Indicative clues from other distinctive 16-fold mappings?

Coherent Reconciliation of Eastern and Western Patterns of Logic (Part #6)

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In discussion of logical opposition, Fabien Schang (An Arithmetization of Logical Oppositions, The Square of Opposition: A Cornerstone of Thought, 2017) makes reference to "blatant analogies" between the pattern of logical connectives and classical Chinese thinking. A related point is made by Jeffrey Z. J. Zhen, in presenting a binary logic framework whose function elements are invariant under permutation and complementary operations (Variant Logic Construction Under Permutation and Complementary Operations on Binary Logic, Variant Construction from Theoretical Foundation to Applications, 2019).

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). The chaos of the times could be said to merit recognition of "monstrous moonshine" and the need for correspondingly "monstrous" possibilities.

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).This section is amended from one on Deprecation of potential correspondences: 16-fold patterns? in a discussion of recognitionof assumptions and unasked questions when facing crisis (Coping Capacity of Governance as Dangerously Questionable, 2019).

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, and how might any such set get "reduced" to 14 in practice? Especially with respect to systemic understanding of the challenges of governance, why:

• With respect to systemic insight:
  • "16-fold table method" of evaluating rival causal hypotheses over time -- the Lazarsfeld Sixteenfold Table (Ronald C Kessler, Rethinking the 16-fold table problem, Social Science Research, 6, 1977, 1; Otis Dudley Duncan, New Light on the 16-Fold Table, American Journal of Sociology, 91, 1985, 1)
  • the 16-fold way now seemingly recognized, beyond the various "8-fold ways" (Ken K. W. Ma, et al, The sixteenfold way and the quantum Hall effect at half-integer filling factors, 2019; Paul Bruillard, et al, Fermionic modular categories and the 16-fold way, Journal of Mathematical Physics, 58, 2017) o which only 9 have been considered possible (Marvellous Onuma-Kalu, et al, A classification of open fermionic Gaussian dynamics, 6 February 2019)
  • the 16 types of discrete multivariate transforms (Adam Brus, et al, Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions, Entropy, 2018)
  • the 16 traditional approaches to mathematical operations (Sixteen Ancient Principles Solving Difficult Mathematics, Vedic Maths)
  • the 16 healthy systemic principles identified by Elisabet Sahtouris (Organizational and Operational Principles of Healthy Living Systems, In: EarthDance: Living Systems in Evolution, 2000)
  • the 16 systemic mega trends (James Wayne, Arrow of Time Phenomena in Social Science and Sixteen Global Mega Trends of Human Society, SSRN, 2014).
  • the 16 principal changes of topological type according to René Thom (Structural Stability and Morphogenesis: an outline of a general theory of models, 1972), namely archetypal morphologies understood as related to elementary catastrophes
  • the 16 stage process of generation of tensegrity structures through the adhesion and fusion of tensegrity cells defining a self-stress space (Omar Aloui, et al. Cellular morphogenesis of three-dimensional tensegrity structures, Computer Methods in Applied Mechanics and Engineering, 346, 2019, April)
• With respect to psychosocial systems:
  • the 16 living principles (George Fewquay, Sixteen Successful Living Principles and Explanation, 2013)
  • the 16 personality types according to the Myers-Briggs Type Indicator, now widely cited (Linda V. Berens and Dario Nardi, The Sixteen Personality Types: descriptions for self-discovery, 1999)
  • the 16 Personality Factor Questionnaire (16PF), namely a self-report personality test developed from the empirical research by Raymond B. Cattell,
  • the 16 types of diversity (Understanding Diversity and Inclusion, FutureLearn)
  • the 16 types of higher educational institutions (Daniel James Rowley and Herbert Sherman, From Strategy to Change: implementing the plan in higher education, 2004)
  • the 16 types of emptiness and the 16 types of compassion identified within the Kalacakra tradition of Buddhism (Vesna Wallace, The Inner Kalacakratantra: a Buddhist tantric view of the individual, 2001); presumably associated with the 16 types of meditation (Nichiren Buddhism Library)
  • the 16 types of wealth accumulation (J. C. Cooke, Traditions of Wealth: sixteen principles for accumulating and protecting your personal wealth, 1990)
  • the 16 types of wealth identified in the Hindu tradition (Ashta Lakshmi: Bestower of Sixteen Types of Wealth; What are the 16 types of wealth mentioned in Tamil tradition? Quora)
  • the 16 principles for peace (James W. Prescott, Sixteen Principles For Personal, Family and Global Peace, The Truth Seeker, March 1989)
  • the 16 principles for building harmony (Sixteen Principles for Building a Sustainable and Harmonious World, Four Worlds International Institute)
  • Sixteen points on which the Bishops accuse the Lollards (Anne Hudson, Selections from English Wycliffite Writings, 1978)
• With respect to patterns and design:
  • the 16-fold patterns of importance in Islamic architecture
  • the 16-pointed star of the CIA emblem
  • the 16 patterns frequently used in guitar chord playing (Nozomiko Yasui, Sixteen types' chord label estimation from acoustic signal of electric guitar, The Journal of the Acoustical Society of America, 140, 2016, 3380).
  • the 16 types of hand gestures (Kaoning Hu and Lijun Yin, Multiple feature representations from multi-layer geometric shape for hand gesture analysis, IEEE, 2015).
  • the 16 Principles of Urban Design (as applied in the GDR)
• With respect to information processing:
  • the 16 types of content considered relevant to content management systems and artificial intelligence (Ronald Maier, Knowledge Management Systems: information and communication technologies for knowledge management, 2007)
  • the 16 types of operations on directories and files (Auditing of Cluster Administration and Operations on Directories, Files, Tables, and Streams, MAPR)
  • the 16 quality dimensions affecting the reliability and authenticity of electronic records (Erik Borglund, A Predictive Model for Attaining Quality in Recordkeeping, 2006).
  • the 16 types of learning from a perspective of knowledge utilization (Claire Dunlop and Claudio M. Radaelli, Systematizing Policy Learning, SSRN, 26 August 2010)
  • the 16 types of feedback (Daniel Keeran, Sixteen Principles of Feedback and Criticism December 2018; Daniel Keeran, Sixteen Principles for Understanding Scripture, November 2016)
  • the 16 principles for breaking bad news (Sixteen Principles for Breaking Bad News, The Washington Post, 10 October 1995)
  • the 16 types of opinion makers identified by James Rosenau (Philip J. Powlick, et al, Defining the American Public Opinion/Foreign Policy Nexus, Mershon International Studies Review, 42, 1998, 1)
  • the 16 Vedic principles for evaluating knowledge (16 Principles of Nyaya)
  • the 16 Precepts for Acquiring Knowledge of Thomas Aquinas
• With respect to strategic management and business:
  • the 16-point marketing plans, for which there appears to be a degree of preference? (Mike Schultz and John Doerr, Sixteen Principles of Influence in Sales, SalesGravy)
  • the 16 supply chain types no recognized (James B. Ayers, Supply Chain Project Management, 2009)
  • the 16 types of alliances (Peter Simoons, Sixteen Types of Alliances, 2004)
  • the 16 types of business meetings (Elise Keith, The 16 Types of Business Meetings (and why they matter), Lucid Meetings Blog, 23 September 2017; Sid Gupta, Enabling "Impossible" Meetings, Knowtworthy Blog, 27 May 2018)
  • the 16 community banking principles (Grameen Bank's Sixteen Decisions, USAID, 1995)
  • the 16 principles of evangelism (B. E. Underwood, Sixteen New Testament Principles for World Evangelism, 1988)
  • the 16 types of strategies in management (Types of Strategies, ZeePedia)
  • the 16 diagrams indicative of viable system modelling (John Stephens, A Set of Conventions, a Model: an application of Stafford Beer's viable Systems Model to the strategic planning process, Systemic Practice and Action Research, 24, 2011, 5)
  • the 16 types of financial portfolio management (Gary Scherling, The Sixteen Principles of Portfolio Management, 2015)
  • the 16 principles of logistics (Chris Paparone, Huston's Sixteen Principles: assessing operation performance during OP Desert Storm, Logistics in War, 18 August 2017)

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:

• A Digital Single Market for Europe: Commission sets out 16 initiatives to make it happen (6 May 2015)
• 16-point Earth Charter (Earth Charter Initiative, 2000)
• China to ban 16 types of solid waste from end of 2018 (EFE, 19 April 2018)
• The Sixteen Points: guidelines for the Great Proletarian Cultural Revolution [of China] (1966)
• Iran lays out 16-point war plan for the supreme goal of toppling Netanyahu (Debka File, 23 February 2019)
• Four parties defend 16-point agreement (The Himalayan Times, 20 June 2015)
• 16 Point Agreement between the Government of India and the Naga People's Convention (United Nations Peacemaker, 26 July 1960)
• 16 Points of the Alt Right (2016)
• Hitler's Sixteen Point Peace Plan (1 September 1939); Hitler's Sixteen Points. The Newcastle Sun, 1 September 1939)

The predominant global strategic configuration in the form of the UN's 17 Sustainable Development Goals (SDGs) suggests the need for extensive reflection on the means of rendering that framework memorable and meaningful at this time -- as the upgrade of the UN's earlier 8 Millennium Development Goals (Systemic Coherence of the UN's 17 SDGs as a Global Dream, 2021; Memorability of 17 Sustainable Development Goals with 169 tasks, 2020).

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).

A particular mystery relates to assumptions regarding Goal 17, namely the Partnership for the Goals, and how this might be understood, as previously discussed (Eliciting Potential Patterns of Governance from 16 Sustainable Development Goals, 2022; Towards a configuration of 16Â SDGs in 3D, 2022). This explored Goal 17 through a polyhedral compound of 16 tetrahedra in 3D, notably presented as an interactive virtual reality model (Experimental interactive animation of a 16-tetrahedra complex of UN SDGs in 3D, 2022).

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

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