Framing Cognitive Space for Higher Order Coherence (Part #3)
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Trigram organization: The BaGua mirror is traditionally presented in two circular forms. Of interest here is how that configuration of 8 trigrams can be related to the cubic format basic to the torus fusion approach presented above.
Comparison of octant organization of BaGua trigram system | ||
Octants with signs (according to Wolfram) | 8-fold BaGua of trigrams (according to Sung) | Trigram octant configuration (following Wolfram) |
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Reproduced from Wolfram MathWorld | Reproduced from Z. D. Sung, The Symbols of Yi King or the Symbols of the Chinese Logic of Changes (1934, p. 12) |
Other experimental animations may be used to suggest other ways of comprehending the cognitive dynamics. As shown below, the moving cubes could be understood as the "cognitive tanks" discussed in the preceding argument (Tank Warfare Challenges for Global Governance: extending the "think tank" metaphor to include other cognitive modalities, 2019). That on the left is reproduced from an earlier discussion (Destabilizing Multipolar Society through Binary Decision-making: alternatives to "2-stroke democracy" suggested by 4-sided ball games, 2016; Neglected recognition of logical patterns -- especially of opposition, 2017).
Comparison of octant organization of BaGua trigram system | ||
Animation of virtual variant (wireframe rendering) | Screen shot of virtual reality variant in 3D (solid rendering) | Number of trigram line transformations between nodes |
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Virtual reality variants: vrml/wrl; x3d. |
Correspondences and analogies: A cubic configuration of the BaGua trigrams draws attention to the nature of the correspondences between them, as is evident from the complementarity between the patterns of lines. Of particular relevance to this argument is the distinctiveness of these patterns, despite a degree of similarity. This is further emphasized by the number of step changes across the cubic configuration (above right), from 3 (across the diagonal through the centre) to 1 (along the edge of the cube). Within the cultural framework of the I Ching, these relationships are articulated through poetic metaphors.
Within the conventions of the various disciplines, correspondences and analogies between domains tend to be viewed with suspicion in the quest for articulations which are natural to the particular domain -- and make no reference to other domains. Of interest in this respect are the various theories of correspondences (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007). The latter clarification was elaborated in the light of the role of correspondence in a fundamental mathematical discovery with regard to the so-called monster group (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007). A valuable discussion of the related nature of analogies has been made by Douglas Hofstadter and Emmanuel Sander (Surfaces and Essences: analogy as the fuel and fire of thinking, 2013), as a further development of Hofstadter's earlier work (Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995) and an extension of his seminal work on music and self-reference (GÃödel, Escher, Bach: an Eternal Golden Braid, 1979). The importance of metaphor is specifically highlighted with respect to the creativity of Albert Einstein.
Given the tragically divisive dynamics of global society at this time, despite the desperate quest for coherence and unity, there is a case for reframing that quest as explored here. Rather than an obsessive focus on similarity, there is a case for exploring difference otherwise -- as is otherwise held to be vital to requisite variety in cybernetic terms. Rather than some kind of "similarity engine" through which to engender unity in conventional terms, the argument is for a form of "difference engine" through which an unconventional form of unity might be engendered.
In this sense each of the trigrams can be considered as indicative of an archetypal form of difference. Organized as a cube, as shown above, the toroidal links between the nodes are then indicative of correspondence relationships -- distinct from the forms of relationship typically sought within any conventional framework. The cube is then an archetypal configuration of correspondences.
Various graphical metaphors can be explored to suggest relationships within that framework. Those on the left below use the toroidal links as tunnels though which spheres travel -- suggestive of a form of "interdisciplinary" thinking. A central sphere is added at the origin -- indicative of the confluence of perspectives with which any cognitive integration might be associated. Those animations on the right suggest other design possibilities.
Alternative representations of cubic 8-fold pattern | |||
Spheres in nodes | Animations of edge movement | ||
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Access X3D variant | Access X3D variant | Access X3D variant |
Eightfold way? The cube of nodes in the animations on the left above can be usefully understood otherwise in terms of various 8-fold patterns, most notably those described as an "8-fold way". There is of course no lack of references to an "eightfold way" with which a pattern of octants might be appropriately associated (Reframing an eightfold way by entangling imagination and reality? 2019). These are seemingly inspired in whatever way, mnemonic or otherwise, by the Noble Eightfold Path of Buddhist practices leading to liberation from samsara, namely the painful cycle of "rebirth" (Eightfold Path, aka: Eightfold Way; 5 Definition(s), Wisdom Library). They include include frameworks as fruitfully diverse as:
Of particular relevance to the emphasis on comprehension of psychosocial organization in this argument are other "eightfold ways" through which distinctiveness is credibly recognized:
An obvious concern is the extent to which such articulations are proven, rather than determined by tradition or convenience. The question applies to any articulation of N-foldness to which credibility is attached for some purpose (as discussed further below with respect to "chunking" and sets of strategic goals). This issue is highlighted by subsequent challenges to the replicability of research on which such sets are based, as in the case of multiple intelligences (Lynn Waterhouse, Multiple Intelligences, the Mozart Effect, and Emotional Intelligence: a critical review, Educational Psychologist, 41, 2006, 4; Trenton Knauer, Psychology's Replication Crisis, Areo, 1 October 2019).
Given any sense of "cognitive valence", what chunks are held to "work" in practice by some, irrespective of the existence of proof or its quality. Whether or not proof is held to be required, how solid is the evidence for frameworks such as the following, otherwise deemed to be credible and to "feel right":
Deadly questions and catalysts for creativity:With the nodes of the cube indicative of mutual irrelevance, according to the conventions of the thinking relating to each node, each can be specifically recognized as incompatible or incommensurable with the others -- each an "anathema" to the others. In terms of creativity however, any combination may well prove to be a trigger to creativity through any perceptible analogies or correspondences. The mix may then be recognized as fruitful with the nodes recognized in this way understood as complementary.
One of the difficulties of any given conventional thinking framework -- as curated by the peer review system -- is that any external reference (to another "nodal" domain) tends to be recognized as a "kiss of death" effectively defining the irrelevance of an argument. Succinctly any such reference is a "turn off". It can be understood as killing creativity within the framework of a particular convention. Such a "kiss of death" is perceived as a threat to the coherence of the domain, outside the scope of appropriate comprehension -- perhaps to be framed as characteristic of a pseudoscience. The pattern of claims and counter-claims is intimately related to the dilemmas of "fake news" (Varieties of Fake News and Misrepresentation, 2019).
Unfortunately, but perhaps appropriate for the times, as argued by Jim Baggott:
There is no agreed criterion to distinguish science from pseudoscience, or just plain ordinary bullshit, opening the door to all manner of metaphysics masquerading as science. (But is it science?, Aeon, 7 October 2019)
The distinctive modalities, perhaps to be confirmed by "non-citation analysis", could be understood as "think tanks" -- Cognitive boundaries of cognitive process containers, as speculatively argued (Tank Warfare Challenges for Global Governance: extending the "think tank" metaphor to include other cognitive modalities, 2019).
In the quest for innovation, one approach is the cultivation of "nasty questions", typically disruptive to practitioners of a given discipline (Checklist of 'Nasty Methodological Questions' -- regarding development analyses and initiatives, 1981; In quest of the most deadly question, 2013). In the current period of global crisis -- seemingly beyond the capacity of conventional thinking -- the uncomfortable, unasked questions merit particular attention (Coping Capacity of Governance as Dangerously Questionable: recognizing assumptions and unasked questions when facing crisis, 2019).
Design of a "difference engine" for innovation? In this light, there is a case for confronting a set of differences as a means of engendering creativity transcending the preoccupations of a particular domain.
Mapping of distinctive preoccupations onto 8-fold supercomputer/BaGua schematic | |
The pattern of the "conceptual model" of the supercomputer, as depicted above, may therefore used to distinguish (and map) mutually contrasting nodes as discussed here. The image on the right shows the first two sections of this argument presented as two nodes in that schema. The six other domains, discussed below, are also indicated in that schema. Understood as complementary, the suggestion is that these are potentially related by a pattern of correspondences -- although any such pattern is necessarily tentative at this stage. Whether these are sufficiently distinct to constitute requisite variety remains to be explored. | ![]() |
There are numerous references to unity, global, integration, interdisciplinarity, and the like, as separately profiled (Integrative Knowledge Project). Despite their attraction over decades, the times are most notably characterized by toxic fragmentation of a high order. What then is the "pattern that connects" such distinctive quests for a coherent sense of identity? As articulated by Gregory Bateson: The pattern which connects is a meta-pattern. It is a pattern of patterns. It is that meta-pattern which defines the vast generalization that, indeed, it is patterns which connect (Mind and Nature: a necessary unity, 1979). To which he added in a much-cited phrase: Break the pattern which connects the items of learning and you necessarily destroy all quality.
The question is how to elicit, comprehend or engage with such a pattern, as can be variously discussed (Engaging with Elusive Connectivity and Coherence, 2018; Walking Elven Pathways: enactivating the pattern that connects, 2006; Hyperspace Clues to the Psychology of the Pattern that Connects, 2003). The argument here is that the pattern is of necessity elusive necessitating a complementarity set of cognitive modalities, as otherwise argued by Magoroh Maruyama (Polyocular Vision or Subunderstanding? Organization Studies, 25, 2004, pp 467-480).
The disparate modalities recognized -- with methodologies alien to each other -- may then be explored as suggestive metaphors, implying the need for a form of "discourse through metaphor" (Metaphorizing Dialogue to Enact a Flow Culture: transcending divisiveness by systematic embodiment of metaphor in discourse, 2019). To "make a difference", the argument here is that the metaphors in a difference engine are primarily visual. It is visual metaphors which offer particular advantages in terms of comprehension of the pattern that connect -- and in navigating that pattern.
A degree of recursion is evident in the cubic pattern as explored here in that the elements of that pattern are also of cubic form. Any paradoxical inconsistency with the requisite variety merits exploration in that light.
Understood otherwise, the quest here is for the nature of the design of a "comprehension computer" in which no particular cognitive modality is either primary or dependable. This is somewhat consistent with the Sanskrit adage: Neti Neti (Not this, Not that).
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