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Pattern language and polyhedral mapping


Framing Cognitive Space for Higher Order Coherence (Part #4)

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Pattern language: The major insight in this respect has been the work of Christopher Alexander in identifying patterns that frame the "quality without a name" with which a "place to be" is associated ( (Pattern of transformations as a dynamic quality without a name, 2012). For him, a "place to be" in a building or a town is only viable to the extent that it is governed by the "timeless way" (The Timeless Way of Building, 1979). Alexander (and his team) identified 254 interlinked patterns as providing a language by which it could be framed. The approach could be extended to cognitive environments, as argued separately (5-fold Pattern Language, 1984).

Recent surveys of the possibility have been made by Helene Finidori (Patterns that Connect: exploring the potential of patterns and pattern languages in systemic interventions towards realizing sustainable futures, ISSS, 2016; Configuring Patterns and Pattern Languages for Systemic Inquiry and Design, Proceedings of the 25th Conference on Pattern Languages of Programs (PLoP), 2018).

Mapping on polyhedra: A valuable overview of the use of polyhedra for mapping patterns is provided by Ulrich Brehm and Egon Schulte (Polyhedral Maps, In: J.E. Goodman, et al. eds, Handbook of Discrete and Computational Geometry, CRC Press, 2017). This includes mapping onto non-orientable surfaces and convex polyhedra.

The possibility of mapping content (other than the surface of the Earth) onto polyhedra is the subject of a variety of separate discussions with images and animations:

The argument was notably illustrated in the latter through the tentative mapping onto polyhedra of the articles of various charters (Universal Declaration of Human Rights, European Convention on Human Rights, and Arab Charter on Human Rights).

Mapping strategic proposals: Another approach has been taken through the experimental mapping of the elements of strategic proposals onto polyhedra:

A particular consideration is the completely mysterious process through which global strategic initiatives are framed in terms of patterns of N-foldness -- in which the reason for whatever is chosen as N remains unexplained in systemic terms. As an extension of the traditional "laundry list" approach to the articles of international conventions, at best it is claimed to be a matter of political convenience. The size of N is seemingly unquestionable and not subject to further comment -- whether or not it is memorable.

Examples include:

Systemic inexplicability? This suggests the existence of an unexplored (unconscious) process through which psychosocial organization is most conveniently and comfortably organized in terms of the cube -- even to the point of being "locked into" one such pattern or another (possibly described as "feeling right"). The various patterns of strategic articulation can be considered in this light -- if only for mnemonic purposes. Understood in this way, the question is framed as to how systemically complete is any explicit pattern of N-foldness -- whether or not additional elements are effectively implicit.

Unusual (and relatively obscure) leads are offered with respect to N-fold strategic articulations of particular importance. For example:

  • 16-fold: Possibilities include the rationalization for the 16-fold Myers-Briggs Type Indicator or the pattern of 16 Boolean functions associated with truth values in logic and the manner in which these are mapped onto a rhombic dodecahedron.
  • 17-fold: There is a strange possibility that the coherence of a 17-fold pattern might be related, if only unconsciously, to the so-called wallpaper group (or plane symmetry group), namely the mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern; such patterns occur frequently in architecture and decorative art, especially in textiles and tiles as well as wallpaper. It has been proven that there are only 17 distinct groups of possible patterns. Cynically it could however be argued that the 17 SDGs can be understood as "global wallpaper" for decorative purposes.
  • 30-fold: This pattern is fundamental to the argument for syntegrity from a cybernetic perspective by Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994). This featured in a configuration of the Earth Summit issues of 1992 (Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues, 1992).

The question could then be asked how any such locking is reinforced (or exemplified) by typical transformations of the cube into related polyhedra -- then to be recognized as "cognitive locking patterns". Is the simpler and more fundamental structure, the tetrahedron, to be considered "systemically meta-stable" with a greater number of dimensions implied rather than explicit.

The question is discussed separately (Global Coherence by Interrelating Disparate Strategic Patterns Dynamically: topological interweaving of 4-fold, 8-fold, 12-fold, 16-fold and 20-fold in 3D, 2019). The concern has been highlighted in more general terms (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980; Examples of Integrated, Multi-set Concept Schemes, 1984).

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