be variously discussed and illustrated (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017).

To the extent that the distinction of 12 unsustainable trends (section #1) and 18 strategic initiatives (#3) is indicative of some unrecognized coherence, it is appropriate to note that these can be effectively mapped onto a compound of 3 tetrahedra (rather than the 2 of the star tetrahedron). This has 18 edges, 12 faces and 12 vertices -- as with its dual. As mapped below, this could be the most compact visualization -- despite setting aside the segments of the second section. Of course the question is whether the labels could be more meaningfully positioned to highlight systemic patterns.

Mapping of Come On issues onto 3-tetrahedra compound (12 vertices="unsustainable trends"; 18 edges="strategies")

(Animations prepared using Stella Polyhedron Navigator)

Sustainable Development Goals: The report makes extensive reference to the UN's Sustainable Development Goals (47 citations), although it is strange that no reference is made to the early report to the Club by Ervin László (Goals for Mankind, 1977) -- especially given the latter's emphasis on the human dimension and the defensive arguments (1.2) with respect to the The Limits to Growth of that same period. Other than their articulation as a checklist, the SDGs are typically depicted as a flat tabular pattern of images, although a proposal has been made to depict them as a flat thematic pyramid. None of these formats offers a systemic sense of the complexities of their interrelationship -- to the extent that these are even recognized or seen as a challenge.

There is a strange sense that an assumption is made that strategic remedies to the global condition can be achieved through what might be caricatured as "keyhole analysis" and "keyhole surgery" -- each condition calling upon the insights of particular specialists, as with the contributors to particular segments of the report. Provocatively it can be usefully asked whether, as framed, humanity is in great danger of scoring an "own goal" -- rather than achieving them as envisaged.
.
The polyhedral argument can however be applied to their memorable symbolic organization through mapping them onto a cube with which "we the peoples" can variously engage (Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful, 2017).

Requisite integrative complexification? In a period in which major investments are made in research and development in domains far beyond simplistic comprehension, it is ironic that the nature of strategic reports like that of the Club should be characterized by oversimplification. Or, rather than "oversimplification", the disparate elements of the report -- and their essentially linear arrangement -- are indicative of a complexity which cannot be contained within conventional "conceptual containers" of commensurate simplicity. The design of more appropriate containers is not however recognized as a challenge. It is in that sense that there is a case for borrowing from the quality of thinking and articulation which is engendering such containers in the natural sciences -- despite the questionable posture of such as Alan Sokal.

It is in this sense that there is a case for continuing to explore the relevance, as an ordered articulation of the most fundamental insights in process of elaboration -- in this case of the Standard Model of Elementary Particles explored with such intensity by physics. The possibility is discussed separately (Beyond the Standard Model of Universal Awareness: Being Not Even Wrong? 2010; Metaphorical Insights from the Patterns of Academic Disciplines: learning from the Standard Model of Physics? 2012; Multiplicity of relational conditions and any "standard model", 2018).

Of relevance to this discussion is the extent to which metaphor (as an aid to comprehension) is explicitly associated with the Chinese encoding -- cited above with respect to the 8-fold BaGua pattern) -- as with the 64 hexagrams of the I Ching, and the 81 tetragrams of the Tao Te Ching and of the T'ai HsÜan Ching (TÀi XuÁn Jing). Such metaphor is evident in the effort to associate a comprehensive integrative cognitive engagement with features of familiar experience by which global governance is notably challenged. This includes psychosocial relationships, environmental categories ("earth", "air", "fire" and "water"), or especially their interrelationships (Douglas Hofstadter and Emmanuel Sander, Surfaces and Essences: analogy as the fuel and fire of thtinking, 2013).

The approach is also relevant to the above argument in that traditionally such patterns are associated with clarifying the relationship between "Earth" and "Heaven". Meriting careful attention are the many correspondences explored in the work of Frank Dodd Smith, Jr. (McKay Correspondence between Physical World and Mental World, 2010)

As argued in this regard, the following figure positions a complete set of tetragrams such as to correspond to the pattern of the standard model of particle physics -- notably presented as a simple "box", in the light of the concern here with geometrical metaphors. Although the pattern of tetragrams has a degree of internal coherence corresponding to that of the standard model, as a tentative exercise it is merely designed to encourage reflection on any more appropriate ordering. A degree of resmeblance to variations of the Rubik cube, and to the pattern of SDGs, suggests the kind of exploratory engagement required for its "resolution" as a meaningful pattern.

The order of rows and/or columns could be changed -- as was done in a second iteration, when columns 2 and 4 were switched to approximately more closely to the criterion of a magic square and its coherence.

Correspondence between distinctions of the standard model and a pattern of tetragrams?

Such configurations could be fruitfully seen as a challenge to the 3-fold or 4-fold articulations of strategic preoccupation at this time. How are problematique, resolutique, imaginatique and irresolutique to be understood as cognitively related with respect to global strategy -- especially given both the aspirations and denial with which they may be variously associated -- and the "goals" by which they may be informed?

Comprehension as inherent in higher dimensionality implied by symbols: The assumption is too readily made by the report that conventional strategic "language" can encompass the complexity with which humankind is confronted -- in a manner which is comprehensible and credible. The question is how the formulation of strategic challenges has the potential for eliciting engagement and action -- rather than alienation and indifference. It could however be assumed that the arguments with regard to complex polyhedral symbols and quantum reality are similarly unable to elicit comprehension and engagement. This ignores the sense in which symbols can have motivational potential through implying insights of a higher order accessible to the intuition -- if not to ordinary reason. That point has been made with regard to poetry by Gregory Bateson in explaining why 'we are our own metaphor', to a conference on the effects of conscious purpose on human adaptation:

One reason why poetry is important for finding out about the world is because in poetry a set of relationships get mapped onto a level of diversity in us that we don't ordinarily have access to. We bring it out in poetry. We can give to each other in poetry the access to a set of relationships in the other person and in the world that we're not usually conscious of in ourselves. So we need poetry as knowledge about the world and about ourselves, because of this mapping from complexity to complexity. (cited by Mary Catherine Bateson, Our Own Metaphor, 1972, pp. 288-289)

The report frequently refers to one of the Club's earlier reports by one of its collaborators (on segment 3.3), namely Gunter Pauli (The Blue Economy, 2009), and to the Blue Planet Prize, This recognizes outstanding efforts in scientific research or applications of science that contribute to solving global environmental problems. Arguably there is however a curious complementarity -- recognized by poets but yet to be fully recognized by science -- between the "external environment" and the "internal environment" within which motivation and engagement are engendered, as can be variously argued (World Introversion through Paracycling: global potential for living sustainably "outside-inside", 2013). As argued above, "global" has "internal" as well as "external" implications -- appropriate to any consideration of a "global brain".

It is therefore appropriate to note the "symbolic" complementarity with a seemingly unrelated preoccupation which is discovering the remarkable possibility of cognitive processes involving higher dimensional forms, in the light of emergent neuronal connectivity in the human brain. As summarized:

Using mathematics in a novel way in neuroscience, the Blue Brain Project shows that the brain operates on many dimensions, not just the three dimensions that we are accustomed to. For most people, it is a stretch of the imagination to understand the world in four dimensions but a new study has discovered structures in the brain with up to eleven dimensions - ground-breaking work that is beginning to reveal the brain's deepest architectural secrets..... these structures arise when a group of neurons forms a clique: each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object. ...

The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner. It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates. (Blue Brain Team Discovers a Multi-Dimensional Universe in Brain Networks, Frontiers Communications in Neuroscience, 12 June 2017)

The suggestion can then be made that theoretical possibilities for the optimum memory architecture of supercomputers might point to unusual ways in which the brain currently "rewires" itself -- using complex symbols as catalysts and triggers -- as a basis for "hypercomprehension" (Imagining Order as Hypercomputing: operating an information engine through meta-analogy, 2014; Prefix "Re-cognition" as Prelude to Fixing Sustainability -- "Pro" vs "Con" ? Speculative review of missing emphases potentially vital for psychosocial balance, 2017).

By what complex symbols should a Club of Rome report be accompanied to engender hypercomprehension and new new modes of action?

[Parts: First | Prev | All] [Visuals] [Links: To-K | From-K | From-Kx | Refs ]