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23rd October 2011 | IN PROCESS

Topological Clues to a Memorable 12-fold Systemic Pattern

 

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Introduction
Imagining a dynamic configuration of relevant "psychopter technologies"
Cognitive implication of  toroidal forms and dynamics
Cognitive implication of spherically symmetrical polyhedra
Cognitive implication of tesseract and related uniform polytopes
Cognitive implication of Mobius strip
Cognitive implication of drilled toroids
Cognitive implication of Klein bottle

Imagining psychopter operating "principles"
Imagining embodiment of psychopter control
Interlocking cycles enabling psychopter operation
Conclusion
References

Annex to Eliciting a 12-fold Pattern of Generic Operational Insights: Recognition of memory constraints on collective strategic comprehension (2011)


Introduction

The main paper argues the need for Experimental clues to a memorable 12-fold systemic pattern (2011) using as a common framework the 12-fold pattern elaborated by Arthur M. Young  with a view to the design of a hypothetical "psychopter" -- a "winged self" (The Bell Notes: A Journey from Physics to Metaphysics, 1979). The possibility was introduced in an earlier paper (Engendering a Psychopter through Biomimicry and Technomimicry: Insights from the Process of Helicopter Development, 2011). Young was the designer of Bell Helicopter's first helicopter, the Model 30, and inventor of the stabilizer bar used on many of Bell's early helicopter designs. His approach to the design of a "psychopter" is inspired by his subsequent aspiration, through generalizing from those technical challenges.

The helicopter had been developed as a result of what subsequently became known as biomimicry (Janine Benyus (Biomimicry: innovation inspired by nature, 1997). The field had emerged in 1950 and was formalized in 2002 as the research network BIONIS: The Biomimetics Network for Industrial Sustainability. As previously argued, Young's subsequent initiative could be fruitfully understood as "technomimicry" -- seeking insight from previous technical discoveries as biomimicry had sought insights from nature. As an exercise in innovative thinking in quest of previously unrecognized capacities, Young's imputation of significance to the elements of the 12-fold pattern in the light of aerodynamics is seen as an indication of a method which can be used with other forms. Here the focus is on topological forms as a sources of clues to the nature of that 12-fold pattern and the relationships between its elements.

In the main paper, emphasis was placed on the manner in which memory and comprehension constrain the scope of any set of operational insights. Given the experiential nature of such insights -- as illustrated by the case of piloting a vehicle -- the complexity of the forms through which they may be variously identified and communicated are recognized as a potential barrier to individual and collective learning and to communication. The following is therefore best understood as a quest for cognitive clues which may be helpfully elicited through the subtleties of topological formalism -- and especially through visualizations offering a sense of the complexity that piloting a "psychopter" may well require. It is a quest for forms of greater complexity, commensurate with the cognitive challenge, with which psychosocial meanings may be associated -- if only for mnemonic purposes.

The main paper emphasizes (in an annex) that other 12-fold sets of clues may be usefully explored for mnemonic purposes, especially by those who are alienated by the forms below (Checklist of 12-fold Principles, Plans, Symbols and Concepts, 2011). .

Imagining a dynamic configuration of relevant "psychopter technologies"

Following Young's assumptions that the schema offers clues to the nature of the operation of the "psychopter" he had imagined, the framework can be tentatively used to interrelate "technologies" potentially indicative of its operation.

The approach taken below is to insert clues to such technologies into the 12 cells of the framework (see Adapting psychosocial insights from learning/action cycles in the main paper), such that the framework as a whole functions as a mental model -- a conceptual holding pattern, however crude that may prove to be. In this sense the framework is not a framework from Young, but rather one suggested by his reflections on the operation and learning challenges of the helicopter -- encouraged by his own mnmonic choices. It is intended as suggestive of "cognitive styles" that might be associated with the hypothetical technologies of the psychopter -- rather than being specifically related to the forms indicated. The preoccupation is not a matter of those forms but rather the patterns of cognitive operations suggested by those forms.

As a design initiative, the focus on "structures" or "patterns" could be understood as a speculative exploration of the "geometrical" path indicated by Christopher Alexander (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) -- and discussed separately (Harmony-Comprehension and Wholeness-Engendering: eliciting psychosocial transformational principles from design, 2010).

The symbols, associated with the physical principles involved in the operation of a helicopter (according to Young) increase in complexity from the upper left portion of the original table to the lower right. To facilitate the following comments, the items added into that framework are presented separately below. The cognitive complexity of "psychopter operation" is then to be understood as increasing in complexity from the upper left to the lower right of the simplified table below. It should be stressed that the purpose is to give a sense of the possible set of cognitive operations as a whole -- recognizing that many arguments and insights could lead to amendment and refinement of the presentation and the items in it.

Inspiration for the development of a "psychopter" might be then be found in a potentially fruitful combination (or configuration) of the following "clues". These are organized as four clusters corresponding to the columns of the original framework -- and inserted into the adapted variant below:

"enabling structure"
(into which whole may be mapped)
"transformative dynamic"
(classes of
transformation)
"imaginative implication"
(confrontation with possibility /
decision / risk / resonance)
"embodiment of insight "
(identification / cognitive dimension )
[1a]
Torus
(continuous surface)
[1b]
process container
(cognitive fusion)
[4a] Mobius strip
(unconventional / paradox)
propulsion / wings
[4b]
paradox
"betwixt and between"
[2a]
Spherically symmetrical polyhedra
(ordered structural integrity )
[2b]
vector equilibirum pumping
(re-configuration of map )
[5a]
Drilled toroids (truncated cube
imbue choice / possibility
(pattern of possible change)
[5b]
control
[3a]
Tesseract
time
(projection into extra dimension)
[3b]
inversion
(inside-out / outside-in)
[6a]
Klein  bottle
digestion / engender
(stepping into the mirror)
[6b]
embodiment
(laying down the path in walking)

Columns: In the discussion which follows, the table is usefully understood as composed of six sets derived from the first two columns of each row, and the last two columns of each row:

Rows: With respect to the organization of the rows, it is appropriate to note the potential cognitive implications of:

Cognitive implication: Given the use of each of these forms as templates on which cognitive significance can be variously "hung" (as "enabling structures"), their comprehension as "maps" then becomes an appropriately suggestive challenge -- especially when a "transformative dynamic" is in operation. It is for this reason that cognitively:

Cognitive implication of toroidal forms and dynamics

[1a] Enabling structure: Toroidal forms, as derived from the circle and intimately related to the sphere, are used here as a surface with which cognitive content can be associated -- onto which it can be variously mapped. Examples, as partially illustrated below, include:

Kalachakra Mandala
(from Wikipedia, enlargement)
Torus
(from Wikipedia)
Global Underground Map
(see enlargement)
Kalachakra Mandala Torus Global Underground Map

[1b] Transformative dynamic: Complementing its role as a mappable "surface", a toroidal form is significant both as a "container" for processes involving flow, and for the vortexes associated with certain flow patterns, as for example:

Animation of blame game
of Knight's moves on torus
Sphere / Torus
transformation
Toroidal design of fusion reactor
(from Wikipedia)
Animation of blame game of Knight's moves on torus Toroidal design of fusion reactor

Cognitive implication of spherically symmetrical polyhedra

[2a] Enabling structure: Spherical configurations of interlocking cycles, as mentioned above, give rise to the emergence of spherically symmpetrical polyhedra of strategic relevance (Configuring Strategic Dilemmas in Intersectoral Dialogue, 1992; Representation of Issue Arenas on Icosidodecahedral Net, 1992). The approach can be extended to the configuration of organizations (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008;  Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance, 2008).

The approach can be further extended to human values (In Quest of Engaging Values: context of the Human Values and Wisdom Project, 2008; Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference, 2008; Psychodynamics of Collective Engagement with Polyhedral Value Configurations, 2008). The argument has also been presented in poster form In Quest of a Strategic Pattern Language: a new architecture of values [also available in PDF].

The cuboctahedron was a central focus of the geometrical and design reflections of R. Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975; Synergetics 2: Further Explorations in the Geometry of Thinking, 1979). He named it the vector equilbirum.

Rhombicosidodecahedral representation
of articles of
Universal Declaration of Human Rights
Icosidodecahedral representation of issue arenas
on a net for Earth Summit (1992)
(see Spherical Representation of Icosidodecahedral Net of Strategies)
Arrangement of 12 Archimedean polyhedra
as a cuboctahedron, around a truncated tetrahedron
(from Keith Critchlow, Order in Space, 1969, p. 39).
[see interactive enlargement and commentary]
Rhombicosidodecahedral representation of articles of Universal Declaration of Human Rights Arrangement of 12 Archimedean polyhedra as a cuboctahedron, around a truncated tetrahedron

[2b] Transformative dynamic:

(Dynamic Exploration of Value Configurations: Polyhedral animation of conventional value frameworks, 2008)

The argument is summarized in a final paper (Embodying Values Dynamically through Alternation: integrating sets of polarized static values through indicative metaphor, 2008).

System duality represented
by transformation between polyhedra

Icosahedron morphing into Dodecahedron
(made with Stella Polyhedron Navigator)
Bucky pumping
Jitterbug
 
Morphing icosahedron  

(Vector Equilibrium and its Transformation Pathways, 1980)

             

Cognitive implication of tesseract and related uniform polytopes

Related uniform polytopes

[3a] Enabling structure:

Representation of 4D tesseract
(reproduced from Wikipedia)
Representation of 4D rectified tesseract
(reproduced from Wikipedia)
Representation of 4D truncated tesseract
(reproduced from Wikipedia)
Representation of 4D tesseract Representation of 4D rectified tesseract Representation of 4D truncated tesseract

[3b] Transformative dynamic:

A 3D projection of a 4D tesseract
performing a simple rotation about a plane which bisects the figure
from front-left to back-right and top to bottom
(reproduced from Wikipedia)
A 3D projection of a 4D tesseract
performing a double rotation
about two orthogonal planes
(reproduced from Wikipedia)
3D projection of a 4D tesseract 3D projection of a 4D tesseract

Cognitive implication of Mobius strip

More provocatively it could be hypothesized that special new demands might be placed on the "pilot" of such a vehicle -- as was discovered in the case of the helicopter

Imagining embodiment of psychopter control

imagination au pouvoir

With respect to the last two columns of the above table

: As an apparently simple, readily comprehensible, topological form, the Möbius strip is mentioned here in anticipation of its further significance below. It is relevant to the construction of a Klein bottle as a much more complex form.

[4a] Imaginative "Initiation":

  cogradix  

[4b] Embodiment:

Cognitive implication of drilled toroids

[5a] Imaginative "Initiation"

Fig. 17: Drilled truncated cube -- a polyhedron approximating a torus, with 64 edges
(Variously rotated with selected faces coloured or not)
Fig. 17a Fig. 17b
Drilled truncated cube -- a polyhedron approximating a torus, with 64 edges Drilled truncated cube -- a polyhedron approximating a torus, with 64 edges
Fig. 17c Fig. 17d
Drilled truncated cube -- a polyhedron approximating a torus, with 64 edges Drilled truncated cube -- a polyhedron approximating a torus, with 64 edges

[5b] Embodiment:

Fig. 11: Selected images of the Yi-globe of József Drasny
reproduced with permission from The Image of the Cosmos in the I Ching: the Yi-globe (2007)

Yi-globe of József Drasny Yi-globe of József Drasny
Yi-globe of József Drasny Yi-globe of József Drasny
These images point to the possibility of a correspondence between the spherical organization of conditions of change
and the more familiar understanding of how the Earth, as a globe, is exposed to light and darkness

Cognitive implication of Klein bottle

[6a] Imaginative "Initiation"

Representations of the Klein bottle
Konrad Polthier (Imaging Maths: inside the Klein bottle,
+Plus Magazine
, September 2003;
View Polthier's animated version (997K) or explore his java applet
Screenshot from video of formation of Klein bottle
developed by University of Hannover
(available with others on YouTube)
Klein bottle

[6b] Embodiment:

Conclusion

tuning


Notes:

Fractal organization (Mandelbrot set):

Design Principles -- 15 Alexander

Imagining psychopter operating "principles"

Imagining embodiment of psychopter control

Description of how to -- without necessarily knowing how to embody those principles in practice -- bicycle description, dynamic equivalent of spiral staircase

Embaie Ferrow (The Five-Point Peace Plan: a Weyanized version of Necker's Cube, 2004)

*** fractal 12 ... 144

Clare Graves. Human Nature Prepares for a Momentous Leap. The Futurist, April 1974, pp. 72-87 [text]


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