Meaningful cognitive navigation?

Representation of Creative Processes through Dynamics in Three Dimensions (Part #7)

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Sustainability in spherical terms: The challenge of psychosocial sustainability, in "global" spherical terms, is also suggestively indicated by the navigational stability achieved through gimbals, as illustrated in the following animations from Wikipedia. Integral to the operation of governors, gimbals are essential to the stability of any magnetic compass, most notably for the navigation of ships at sea. Metaphorical use of "strategic compass" lends itself to speculative exploration with respect to strategic governance (Global Governance via a Double-breasted Strange Attractor: cognitive implication in a dynamic sexual metaphor, 2009). The dial of such a compass typically indicates a range of intermediate directions between the poles of North and South.

Illustration of a simple two-axis gimbal set; the center ring can be vertically fixed	In a set of three gimbals mounted together, each offers a degree of freedom: roll, pitch and yaw

Such animations recall the design of the time machine which featured so significantly in the science fiction film Contact (1997) based on the novel by Carl Sagan. The early conceptual design of the device was based on one of the primary shapes in geometry, namely a dodecahedron. This was eventually modified to a spherical capsule that encased the traveller -- a "pod" implied by addition of a central sphere in the images above. Does this suggest how the sustainable cognitive navigation of such as Nikola Tesla might be imagined -- somehow "encased" within such a rotational dynamic? Given the relevance of the thinking of Buckminster Fuller to this argument, it is appropriate to note the inspiration he found (when at the US Naval Academy) in the challenge of gunnery targetting in a vessel in turbulent sea -- and the dependence on gimbals of ship gun fire control. This again recalls the framing of policy science by Geoffrey Vickers (Freedom in a Rocking Boat: t: changing values in an unstable society, 1972).

"Constellation language" as pattern language: Such suggestive experiments call for further investigation of how spherical rotation is to be understood in terms of engaging with "constellations" of concepts as meme complexes (Spherical Configuration of Categories to Reflect Systemic Patterns of Environmental Checks and Balances, 1994). As explored by Beer, this would have implications for enabling discourse (Spherical Configuration of Interlocking Roundtables: internet enhancement of global self-organization through patterns of dialogue, 1998). Could Tesla's preoccupations be fruitfully understood in terms of constellations of concepts he perceived -- and engendered -- from within his universe of knowledge?

The recognition of constellations as a form of pattern language can be used to relate the above argument to the much-cited work of Christopher Alexander (A Pattern Language, 1977; The Nature of Order: an essay on the art of building and the nature of the universe, 2003-4). The former can itself be used experimental as a template for the detection of "constellations" of memes, as separately explored (5-fold Pattern Language, 1984). With respect to conceptual order, Alexander's work resulted in his articulation of New Concepts in Complexity Theory (2003). He has developed this in ann unusual manner (Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole. International Journal for Unconventional Computing (IJUC), 5, 2009). Through his recognition of 15 patterns of transformation, his work suggests the possibility of adapting these from a cognitive perspective, as separately explored (Tentative adaptation of Alexander's 15 transformations to the psychosocial realm, 2010; Harmony-Comprehension and Wholeness-Engendering: eliciting psychosocial transformational principles from design, 2010; In Quest of a Dynamic Pattern of Transformations, 2012).

As noted in that respect, given the discussion above of the icosahedron for mapping purposes, it is intriguing to note that the simplest polyhedron with the geometric properties that could "hold" these 15 transformations is the icosahedron through its 15 great circles -- as indicated in the Wolfram Demonstration Project of a dynamic variant by Sándor Kabai (Fifteen Great Circles on a Sphere). The intimate cognitive relationship between "constellations" and "patterns" call for further investiogation. The preoccupation of this argument is however the challenge to comprehensibility of configurations of patterns as the number increases beyond George Miller's Magic Number Seven, Plus or Minus Two (1956), through 12, to 15 and beyond. This is especially challenging if the number of cognitive "metabolic patheways" for sustainability is of higher order, as discussed separately (Comprehension of Numbers Challenging Global Civilization, 2014).

Meaningful cognitive navigation: There is no conventionally acceptable reason why patterns of a particular configuration are held to be meaningful and to "work" -- as exemplified by golden rectangles favoured in design. This is further exemplified in the case of 12-foldness (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011). However, from the mathematical perspective appreciated by Tesla, these are each recognized to have distinctively valuable properties -- as with 12, 9, 8, 7, 6, 5, etc. Sets of concepts are typically clustered assertively in such patterns (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980).

The "missing link" is between how a given pattern is believed to be meaningful in a particular case and any formalism offered by mathematics -- typically completely indifferent to the cognitive and psychosocial implications. It is this link which is vital to transcending widespread reliance on the default pattern of polarity -- with all the dysfunctional us-and-them consequences. This is especially disastrous when simplistic patterns are reinforced by simplistic theological considerations with regard to necessary belief. Hence the potential role of mathematical theology (Mathematical Theology: Future Science of Confidence in Belief, 2011)

With respect to this argument, it is the manner in which "charged" conditions derive from various polarities -- most obviously "positive" or "negative" -- can be reframed by such metaphors. These then constitute vehicles to "carry" comprehension (Metaphors as Transdisciplinary Vehicles of the Future, 1991; Discovering Richer Patterns of Comprehension to Reframe Polarization, 1998). Especially intriguing, given Tesla's preoccupation with the sphere in relation to energy, is how spherically symmetrical polyhedra (like the icosahedron) then function as approximations to a sphere. The simplest such polyhedra are the most readily comprehensible, but are far from the approximation to a sphere offered by the more complex forms (necessarily far less comprehensible), whereas -- paradoxically -- a sphere is readily held to be inherently comprehensible, even a symbol of simplicity.

Such considerations frame possibilities for exploration in relation to global governance, constrained as it is by the "energy" of polarizing mindsets (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008; Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008).

An argument has been made for seeking to benefit from the wisdom of non-western cultures (Susantha Goonatilake, Toward a Global Science: mining civilizational knowledge, 1999). In the case of Chinese culture, consideration could be given to mapping a more complex set of insights, as systematically articulated in the I Ching, onto polyhedra of relevant complexity, as argued separately (Toroidal mappings of wisdom questions and answers, 2012). One example is reproduced below. Of relevance to the theme of creativity here is its explicit encoding within that pattern and recognition of the manner in which it variously plays out through the dynamics of change and associated decisions. The mapping below suggests the possibility of a cognitive compromise between "complexity" and "simplexity" from the perspective of the controller of the "vehicle".

Drilled truncated cube of 64 edges with I Ching hexagram names (some faces rendered transparent)

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