Enabling software for insight packaging

Enabling Wisdom Dynamically within Intertwined Tori (Part #9)

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The exploration of cognitive possibilities and implications of "packaging wisdom" is enormously facilitated by the Stella: Polyhedron Navigator software application developed by Robert Webb, from which the above images were generated (as with many polyhedra in Wikipedia). Its potential relevance to structures of governance has been discussed separately (Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008).

However the static imagery reproduced here fails to convey its function as a catalyst to imaginative consideration of possibilities when interactive use is made of its many dynamic features and of the numerous possibilities for their export into other formats (video, 3D imagery, etc). Potentially of great significance is the transformative "morphing" between topologically related structures -- surely offering vital possibilities for the comprehension of  transformations between  psychosocial structures of great complexity. The application enables access to hundreds of such structures -- a cognitive resource as yet virtually unexplored. In a period when governance is faced with engaging with time in new ways, any application which explicitly offers access to 4D projections (such as some examples above) merits careful attention.

It is all too readily assumed that "we" are about to agree on a worldview and a course of action in response to the emerging crises of the times. There is little evidence that this will be the case, as discussed previously (The Consensus Delusion: mysterious attractor undermining global civilization as currently imagined, 2011). This raises the question of how to integrate or eliminate alternative (and mutually hostile) perspectives. The US has exemplified this cognitive stance, ironically articulated by the policy "you're either with us or against us" (Us and Them: Relating to Challenging Others, 2009).

Of greater potential is the ability to engage dynamically with the set of alternatives. This could be understood as the implicit ideal of "democracy" -- severely distorted by emphasis on the static oversimplification of the singular perspective resulting from a majority vote at a moment in time. This only offers the momentary illusion of unity -- consensus as a delusion.

The extensive range of variously interrelated polyhedra offers a way of holding a wide range of alternatives -- dynamically. The dyamics can be understood as alternation between disparate forms, as most obviosuly implied by the ideal of democracy in its richer sense. The range of possible geometrical transformations between alternative worldviewes is what merits exploration.

Especially interesting in this respect is the distinction between:

• forms capable of holding distinct insights through resonance
• forms related by transformational morphing of their geometry, as containers for alternative worldviews
• alternative ways of understanding polyhedral features as cognitive templates for a set of insights.

Cognitive "feel": The last emphasizes the contrasting cognitive "feel" of an insight variously associated with:

• a point or vertex as a nexus of relationships, namely the fundamental sense of a "crossroad" between different ways, notably offering a point of view -- perhaps experienced as an advantageous overarching "overview". As a place, crossroads have always offered a focus as a gathering point around which communities formed -- often with protective fortification
• a line as a vital relationship between distant points or conditions, notably evident in strategic articulations of "My Way" -- the insight into the how of viable change from Condition A to Condition B. This has always been valued as a "way" of relating, as exemplified by the sense of "correspondence" and the dilemma of whether to move in one direction or the other. The protection of a "way" or "route" has long been a strategic preoccupation.
• an area defined by a set of intersecting lines as boundaries, and offering a stable sense of a protected territory. Insight is then more particularly associated with a "field" of action -- as a "face" turned to the world.

These associations offer the implication that the cognitive relationship between them might be fruitfully explored in terms of the Euler characteristic, which for any convex polyhedron's surface has:

V - E + F = 2 (where V = number of vertices, E = number of edges, and F = number of faces)

The Euler characteristic for a sphere is also 2, as it is for spherical polyhedra.

Potentially this offers an unusual approach to the exploration of cognitive perspectives, worldviews and belief systems.

The software mentioned above enables selection and exploration of polyhedra based on any number of such elements. It also enables selection of polyhedra based on the number of internal "cells", namely three-dimensional elements which (as volumes) are part of a more complex polyhedron. This is indicative of a fourth mode of cognitive identification with an insight, as separately discussed (Metaphorical Geometry in Quest of Globality, 2009; Geometry of Thinking for Sustainable Global Governance, 2009; Geometry, Topology and Dynamics of Identity, 2009).

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