Pathway "route maps" of potential psychosocial transformation?

Memetic Analogue to the 20 Amino Acids as vital to psychosocial life? (Part #8)

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As emphasized, the question is the possible psychosocial engagement with the configurations above -- rather than their potentially interesting geometrical and mathematical properties.

The mapping exercises above suggest that it is best to explore the possibility of "route maps" at different layers of complexity -- considering the easier to understand (the "highways"), with which it is possible to engage cognitively, before the potential implications of the more complex (based on less evident relationships).

Polyhedra as processes: In exploring such "route maps", as a metaphor, it is useful to consider that the individual polyhedra are better thought of as dynamic process complexes, rather than as static structures as is the conventional approach to them. Then, beyond their role as "stations" on the map (where it is possible to switch "lines"), they can be thought of as resembling engines or dynamos, in some way, through which the "lines" are enabled with motive power. It is with such reframing that the metabolic role of the 20 proteinogenic amino acids may be fruitfully understood in relation to metabolic pathways by which biological life is sustained -- not as static compounds but as enabling processes.

Buckminster Fuller makes the point that all systems may be understood as polyhedra, the possible corollary that systems may be represented by polyhedra merits exploration. In that sense complex systems could be, in principle, fruitfully mapped onto complex polyhedra such as to highlight vital complementarity and necessary communication patterns (notably feedback loops). For Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975):

• Synergetics is the geometry of thinking. How we think is epistemology, and epistemology is modelable; which is to say that knowledge organizes itself geometrically... (I, 905.01)
• Any conceptual thought is a system and is structured tetrahedrally. This is because all conceptuality is polyhedral. (I, 501.101). By tetrahedron, we mean the minimum thinkable set that would subdivide Universe and have inter- connectedness where it comes back upon itself. (I, 620.03)
• All systems are polyhedra: All polyhedra are systems. (II, 400.56)
• Human thoughts are always conceptually and definitively confined to system considerablility and comprehension....All systems are subject to comprehension (I, 400.07-20)
• Initial comprehension is holistic. The second stage is detailing differentiation. In the next stage the edges of the tetrahedron converge like petals through the vector-equilibrium stage. The transition stage of the icosahedron alone permits individuality in progression to the omni-triangulated spherical phase. (I, 1005.63)
• Dimension begins at four. Four-dimensionality is primitive and exclusively within the primitive system's relative topological abundances and relative interangular proportionment. Four-dimensionality is eternal, generalized, sizeless, unfrequenced. (II, 1033.611)
• All conceptually thinkable, exclusively metaphysical experlencings are fourfoldedly characterized...(systematically, topologically, angularly, numerically). All generalized principles are conceptually thinkable and fourfoldedly definable. Generalization is conceptually (i.e. systematically) imaginable independent of (5) frequency. (II, 1072.22)
• By tetrahedron, we mean the minimum thinkable set that would subdivide Universe and have interconnectedness where it comes back upon itself. (I, 620.03)

Patterns of order: The conventional approach to polyhedra is as patterns of order, hence the title of the study of Keith Critchlow (Order in Space, 1969) from which the configuration above was adapted. The concern here is however with psychosocial life, namely the nature of order in cognitive space -- or with that of the noosphere. It follows that the multi-volume study by Christopher Alexander (The Nature of Order: an essay on the art of building and the nature of the universe, 2003-4) then calls for similar reframing in psychosocial terms. A first exercise to that end was the adaptation of the 254 interlinked patterns as originally elaborated by Alexander (A Pattern Language, 1977) into a similar pattern of psychosocial analogues (5-fold Pattern Language, 1984).

Alexander developed the insights arising from his research in subsequent papers (New Concepts in Complexity Theory: an overview of the four books of the Nature of Order with emphasis on the scientific problems which are raised. 2003; Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole, International Journal for Unconventional Computing (IJUC), 2009). The latter emphasized the need for a geometrical approach, partly justifying the separate argument (Harmony-Comprehension and Wholeness-Engendering: eliciting psychosocial transformational principles from design, 2010). This included sections on:

• Use of pattern language for the material world as a template
• Tentative adaptation of Alexander's 15 transformations to the psychosocial realm
• Systemic comprehensiveness of sets
• Geometrical configuration of Alexander's 15 transformations
• Relevance to global governance in the psychosocial realm
• Associating qualities of harmony and wholeness with geometry
• Beauty as a verb: de-signing the future, human nature and the environment

Basic route map? The following simplified map, based on those above, offers a sense of particular transformational pathways between patterns of order -- in which prime numbers appear to play a determining role as indicated above. The colouring of the "routes" serves to highlight pathways of contrasting significance. Arguably some of the features derive simply from design choices, although the degree of symmetry calls for future comment.

Map highlighting distinctive relationships pathways between spherically symmetrical polyhedra (regular and semi-regular) F=faces, E=edges, V=vertices (Total of these in parenthesis) [Total reduced to prime number, other than 2, in square brackets]

Some points of interest include:

• division of the map into upper and lower portions (ignoring the extent to which 12 is common to both portions):
  • upper (red routes): based on 24 specifically (excluding consideration of 12, whether its divisors or multiples, 36, 48, 60, etc)
  • lower (blue routes): based on 60 specifically (excluding consideration of divisors or multiples, 120, etc)
• central dependence on a 12-fold complex (green routes):
  • those directly associated with the truncated tetrahedron (at the top)
  • those directly associated with the tetrahedron (at the centre)
• particular routes of special relevance to this argument, linking the dodecahedron and the icosahedron:
  • "route 20" (cyan route)
  • "route 30" (yellow route)
• four horizontal routes of potential interest (marked with arrows), deriving from equality of the feature totals of the polyhedra so linked
  • upper route: 37-37
  • central core route: 13-13
  • central route: 61-61
  • lower route: 182-182 (namely 7x13 to 7x13)
• emergence of 37 as fundamental to one horizontal line (at the top), namely as a multiple of 2
• curiosities of potential significance include
  • special "routes" (uncoloured) based on reversed numbers 26 (2x13) and 62 (2x31), each with prime factors significant elsewhere in the map
  • prime numbers "hidden" in other features of the map

Note that other potentially significant relationships could be added to the map above, as with those associated with 19 as a prime number.

Implication of 64 (namely 2⁶): The main paper is focused on the mapping of the 64 codons or hexagrams -- with the mystery of analogues to the "20 amino acids" discussed above. The question might then be asked how 64 is to be associated with the above mappings. As 2⁶, it is of course visibly associated with the truncated tetrahedron in the polyhedral map.

This could also be considered as deriving in part from the manner in which 2, as the first prime, was stripped from the feature totals in order to highlight other prime factors. The stripping of 5 such 2s from the central Platonic polyhedra -- configured around the tetrahedron -- suggests a patterning based on 2⁵, namely 32. A further factor of 2 could be associated with the manner in which the tetrahedron (understood as a process with implied directionality) can be configured in two forms, as argued by Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975) and 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

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