Radical recursivity of cognitive implications of topology and geometry

Systemic Coherence of the UN's 17 SDGs as a Global Dream (Part #3)

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Strategic organization in checklists: The argument here is extensively illustrated below by the use of polygonal and polyhedral forms which are the preoccupation of geometry and topology. Curiously this preoccupation tends to be unrelated to the manner in which strategies of governance are articulated -- or the manner in which institutions and communications are organized. It is however of greater relevance to the organization of computer memory (Torus interconnect -- as used in supercomputers, 2019).

Strategies tend to be articulated in checklists strangely constrained by particular numbers -- without any explanation of why a set of any given size "works":

• 8: notably including the Buddhist Noble Eightfold Path, and "imitations" in physics and policy analysis, as well as the Millennium Development Goals of the UN
• 10-foldness: Habitual use of a 10-fold strategic framework? (2020)
• 12: Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources (2011)
• 14: 14 Grand Challenges for Engineering in the 21st Century of the National Academy of Engineering
• 15: 15 Global Challenges of the Millennium Project
• 16: 16 global challenges identified by Policy Horizons Canada (The Next Generation of Emerging Global Challenges, Horizons, 19 October 2018).
• 17: Sustainable Development Goals of the UN
• 20: Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights (2018)
• 30:  Universal Declaration of Human Rights

A sense of geometry is recognized in metaphoric references to "institutional geometry" -- but without any use whatsoever of that discipline in the design of institutional architecture (variable geometry, "multi-speed Europe") . The discipline has however some limited applications in table seating arrangements, the design of processions and parades, and military configurations. The elements distinguished in such strategies may well be recognized as "topics" of concern -- but without any reference to the discipline which shares the etymological origins of the term, namely topology. It is especially ironical in that, as the method of topoi, topics are fundamental to memorability and the techniques of enhancing it (Sara Rubinelli, Ars Topica: the classical technique of constructing arguments from Aristotle to Cicero, Springer, 2009; Frances Yates, The Art of Memory, 1966)

Mapping strategies in 3D: It is possible to engage in exercises through which any set of strategies can be represented in three dimensions -- mapped onto polyhedra -- rather than in one-dimensional checklists:

• Identifying Polyhedra Enabling Memorable Strategic Mapping: visualization of organization and strategic coherence through 3D modelling (2020)
• Psychosocial Implication in Polyhedral Animations in 3D (2015)
• Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors (2008).

To some extent such exercises can be compared to the symbolic preoccupations of sacred geometry or to the insights associated with projective geometry (Olive Whicher, Projective Geometry: creative polarities in space and time, 1986). However the concern here is how the well-defined sets of distinctive operations associated with geometry or topology may be understood as having a degree of cognitive correspondence with the disparate elements of a set of strategies or concepts.

Radical recursion: This operational approach raises the question as to whether there is a radically recursive approach to engagement with both any topological configuration and any configuration of strategies. This is potentially consistent with the arguments of George Lakoff and Rafael Núñez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000). This would then offer the possibility of reframing the comprehensibility, memorability and coherence of complex strategies -- and the cognitive engagement with them.

Recursive has a mathematical significance. From a cognitive perspective it raises the question of degrees of cognitive self-reference -- potentially irrelevant to mathematicians (Hilary Lawson, Reflexivity: the post-modern predicament, 1986). Aspects of the argument are developed by Douglas Hofstadter (I Am a Strange Loop, 2007) in a sequel to his seminal study (Gödel, Escher, Bach: an Eternal Golden Braid, 1979).

For Steven M. Rosen (What is Radical Recursion? Seed, 4, 2003):

Recursion or self-reference is a key feature of contemporary research and writing in semiotics. The paper commences by focusing on the role of recursion in poststructuralism. It is suggested that much of what passes for recursion in this field is in fact not recursive all the way down. After the paradoxical meaning of radical recursion is adumbrated, topology is employed to provide some examples. The properties of the Moebius strip prove helpful in bringing out the dialectical nature of radical recursion. The Moebius is employed to explore the recursive interplay of terms that are classically regarded as binary opposites: identity and difference, object and subject, continuity and discontinuity, etc. To realize radical recursion in an even more concrete manner, a higher-dimensional counterpart of the Moebius strip is utilized, namely, the Klein bottle. The presentation concludes by enlisting phenomenological philosopher Maurice Merleau-Ponty's concept of depth to interpret the Klein bottle's extra dimension

Ole Bjerg (Accelerating Luhmann: Towards a Systems Theory of Ambivalence, 2006):

A radical recursivity is created in which the complexity drop between system and environment can no longer be taken for granted, and in which the very difference between system and environment is in danger of collapsing. This was precisely the problematic I wanted to demonstrate in the Gedankenexperiment above.

Underlying subtlety: The argument here is that the valuable distinctions, so clearly articulated with regard to mathematical operations, are usefully understood as instances of more fundamental cognitive operations which may well be evident in a variety of domains -- under other names. The difficulty is that any effort to name and define such operations within one discipline detracts from the subtler and more general understanding with is thereby denatured. Such definition, however valid on its own terms, is then to be recognized as a form of reification -- a cognitive instance of misplaced concreteness.

The point is usefully made by Christopher Alexander in emphasizing recognition of a "quality without a name" within well-designed environments (The Timeless Way of Building, 1979). For Alexander, this quality is objective and precise, but it cannot be named. This is a central quality which is the root criterion of life and spirit in a man, a town, a building, or a wilderness -- inviting discussion in more general terms (Pattern of transformations as a dynamic quality without a name, 2012).

Spectrum or spectra? A case could be made for presenting the contrast between objective distinctions (as advocated in the disciplines of science) at one end of a spectrum -- a spectrum of recursivity somewhat analogous to the autism spectrum. At the other extreme would be forms of participative cognitive engagement with reality -- readily deprecated from the other extreme as pseudoscientific and highly subjective (Henryk Skolimowski, 1994. The Participatory Mind: a new theory of knowledge and of the universe, 1994;  Darrell A. Posey, Cultural and Spiritual Values of Biodiversity, United Nations Environmental Programme, 1999). Those imbuing significance in icons would then be closer to the latter -- whereas any sense of meaningful  discourse with the features of nature would be even closer.

The difficulty for those claiming preference for either extreme is the extent to which they are obliged to engage in the modality of the other. Thus those preferring subjective engagement are commonly obliged to make objective use of the technology engendered by the other. It is of course common for those depending professionally on an objective perspective to indulge in psychoactive substances in quest of the perspective offered by theo other extreme. 

Jones** degrees of reification concentric 7-fold axes of bias

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