28th May 2008 | Draft
Polyhedral Pattern Language
Software facilitation of emergence, representation
of psycho-social organization
- / -
Also available in a PDF
version for printing convenience. Sequel to Towards
Polyhedral Global Governance: complexifying oversimplistic strategic metaphors (2008).
Associated with: Polyhedral
Empowerment of Networks through Symmetry: psycho-social implications for organization
and global governance (2008), Configuring
Global Governance Groups: experimental visualization of possible integrative
relationships (2008) and Configuring
Global Governance Groups: experimental animations and video sequences (2008)
PART A: Polyhedral mapping experiments and use of Stella Navigator
-- Focus and psycho-social relevance
-- Currently relevant features of Stella
-- Possible additional features
-- Possible applications relevant to psycho-social organization
-- Pattern language
-- Test applications
-- Mapping possibilities with regular polyhedra
PART B: Future extension to tensegrity representation
-- Psycho-social operationalization of polyhedra through tensegrity representation
-- Process of use
-- Multi-dimensional heuristic work space
-- "Cognitive circuits"
PART C: Meta-patterning considerations from other cultural perspectives
-- Patterns as enabling emergence of a "quality without
-- Quality of space as a central challenge of governance
-- "Spirit of team": vibration and resonance
-- Insights from Chinese culture
-- Pattern dynamics: change, alternation, resonance
-- Possibilities of "variable geometry" in psycho-social
-- Comprehension of strategically appropriate patterns through
the fourth dimension
-- Homeostatic equilibrium: necessary "human sacrifice" to the "gods"
CONCLUSION: "Globality", viability and
The significant problems we face can not be solved at the same level of thinking
we were at when we created them (Einstein)
Learning: Governance needs a new language?
Part A is effectively a commentary on the polyhedral exploration software
Stella Navigator, produced
by Robert Webb (Stella:
Polyhedron Navigator. Symmetry:
Culture and Science, 2000); a helpful overview of
the application is provided in Wikipedia. Its most recent version
provides unique access to polyhedra in both three and four dimensions. Demo
versions (3D or 4D) may be downloaded free of charge;
manual is available.
The commentary follows from a recent study of the relevance of polyhedra
to global governance (Towards
Polyhedral Global Governance: complexifying oversimplistic strategic metaphors,
Here "polyhedral" is specifically used to convey
the need to explore "many-sided" forms of psycho-social organization.
These constitute an integrative challenge of governance from the world to
the local level -- if not to personal self-governance and identity. In that
respect "global" is also to be understood in its integrative sense
of a "whole"
and not only in its geo-political sense of world-wide (cf Future
Generation through Global Conversation: in quest of collective well-being
through conversation in the present moment, 1997) .
The concern here with polyhedra dates from work within the context of the
Union of International Associations in the period 1997-2000 on the online,
multi-media, interactive representation of complex networks of international
organizations, world problems, global strategies and human values, notably
developed from 1972 within the Encyclopedia
of World Problems and Human Potential. The later work formed part
of a project funded by the European Commission (Ecolynx:
an information context for biodiversity conservation, 1997-2000)
and subsequently evaluated positively by the World Bank for a development
Interactive Contextual Environmental Planning Tool for developing countries,
1998). In that period various experiments were undertaken to enable online
users to associate particular portions of such networks with polyhedra
in virtual reality (VRML) in order to facilitate their comprehension and
as a point of entry to text profiles of the entities in the networks. Those
in Figures 1 and 2 below were generated online directly from the databases,
for example. Although the databases are still online --
some being freely accessible -- the
transfer to a new platform has meant that these experiments are no longer
A range of these facilities is described elsewhere (Information
Visualization and Sonification: displaying complexes of problems, strategies,
values and organizations, 2001). The concern here however is to identify
concrete possibilities and applications for the future.
Part B considers the possible future extension of Stella to tensegrity
representation. Part C evokes a range of meta-patterning considerations,
notably from other cultural perspectives.
PART A: Polyhedral mapping experiments and use of Stella Navigator
Focus and psycho-social relevance
It should be stressed that the Stella software has been primarily, if
not uniquely, developed for exploration of the geometry of polyhedra. Any
associated possible uses in the above context are therefore incidental.
The purpose of this commentary is to determine how it may already be used
for the exploration of psycho-social organization and how it might possibly
be extended to facilitate further explorations of that kind.
The argument for the use of polyhedra has been developed in the earlier
Polyhedral Global Governance: complexifying oversimplistic strategic metaphors,
2008). Basically the argument is that governance of any kind is cognitively
challenged by the complexity of the psycho-social oranization that needs
to be ordered and comprehended. Use of hierarchical organization charts,
bullet points and simple mind maps is not adequate to the complexity and
need for coherence.
Polyhedra, especially those of higher complexity, offer
representational devices onto which complexity can be projected in such a
manner as to enhance mnemonic possibilities and a sense of transformational
potential -- especially when these are reinforced by properties of regularity,
symmetry and appropriately variegated colouring. The concern in what follows
is therefore with the use of polyhedra as "conceptual coat-hangers" (integrative
memory aids or "cognitive prosthetics") and how the features of
the Stella applications might be used for such purposes -- now or
in the future..
The focus here is therefore both on how the application can be currently
used for that purpose and how it might be extended in support of other uses.
Additionally there is the question of whether such an application suggests
unforeseen approaches to facilitating the emergence, representation and transformation
of psycho-social organization (whether groups, organizations, networks, problems,
strategies, concepts or values).
This focus on facilitating psycho-social organization, its emergence
and representation (especially through symmetrical polyhedral forms of tensegity),
depends on the confluence of several essentially independent lines of investigation
-- some of which have been unfortunately inhibited by intellectual property
rights. These are:
- the purely mathematical (geometrical) representation of polyhedra on
which symmetrical tenesgrities are based,
- the analysis of non-linear dynamics typical of tensegrities
- the challenges of tensegrity for architects in the construction industry
- the implications for concept formation associated with the work on conversation
theory and interaction of actors, based on the prismatic tensegrity
- the implications of spatial metaphors in physical space for the organization
of cognitive and social space
The relevance is foreseen in relation to:
- emergence and support for "polyhedral" forms of "global" governance,
as previously argued (Towards
Polyhedral Global Governance: complexifying oversimplistic strategic metaphors,
- emergence and support for new forms of organization, in which third order
cybernetics is consider significant, as previously argued (Consciously
Self-reflexive Global Initiatives: Renaissance zones, complex adaptive
systems, and third order organizations, 2007)
- emergence and support for new forms of virtual organization within social
network and gaming environments, because of the potential there for early
uptake and dynamic development, for reasons noted elsewhere (Engaging
with popular games, 2008), encouraging such uptake in virtual
networks of excellence where issues of collective intelligence are significant
of the Future: for networking through think-tanks, 2005)
- cognitive significance of the spherical metaphor in dialogue (Spherical
Configuration of Interlocking Roundtables: Internet enhancement of
global self-organization through patterns of dialogue, 1998),
in ordering knowledge (Spherical
Configuration of Categories -- to reflect systemic patterns of environmental
checks and balances, 1994), in funding flows (Spherical
Accounting: using geometry to embody developmental integrity,
2004), and in learning spaces (Coherent
Organization of a Navigable Problem-Solution-Learning Space,
|Figure 1: Mapping of problems and
organizations onto selected polyhedra in virtual reality
(extract from Exploring
Intelligible Associations: integrative modes and metaphors,
as presented to the German Research Centre for Artificial Intelligence)
|Selected issues relating to "discrimation
||Selected components of the "EU system"
|Figure 2: Selected screen shots
(click on each for navigable version in virtual
reality; possibly with the free
browser Cortona plugin
-- available for PC,
X, and Pocket
PC platforms --
mouseover nodes or faces for entity names;
hotlinked to text profiles)
|Interlocking world problem loops
displayed as a "polyhedron" of intersecting planes
||Clusters of interlocking problem loops with links between them
||International organizations mapped
onto faces of an (incomplete) spherical polyhedron (larger file, slow
Currently relevant features of Stella
The general features are detailed in the original paper by Robert Webb (Stella:
Polyhedron Navigator. Symmetry: Culture and Science,
2000). They are of course presented in detail in the current help
with the applications.
The following is a commentary on features of special interest that enhance
the mnemonic function that might prove significant
in various institutional and strategic design situations:
- selection/deselection: Faces or vertices of a polyhedron
may be independently selected for subsequent operations.
- 2D/3D network mapping: Polyhedra may notably be represented
- 3D form, which can be rotated, enlarged, etc
- 2D form, as a map of the faces (net map)
- The two forms may be positioned in facing screen windows with some
changes made to one then reflected in the other.
- colouring: A complete sepectrum of colours may be used
to distinguish faces according to various schemes. It
is less evident to what degree the transparency can be increased
to view through a polyhedron
- images: Application of images to faces is excellent.
This could already be used to represent on an appropriate polyhedron::
- logos of organizations collaborating
in a coalition
- faces of representatives, stakeholders, sponsors, collaborators
in a collective endeavour
- faces of organization members, contacts or friends in a network
- faces of participants in a meeting
- This is the basis for any relevant web page, allowing the global
representation of such organization to be explored with a virtual reality
- A list of images may be submitted for random allocation to faces
of a selectged polyhedron.
- labelling: Having selected a face or vertex, text may
be associated with it in two ways:
- using "Edit->Text
for Face/Vertex (or using Ctrl+T). Lengthy labels do
not wrap within the face (and why should they). The labels stay
upright when the structure is rotated.
- applying text already converted into an image (as described above),
presumably allowing more text in a wider range of formats. But
the image would then not remain upright on rotation.
- Typical labels might include names of:
- people (contacts, collaborators, friends, etc)
- organization units, collaborating organizations, sponsors
- problems and elements of a problem
- strategies and components of a strategy
- values basic to an ethical charter
- on-the-fly vs pre-set images/labels: A distinction
could be made in practice between:
- a pre-selected polyhedron to whose faces and/or
vertices images and/or labels were associated
- a polyhedron selected in a meeting (say), to which labels and/or
images were variously attached
- a pre-selected polyhedron whose pattern of labels and/or images was
then modified in the meeting (adding extra people, stakeholders, etc)
- between structures: Morphing from one structure
to another (notably duals) has been implemented in a variety of ways.
It is not yet clear what happens to labels in the process. However with
respect to transformation between two arbitrary forms, this cannot
be done in Stella
- from 2D to 3D: Flat net structures can
already be folded (morphed) into the 3D variant -- and vice versa.
One practical example of this challenge is illustrated by the use of
the icosidodecahedron net structure as a mapping
of strategic challenges
from the Earth Summit (Rio de Janeiro, 1992) [image***]
The above representation suggests a distinct between:
- "incommensurable" thematic concerns encoded by the 6 "great
used in the 1992 exercise: P = population, security; W = well-being, health;
L = learning, education; T = trade, production; E = environmental, impacts;
R = regulation, equity (Inter-sectoral
Strategic Dilemmas of Sustainable Development)
- the various specific issue areas (encoded here as keyword-labeled triangles),
which emerge from the interplay between any three of those themes
(P, W, L, T, E or R); expanded
descriptions of each triangle are provided separately (Significance
of 3-domain Dilemma Codes)
- the distinct and relatively complex arenas (encoded here as
unlabelled, or transparent, pentagons), possibly to be considered as the
dialogue environments in which some reconciliation is
sought between the 5 associated (triangular) issue arenas -- relatively
unconstrained, in each case, by the absence of one of
the 6 great circle themes
Framed in this way, it is how the configuration of elements offer a degree
of integrity to the variety of otherwise fragmented elements in the global
debates (cf Spherical
Configuration of Interlocking Roundtables: Internet enhancement of global
self-organization through patterns of dialogue, 1998).
Possible additional features
There are clearly several options in this respect:
- additional features incorporated into subsequent releases of Stella
- separate modules (plug-ins) for optional use with Stella.
In this case the approach is to get a module to work for a particular
class of polyhedra, as with geodesics, and thereafter to build
up plug-ins for various interesting classes of polyhedra.
- development of a distinct variant of Stella for
the organization of data
- export to third party packages: Stella already
provides for export in a variety of forms. The question is what might be
the input constraints on other packages
It is important to recognize the prime function of Stella in considering
such options. Such changes might simply complicate unnecessarily a well-honed
application. One alternative is of course to allow users to select additional
tool bars for facilities unrelated to the primary function -- such as some
Labelling and images: As it currently functions, Stella ensures
that colours, labels and images "stick" to surfaces to
a very useful degree when rotated, etc. However, colours seem to stick over
a wider variety of transformations -- including morphing -- than labels or
images. Colours are also appropriately reflected in both 2D and 3D versions?
It would be convenient if labels and images applied to a face in 2D net
representation could be preserved rather than lost when the image is folded
into 3D. To what degree can labels and images be preserved
through a greater variety of transformations
External links: These could be of various types:
- links to external
web pages: Hotlinking
from faces or vertices is not currently provided.
- links to sound files: An interesting possibility is
to active a sound file associated with a particular face or vertex --
perhaps a key statement or commitment by a stakeholder
- links to other applications: These might include PPTs
associated with progress reporting of an organization associated with a
particular face or vertex.
All such links would currently require significant effort
to export from Stella to VRML and might therefore be more appropriate
in a separate application.
Identification of usable representations: With respect
to on-the-fly input, one interesting feature would be to be able to call
up (and/or select) a list of polyhedra with user-specified numeric properties,
based on numbers of faces, edges, and/or vertices. Whilst polyhedra may
be selected by type through a drop down menu, and many properties of any
selected polyhedron are listed, there is no apparent means to search on such
As an alternative, there is of course the Wikipedia List
of uniform polyhedra, presented in tabular form, with images
(in fact created using Stella) and with links to entries in
Wikipedia on each. The table permits polyhedra to be identified
by numbers or faces, edges or vertices. However the tabulation only includes
a small subset of the polyhedra available through Stella. In
Wikipedia the typology
of uniform polyhedra
is usefully described
Thus if one had an organization with N major divisions, what
polyhedra might one project (map) it on to -- in terms of faces, edges or
vertices? Could the user run through a proposed list of possible "good
make a selection?
How might one distinguish between primary features and secondary
features, namely if each division had sections, how might these be attributed
to smaller faces, etc? Or is the divisional level to be associated with groups
of faces appropriately shaped and coloured?
sets of linked entities: In the earlier online exploration, a set
of linked entities was imported (effectively as output from a search process
by keyword) and then fitted, according to a (crude) algorithm. The
interface then allowed the user to intervene in the process (see image ***).
- The question is what kind of input format might be processed
by such an algorithm -- clearly things could be made more or less sophisticated.
That version put face or node labels into mouseover for VRML display and
provided for hotlinking. Traces of this are still evident in the
Java spring map version currently operational online.
- More interesting is the possibility to import an organizational
nested hierarchy structure (line by line), or more generally a formatted
network (links indicated to other nodes from each line), with a text label
(for mouseover display) and possibly a URL (for hotlink). Input formats
of this kind are common for network analysis and organization chart display
- Given the variety of entities that might be so input as a list (possibly
of files), consideration could be given to distributing them across the
Already Stella provides for inputting a list of images to be randomly
distributed to faces on a selected polyhedron.
- randomly: as is currently done for colours in "rainbow mode" --
thereby extended to a list of images, sound files or labels, or possibly
all three (CSV delimited) since they are not incompatible on a surface
- ordered/clustered in some way (in the light of the following discussion
on matching) -- raising the question of cognitively meaningful design
metaphors for such distribution
- One of the possibilities, if the image has directionality and it is not
feasible to turn it as the polyhedron is rotated (as is currently done
with the label), is to provide for a means of turning the polyhedron so
that the image on a face is upright
- Another possibility is to envisage a parallel split screen window (substituting
for the net map, for example) in which items of information from such an
imported list, and relating to each (numbered) face or vertex, could be
listed in note form. The items so listed might include: name, geographical
base, fund allocation, date, e-mail, etc. Whether this is open to editing
in that mode, prior to subsequent export, could be considered. It might
be easier to organize hotlinking such a parallel display.
With an easy input of a nested hierarchy of an organization structure,
or array of nested strategies, this would enable a quick flip into
a really integrative polyhedral overview of the initiative. Presumably outputs
in a corresponding format might be made. One example of these approaches
is the application Decision
Matching and "fitting": Implicit in the previous
point is the issue of how best to "fit" the
structure to an appropriate polyhedron, or possibly a set of alternatives
amongst which the user can choose or switch.
Clearly solutions vary greatly from simple
to very difficult depending on how good a match is required. Issues include:
- Ability of the user to specify the goodness of fit, or accept a default
- Preference would clearly be for a polyhedron with as much symmetry
as possible, but some numbers are easier to match to high-symmetry polyhedra
- Acceptance of blank faces where fitting cannot be achieved. Indeed one
variant originally developed in VRML had either blank faces,
or possibly an incomplete polyhedron where fitting could not continue --
or where the user specified a more complex polyhedron than was necessary
- Complexes of faces: With respect to nesting, clearly several approaches
might be taken:
- the smaller (secondary) face approach (mentioned above)
- ability to allocate standard sets of faces (eg a pentagon surrounded
by squares on edges and triangles at vertices) to portions of a hierarchy
or to a network with particular local connectivity
- representing each nesting by a different polyhedron, whereby
clicking on a face would display a nested polyhedron of a lower hierarchical
Clearly links should not be assigned to faces that share an
edge, which would make a solution impossible most of the
Concentric polyhedra: The possibility of having concentric
polyhedra (that could be displayed in wire-frame mode or with relatively
high transparency) differently rotated. Seemingly this is
possible, although trickier to arrange with Stella as it is.
A related possibility is to play with a light source from that centre
such that, according to rotation of the concentric polyhedra, the light only "got
through" certain "aligned" facets and not otherwise -- as
an indication of consistency between different kinds of psycho-social structure
(values, strategies, institutions and problems, for example).
The large set of polyhedra of distinct types together constitute a repertoire
of patterns of order. As such they are a resource on which to call for subtler
forms of psycho-social organization.
The key initiative with respect to pattern language has been that of Christopher
Alexander and his team (A
Pattern Language, 1977; The
Timeless Way of Building, 1979). The idea of a pattern language
appears to apply to any complex engineering task, and has been especially
influential in software engineering where patterns have been used to document
collective knowledge in the field. In a subsequent study (The
Nature of Order, 2003-2004) the mostly static patterns from A
Pattern Language have been amended by more dynamic
sequences, which describe how to work towards patterns.
Alexander's earlier pattern language insights have been adapted experimentally
to explore a more generic 5-fold
Pattern Language (1984) of relevance to psycho-social organization:
- Physical environment: an adaptation of Alexander's own pattern description
- Socio-organizational environment: the pattern as it applies to the organization
of social groups, organizations and networks.
- Conceptual environment: the pattern as it applies to the organization
of a conceptual framework or a body of knowledge.
- Intra-personal environment: the pattern as it applies to the organization
of modes of awareness adopted by a person.
A question to be explored with a polyhedral software application is the
extent to which such patterns can be suitably, and memorably, represented
by families of polyhedra. This is the crucial question,
determining the relevance of this approach.
Is the taxonomy of psycho-social
organization now in what might be termed a pre-Linnaean stage, given the
significance that came to be attached to Linnaean
taxonomy? Of interest in this respect is the role first played in flowering
plant classification of the number
of stamens in the bloom. It might be asked whether conceptual models (including
their strategic and organizational reflections) could not be usefully
distinguished by the kinds of numbers used too distinguished polyhedra
Comprehension and Communication of Sets: the role of number,
It would be very interesting if any periodic table of polyhedra -- each
understood as a classification -- could be understood as providing insight
into a classification of classification systems (cf Birger Hjørland,
Lifeboat for Knowledge
2008). What indeed are the Patterns
of Conceptual Integration (1984) in the light of the range of challenging
examples (cf Patterns
of N-foldness: comparison of integrated multi-set concept schemes as forms
of presentation, 1980)? How such a periodic table might be "tuned"
is fundamental to any response to the divisive psycho-social initiatives
that are a preoccupation of governance (Tuning
a Periodic Table of Religions, Epistemologies and Spirituality -- including
the sciences and other belief systems, 2007).
Also of interest in this context s is the possibility of considering each
polyhedron as modelling a learning system. This would then relate to
the literature on the classification of learning systems, currently of relevance
to artificial intelligence research (Douglas J. Pearson and John E. Laird,
Learning of Procedural Planning Knowledge in Challenging Environments,
2005). Of relevance to understanding through polyhedra is the investigation
of adaptive learning of geometry (Harri Ketamo, An Adaptive
Geometry Game for Handheld Devices, Educational
Technology and Society, 6 (1) 2003).
Possible applications relevant to psycho-social organization
Team building and associated strategy:
- syntegration: One potential
area of application is in building up teams. Relevant in that respect is
the work of Stafford
Beer (Beyond Dispute: the invention of team syntegrity,
1995) and the franchised process of syntegration. The focus in this case
is in building psycho-social structures based on the icosahedron.
- social networking: Another variant of this is as an
extension of social networking and the current interest in enabling visualization
and mapping of such networks -- typically of friends and contacts. The
question is whether more coherent structures can self-organize, effectively
using suitable polyhedra as catalysts or templates. This might prove a
desirable additional option for those already enabled to list out such
networks by name or in some other order, or based on some criteria. One
reason for such developments, beyond the simple naming of members of a
network, is that there are complementary qualities and characteristics
important to the construction of teams with coherence. There may be a case
for having a diversity of such qualities. An early proposal to that end
Questing or Twelving: Proposal for a large-scale small-group development
process, 1976) points to possibilities
that have yet to emerge from social networking.
- online gaming guilds: As discussed in the earlier
with popular games), a more probable early use of polyhedral
representation of teams is in the design and management of online interactive
gaming teams ("guilds")
-- especially where a given polyhedron holds the "secret" of
the coherence of such a guild and therefore is fundamental to its strategy
and competitive advantage. In that respect, given the increasing overlap
between such gaming simulations and electronic warfare, it is probable
that polyhedra of appropriate complexity may be the secret to strategic
success in reality. However Peter Gould and Anthony Gatrell (A
Structural Analysis of a Game: The Liverpool v Manchester United Cup Final
of 1977, Social
2 1980, 3) used the q-analysis, or
polyhedral dynamics, of Ron Atkin to define and operationalise
intuitive notions of structure in a soccer match between Liverpool and
Manchester United. They found that the injection of q-holes, or obtrusive
objects, by the defence of one team appeared to contribute to the fragmentation
and loss of the other.
- research laboratories and "centres of excellence":
Given the interdisciplinary challenges of such environments, mapping relationships
onto a polyhedral form of adequate complexity (such as to highlight complementarities)
might fruitfully clarify the integrative nature of the undertaking (cf
of the Future: for Networking through Think-tanks, 2005). The
approach could also be applied to the "networks of excellence" promoted
by the European Commission.
- sporting teams: Mapping the members and/or functions
of such teams onto polyhedra could provide an appropriately visible sense
of the integrity of the group and its vital complementarities -- in contrast
with the simplistic schematics used for this purpose, notably in communicating
through the media. Of interest is whether complexifying the polyhedra used
would enable additional insights to be conveyed in team training. Clearly
of greater interest is the possibility that a set of interrelated polyhedra
might reflect the repertoire of strategies that the team might deploy against
an opposing team. Of further interest is the possibility that the two teams
might be usefully mapped onto the same polyhedron. There is even the possibility
that the set of teams in a competition might together be represented in
this way -- raising questions about how,
as with the planes of a crystal, cognitive fascination is activated and
engaged by reflection and refraction amongst the set of teams as a whole.
This consideration might open the way to development of multi-sided ("polyhedral")
games -- beyond the ubiquitous, binary, polarizing pattern to which politics
is typically reduced.
Complementarity vs Imbalance: Especially important to
team building, and the formation of coherent coalitions of stakeholders,
is to ensure a requisite variety of complementary elements (whether people,
organizations, strategies, values or concepts). The symmetry properties of
the polyhedra can be used to distinguish such elements, notably by colour.
Use of polyhedra in this way also serves to highlight possible imbalance.
Mapping and encoding psycho-social functions: The value
of a polyhedral pattern language is clearly associated with the degree to which
cognitive significance can be usefully mapped onto its features such as to
highlight and hold complementarities and contrasts. This may be primarily
a matter of exploration within the contexts for which the mapping is to be
used, whether a small group or a large community of interest. It may be a
communication device, symbolizing an initiative, irrespective of whether
the mapping is universally acceptable. The range of geographical projections
of the world points to the kind of variety that is possible and variously
In its simplest form, the question is if a set of specific psycho-social
functions is distinguished -- whether as principles, action programmes,
values, qualities, etc -- is it helpful to map these onto a polyhedral form
rather than present them solely as a checklist? Many such sets have been
elaborated with different numbers of elements. Clearly a match can be attempted
purely on the basis of the number (Representation,
Comprehension and Communication of Sets: the role of number, 1978).
An unfortunate feature of many such extant checklists is that, because of
their simple structure, no attempt is made to consider the relationships
between elements of the set -- relationships which may be of considerable
importance to the integrity and viability of the set when applied. Agenda
21, as formulated by the UN Earth Summit (Rio de Janeiro, 1992)
is an example of an asystemic set of articles in that the relationships between
the disparate parts are not considered. A mapping onto a polyhedron may highlight
useful questions about relationships implied by the polyhedral pattern. These
can lead to useful reconfiguration of the set.
Of particular interest is the case of sets of functions that are considered
well-defined and complete. The Myers-Briggs
Type Indicator is one example,
with its 16 types. These could be mapped onto the vertices of an octagonal
prism or the edges of a square
antiprism. Clearly the 12 astrological types, as with any other 12-fold
set, may be mapped onto a wider variety of convex polyhedra of greater symmetry
icosahedron; edges: cube,
faces: dodecahedron,) as well as non-convex forms (edges: tetrahemihexahedron;
less symmetrical forms. Even those with more complicated names are readily
Given the importance of duals in
relation to the geometry of many polyhedra, the significance of any corresponding
mapping is of great potential interest. A dual of a polyhedron is one in
which the vertices of the first correspond to the faces of the second. This
implies an interesting relationship in alternating, through the dual, between:
- vertices used to map the nodes in a network of people,
institutions, problems, concepts, -- with the edges of the polyhedron then
indicating the links between them,
- faces used individually to map people, institutions,
etc -- namely one per face -- with the edges linking the interface to other
people, institutions, concepts, etc (across the edge)
more intriguing is the manner in which the form of a polyhedron may be usefully
"decoded", recognizing the specialized interests that have explored
this -- such as anthroposophy with respect to "projective
geometry" and others with various
approaches to "sacred geometry".
Mapping systems to highlight viability: Governance of
any kind is called upon to deal with systems of increasing complexity. Such
systems may be represented on hierarchical charts or systems diagrams of
many kinds -- in two dimensions. Recognizing the arguments of Buckminster
Fuller that polyhedra are to be understood as systems, 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).
Seeding organization emergence: crystal / saturation /
Transformation of organization: Identification of pathways,
and transitional forms, through which an organization might evolve from one
polyhedral form to another such form, possibly more complex. Stella already
offers a number of possibilities for such transformation.
Significant issues of cognitive perspective: The cognitive
mapping onto a surface that can be formed into a sphere raises interesting
- as a spherically symmetrical polyhedron, it can only
be viewed from one "side" and therefore has to be rotated manually -- or
set to rotate -- in order to expose the other "side", and see "over the
horizon". This raises the question of how the whole is to be understood
- as an unfolded flat net, only one side can be seen,
since it lies flat. This raises the question of the other "side" which
is potentially trivial since the whole net map is visible -- unless any
image can only be attached to one side. This is especially significant
when the flat net is folded under user control into spherical form because
then the image is typically on the outer surface of the polyhedron, namely
on the side currently hidden when the net lies flat -- unless the image
is somehow allowed to be visible through each face of the polyhedron
- from within the polyhedron, which is often an option
for a user who may navigate in virtual reality though the side of the polyhedron
to view it from within. Here the question again is whether any images are
apparent and the cognitive significance of having to rotate the polyhedron
to understand the whole from within.
Communicating meeting outcomes: The process whereby an
integrative synthesis is derived from the insights expressed at a meeting
-- the global "sense of the meeting" in Quaker terms -- could be
understood in terms of the ability to produce a mapping of them onto a suitable
polyhedron. This could then be a visual complement to a press release --
even an index to its elements (on a web page).
Curiously this echoes the intuition associated with the use of gold "nuggets"
as a significant meeting product, or even the discovery of "diamonds" in
the meeting process. To the extent that the pattern of such insight is reflected
in a concluding declaration, its elements could also be usefully mapped onto
a polyhedron (Patterning
Archetypal Templates of Emergent Order: implications of diamond faceting
for enlightening dialogue, 2002; Structure
of Declarations: challenging traditional patterns,
1993) possibly even to be associated with song (A
Singable Earth Charter, EU Constitution or Global Ethic? 2006).
In this context, in relation to discussion of tensegrity structures below,
Ronald J. Barnett and Gregory W. Cherry have applied for a patent on Tensegrity
Communication of more complex forms of organization: Just
as a spiral staircase does not lend itself to comprehensible verbal description
without any illustration (if only gestures), so there may be many forms of
coherent organization that could well depend on the kind of cognitive prosthetic
provided by a polyhedron of whatever degree of complexity. As with the spiral
staircase, this may enable transition from one level to another. The polyhedron
then functions as a mnemonic of a superior degree of order to bullet pointed
charts, other checklists and complex organizations charts that do not enhance
memorability. Without such support, higher degrees of ordered complexity
become essentially unsustainable.
Configuration of the parts, with which people may variously and separately
identify, helps to determine whether, as a confguration, a larger and deeper
sense of identity and significance emerges. The question is then whether
the emergent organization corresponds to a mode of organization with which
people are already familiar (experientially) but for whose patterns no adequate
description has as yet been found -- as with an "unformed" sense of community
Insightful discussion of the associated communication and comprehension
challenges is provided by mathematician Ron Atkin (Multidimensional
Man; can man live in 3-dimensional space? 1981; Combinatorial
Connectivities in Social Systems; an application of simplicial complex structures
to the study of large organizations, 1977) as summarized elsewhere
organization determined by incommunicability of insights, 1995).
Such considerations point to the possibility of using interrelated polyhedra,
of different degrees of complexity, to map psycho-social issues (over) simply,
comprehensibly, and more challengingly -- such as to elicit a greater degree
of imaginative engagement. Exploration of the transformations between these
degrees of complexity enable learning pathways to be highlighted. They also
point to patterns of insight and order that are more likely to be forgotten
-- and which are effectively meta-stable and unsustainable, namely which
lack adequate mnemonic reinforcement.
It is appropriate to consider a wide variety of test cases, which may help
to render the use of Stella credible as a pattern language tool in domains
in which this might not otherwise be the case:
- Governance focus:
- UN Specialized Agencies: The most prominent of these
could be mapped onto a polyhedron (using their logos, for example,
below). Of interest would be to complexify the
polyhedron to varying degrees to enable addition of secondary UN agencies.
The challenge would be to find an instructive mapping of all such agencies
onto a polyhedron of suitable complexity. One use would be to be able
to increase or decrease the complexity for different purposes and audiences.
- European Union agencies: A similar approach could
be taken to the UN case (as was done in an earlier experiment, illustrated
- UN Declaration of Human Rights: A mapping of each
of the 30
Articles onto a polyhedron, if only as keywords could be very
instructive (whether or not hotlinking to complete texts was feasible).
- Groupings of countries: Significant groups proposed
for purposes of governance
(for example, the Group
of 20 -- industrial or the G20 Group
of 20 -- developing) could be fruitfully explored by mapping each
country onto a face of an icosahedron. But the lines and challenges of
communication and coordination could be better highlighted by using an
icosidodecahedron that interrelates negotiating arenas
between clusters of 5 countries -- although a key challenge would be
how the countries are then positioned in relation to such arenas (a complexification
into 3D of the conventional challenge of configuring placement at a negotiating
table). (Note: this was done, using Stella, as an exploratory
exercise in a separate
- Symbolic and mythical focus:
- Pantheons: A mapping of the Olympian Dodekatheon, as suggested
the Dodekatheon), could prove of great interest if appropriate
relationships could be highlighted
- Zodiac: A representation on a dodecahedral form,
as suggested earlier (Engaging
with popular astrology), could establish relevance in a
wide variety of contexts, especially if colouring and symmetry could
be used to exemplify integrative relationships through complementarities;
more complex dodecahedral forms might also be used. Collapsing the
form down to its 3-fold and 4-fold elements might also be instructive
in valued ways. The mapping could be done through astrological signs.
It is appropriate to note the extensive interest in non-cubic (including
dodecahedral) dice in parts of the widespread (online) role playing
community with mythical interests, as discussed earlier (Engaging
with popular games). Many might be intrigued by
the potentials of the polyhedral manipulation of such a mapping.
- Sephiroth: The challenge of mapping the central
symbolism of the Kabbalah of Judaism onto polyhedra has been variously
explored by many including Anders Sandberg (Some
Random Thoughts about the Occult Correspondences of the Platonic Solids
and Their Symmetries). Such possibilities are a focus for
a variety of studies, using polyhedra, which the capacities of Stella could
further enable (for example: Sacred
Geometry of One and the 13 Sephiroth Tree of Life, 2003;
Stephen M. Phillips, The '120
Polyhedron' and the '144 Polyhedron' as the Exterior and Interior of the
Inner Tree of Life).
- Apostles: Mapping the 12 apostles of Christianity
onto a dodecahedral form could be considered very significant to many,
especially if their characteristics, and relationships between them,
could be aesthetically highlighted by colour and symmetry.
Self-reflexivity might even be further enhanced by mapping Christopher
Alexander's set of patterns onto a suitably complex polyhedron.
Of related interest, in practice, is the possibility of using Stella to
enable people to construct and share polyhedral mappings in support of their
worldview, much as photographs and video clips are now exchanged worldwide:
- celebrities and idols: Clearly it would be a relatively
simple matter to apply images to the surfaces of an appropriately selected
and coloured polyhedron, whether to be printed as an image, attached to
an e-mail, applied to a website -- accessible as a manipulable virtual
reality representation or not.
- bar coding access to sound files: The capacity of some
portable phones to scan bar codes, suggests the possibility of variously
bar coding the surfaces of a polyhedron to evoke distinct voice messages
or songs from each surface.
- meeting conclusions: Associating the key conclusions
of a meeting (strategic elements, principles, or values, etc) with the
faces of a polyhedron (whether as keywords or phrases, or additionally
capable of triggering display of other information), would allow them
to be widely disseminated as image or virtual reality files. The technology
is even available to encase such a polyhedron in a transparent ball of
plastic (of tennis ball size) as a significant form of "executive
for which there is indeed a significant market. Such "balls" might
even be of interest for the public relations of complex intergovernmental
Success with a number of these test cases would offer powerful symbols,
in polyhedral form, of the integrative identity of topics that are otherwise
considered to be regrettably quite fragmented in the understanding of many.
Such a possibility was notably seen as relevant on the occasion of the establishment
of the Mediterranean Union (Mediterranean
Union: a symbolic challenge).
|Figure 4: Application
of 12 UN Specialized Agencies to faces of a dodecahedron in Stella
progressive unfolding from 3D to 2D
|Figure 5: Complexification of the
above UN Agency example
(from dodecahedron to icosidodecahedron) using Stella
with subsequent morphing to
yet more complex forms (by various methods),
suggesting increasing challenges
(and possibilities) of communication and integration amongst the set of
agencies so mapped;
diagram for the icosidodecahedron is
also included (as an indication of possible communication pathways)
Mapping possibilities with regular polyhedra
Of particular interest is the manner in which use of mappings (whether for
G8, G20 or L20) further down the table (namely more complex) ensures that the
direct connectivity required of a given country is reduced. Thus in the G20
mapping onto an icosahedron, all triangular edges border other triangular edges
and all verticies connect with other triangular vertices -- there is no "space",
whatever flexibility that signifies. In the icosidodecahedron, however, only
the vertices of the triangles are connected. In the rhombicosidodecahedron,
the triangles do not connect with one another directly.
Such complexification introduces "openness" and points to the challenge
"sparseness" rather than the need for "tight bonding" to
ensure viability and integrity.
Such opennes, as noted below, can only be achieved in practice through
embodying tensegrity principles into both communication
pathways (and dissociative resistances)
between the countries, thereby constituting the emergent whole and its coherence.
PART B: Future extension to tensegrity representation
Psycho-social operationalization of polyhedra through tensegrity representation
A major difficulty with abstract forms such as polyehdra is how they engage
with psycho-social organization -- irrespective of their inherent aesthetic
properties and appreciation of them as "sacred geometry". And,
irrespective of recognition of their role in the architecture of biological
cells (and radiolaria),
this difficulty is evident in efforts to use such forms in the architecture
of buildings -- especially those polyhedra of greater complexity.
It is in
this respect that learnings from their application through tensegrity --
tensional integrity -- to unusual constructions (such as geodesic
are of significance (see Documents
relating to Networking, Tensegrity, Virtual Organization). Tensegrity
is the means through which polyhedral forms are "operationalized" in
building and therefore, with some probability, in psycho-social organization.
This raises the question of whether an as yet undiscovered "geodesic" form
of psycho-social organization might notably be of great relevance to global
As an additional feature therefore, the capacity in Stella to
generate tensegrity representations of polyhedra would be an advantage --
where this is possible and appropriate . A principal
reason is that there is a range of arguments suggesting that the viable structure
of the more complex polyhedra -- if constructed -- is dependent on the kinds
of distribution of forces associated with the tensegrity variant. This is
notably true at the level of the biological cell (Donald E. Ingber, Tensegrity
and Systems Biology, Journal of Cell Science, 2003).
As defined by R
Buckminster Fuller (Synergetics: explorations in the geometry
of thinking. 1975):
A tensegrity system is established when a set of discontinuous compressive
components interacts with a set of continuous tensile components to define
a stable volume in space.
As models, the tensile elements (tendons) can be cables or strings, functioning
like a network. The compressive elements can be beams or rods (struts) and
function as spacers to prevent the network from collapsing. Despite the generality
attributed to tensegrity principles (and explicit in the subtitle of Fuller's
study), it should be stressed that most of the literature recognizes only
their application to material structures. Of interest to any exploration
of tensegrity are the following:
- Within the architectural context, the application of studies
of management cybernetician Stafford Beer on "syntegrity"
(synergistic tensegrity) in team building are ignored -- perhaps necessarily
so. This is equally true of those of cybernetician Gordon
Pask on the Fuller-Snelson prismatic tensegrity as a Borromean
link model of the interactions in a minimal stable concept; it
has been extended to modelling entailment meshes of concepts
as spin networks. He noted that "a tensegrity, or tensionally
integral structure, is an organizationally closed system, informationally
open, viable system and an organism" (Interactions
of Actors (IA), Theory and Some Applications, 1993). This
work, a generalization of Pask's conversation
theory and his work on
self-organization and coherence, has subsequently been variously developed,
notably by Nick Green (Axioms
from Interactions of Actors Theory, Kybernetes, 2004);
he has considered the isotopy of the orthogonal Borromean link and
the icosahedral tensegrity. Such work is presumably highly relevant
to the challenges of psycho-social organization.
- Curiously, whilst the concept of "network" has proven valuable in both
material, psycho-social and abstract contexts, the interplay of forces
fundamental to tensegrity has not as yet -- even though "network" is inherently
related to that dynamic in practice. The same might be said of "virtual
organization" in cyberspace. A noted weakness of psycho-social networks
in practice may however be their tendency to design out "tension" -- which
features in the "hierarchical" forms to which they are a reaction -- thereby
inhibiting their capacity (Tensing
Associative Networks to contain the Fragmentation and Erosion of Collective
Memory, 1980; Tensed
Networks: balancing and focusing network dynamics in response to networking
- Both in the architectural context, and in the non-architectural application
of tensegrity developed by Stafford Beer, issues of priority and intellectual
copyright have proven to be extremely important -- even disagreeable --
possibly even to the point of inhibiting further development. It is therefore
interesting to speculate, in the light of "syntegrity", on
the possible intellectual copyright with respect to the application
of tensegrity to psycho-social organization. Of related interest is any
patent constraint on the application of tensegrity construction methods
to dome-like "buildings" constructed virtually in cyberspace or to any
tensegrity art in that context. Given the fundamental role that Pask's
focus gave to tensegrity in relation to interaction between actors,
the emergence of a concept, and self-organization, one might ask how the
important sense of "territory" is held in that context, and -- provocatively
-- whether this is itself implicated in such considerations in unsuspected
ways (cf Einstein's
Implicit Theory of Relativity -- of Cognitive Property? Unexamined influence
of patenting procedures, 2007)
|Figure 8: Indications for Construction of
Tensegrities from Polyhedra
on the assumption that having polyhedral coordinates in great
precision in Stella, possible tensegrity form-fitting could be readily
tested by appropriate algorithms
Tensegrity design: The most practical,
accessible and focused summary of the challenge (for architectural
purposes) is provided by:
Valentín Gómez Jáuregui: Tensegrity
Structures and their Application to Architecture,
Tensegrity Models (2008), as elaborated by Robert
Burkhardt, offer imaginative indications of possible "operationalizations"
of polyhedra in the creation of new kinds of psycho-social organization.
The following examples (from an extensive list), based on polyhedra,
raise the questions: how might organization like that be experienced,
how might it be recognized, and how might its emergence be facilitated:
Access to such virtual reality models requires a browser
plugin (eg free
browser Cortona plugin for PC, Mac
OS X, and Pocket
support for tensegrity construction:
- Robert Burkhardt has developed his own software
to fabricate his style of double-layer tensegrity dome and sphere
from geodesic breakdowns. This a front end which
produces input for his tensegrity computation software. The software
requires some sort of back end to use the product
to finish off the tensegrity computations before moving on to VRML.
He believes that the existing software could be adapted
to output in a form suitable to another package (such as ANSYS).
- Diego Budavari and Valentín Gómez Jáuregui are
in process of developing a computer programme: Tensegrity Simulator
- Jason Evelthon Charalambides (Computer
Method for the Generation of the Geometry of Tensegrity Structures,
University of Texas, 2004) provides a comprehensive survey
of the literature and states the focus of the computer program
developed as follows:
- Tensegrity is a technology that can be applied to structures
and its use can influence the construction time efficiency
and construction project management in general. However,
a significant drawback for a systematic application of tensegrity
structures in the building construction industry is the particularly
complex geometry that engineers and architects have to generate,
in a two or three dimensional virtual or physical environment.
The objective of this dissertation was the development of
a computer based utility that will facilitate the design
professional to devise and construct a specific morphological
variation of tensegrity structure systems. The development
of this utility was based on a methodology that identified
and included parameters that can be associated to the schematic
design and design development phases of a design project.
The main contribution of the developed computer program is
the efficiency with which virtual models of a tensegrity
structure can be generated, facilitating the designer in
decision making during the design process. Emphasis was given
on the development of an interactive graphical
simulation/visualization environment for the computer program.
This feature assists in the generation and modification of
the numerical input, with parameters defined by the user,
and allows unobtrusive regenerations of alternate solutions
within the computer virtual environment.
- The author notes that David Georges Emmerich
1988) developed a systematic method
of deriving tensegrity forms from a range of Platonic and
Archimedian polyhedra (citing A. Hanaor, Beyond
the Cube: the architecture of space and polyhedra, In: F. Gabriel
(Ed.), Tensegrity: Theory and Application, 1997)
Relevant tensegrity mathematics: Hugh
Kenner (Geodesic Maths and How to Use it, 1976), notably
a chapter on choosing a polyhedron.
Sets of Rules (Anthony Pugh, Introduction
to Tensegrity, 1976)
Unambigious set of rules: It may well be that such a
set is "buried" in the many attempts to develop algorithms to derive
tensegrities from polyhedra. However such a set does not appear
to have been clearly articulated in a manner that lends itself
to immediate use.
- Circuit pattern associated
- The tendons define the edges of a polyhedron, which need
be neither regular nor semi-regular. Four tendons and two
struts meet at each junction to form a vertex of the figure,
so at least four edges must meet at each vertex of a polyhedron
used as a basis for a circuit-pattern figure..
- When the struts are joined, they form circuits of struts,
hence the name circuit pattern for this strut-tendon
relationship. The circuits of struts follow the lines of
circuits of tendons, which can be traced on models of appropriate
- The circuits of struts interweave with each other, passing
under one circuit, then over the next, under the next, and
- A network of tendons surrounds a series of circuits of
struts, the tendons pulling inwards like the skin of a balloon,
the struts pushing outwards like the air in the balloon.
- There is a junction of struts and tendons outside the midpoint
of each strut, so there will be the same number of junctions
as there are struts.
- Circuit pattern, based on geodesic polyhedra (alternate
method), derived from an existing polyhedron (called its principal
- Triangulate any faces that are not already triangles
- The edges of each triangles are divided into equal numbers
of equal parts and then lines drawn between the points established
to define a triangular grid on each face
- With a sphere drawn through the vertices of the principal polyhedron,
lines from the centre through all line instersections to that
sphere then constitute the vertices of the geodesic polyhedron
-- these are then joined to reproduce the pattern of lines on
the surface of principal polyhedron
- Circuit pattern tensegrity systems can be based on any such
geodesic polyhedron, provided that the faces of the principal
polyhedron were subdivided to a frequency which is a multiple
- Patterns can be based on other polyhedra by
following the symmetries of the figure to provide a network of tendons,
then to add in the struts.
One of the advantages of such structures is as a representation of a configuration
of polarizing factors in social organization -- forces which may be essential
to its viability, as discussed elsewhere (From
Networking to Tensegrity Organization, 1984; Groupware
Configurations of Challenge and Harmony: an alternative approach to alternative
organization, 1979; Implementing
Principles by Balancing Configurations of Functions: a tensegrity organization
Just as tensegrity principles are fundamental to the architecture of the
biological cell, they may also be fundamental to the coherence of psycho-social
organization and community -- to community "architecture". Such
tensegrity structures may be especially significant in determining the patterns
of (electronic) communication essential within cyberspace to the viability
of an organization, a community or some other collective initiative.
One of the challenges in deriving tensegrity structures for architectural
purposes is what is termed "form-finding" (cf Milenko Masic, et
al, Algebraic tensegrity form-finding, 2005). There is a case for
understanding the challenge of matching or fitting psycho-social organization
to polyhedra (discussed above) as an analogous process of "form-finding".
In both cases a polyhedron provides a template for the solution, but the
challenge is to find it. Hugh Kenner (Geodesic Maths
and How to Use it,
1976) offers guidance on "choosing a polyhedron" (ch. 11) which usefully
frames the challenge.
The challenge is to "massage" chaotic network representations into a "global"
configuration as primitively envisaged as a challenge to mathematics (Preliminary
Clarification of Some Problems of Processing Networks of Entities -- in order
meaningfully to map psycho-social relationships, 1973). This may now be more
readily feasible with the aid of "polyhedral" network analysis (cf P. Doreian, Polyhedral
Dynamics and Conflict Mobilization in Social Networks, 1981).
Process of use
In its current form, Stella necessarily calls for a degree of familiarity.
With respect to its relevance to psycho-social organization, one challenge
is to make evident which features it is more fruitful to use for what purposes,
in what sequence and by whom.
In reflecting on the potential relationship between polyhedral structures
and the dynamics of governance, it is interesting to reflect on the success
of the online design environment, SodaConstructor --
a Java-based simulator -- open to popular participation. It allows participants
to design a wide variety of mechanical systems empowered by parameter-controlled
muscle-like dynamics and constrained by "gravity". It is interesting
Stella application is associated with a "3D
minesweeper game", played
on polyhedral surfaces -- recalling the popularity of Tetris and
Minesweeper (which uses cells of different shapes: hexagonal, octagonal,
users of Stella may
post interesting models into a collective
repertoire. Several mind mapping software packages make use of hexagonal
modelling which therefore help to reinforce the argument for exploring 3D
A proposal has been made
to adapt the SodaConstructor approach to the representation or design
of complex institutional structures variously empowered by sectoral budget
the Representation of Europe: visualizing the coherence of international
institutions using dynamic animal-like structures, 2004). Clearly
the future evolution of psycho-social organization, based on tensegrity principles,
could encourage similar online exploration.
Multi-dimensional heuristic work space
A focus to the confluence envisaged here may be given in terms of the kind
envisaged in a classical paper by Douglas
Human Intellect: a conceptual framework, 1962),
Schroeder appears to offer the most significant synthesis, in relation to
the above argument, especially given his extensive reference to tensegrity
(as the "defining figure" in the workplace he proposes) and his association
of it with the pattern language of Christopher Alexander. His study focused
... three innovations that suggest an alternative
approach to structuring information systems: a multidimensional heuristic
workspace, a resonance metaphor for information, and a question-centered
approach to structuring information relations. Motivated by the need for
space to establish a question-centered learning environment, a heuristic
workspace has been designed. Both the question-centered approach to information
system design and the workspace have been conceived with the resonance
metaphor in mind....
This revised view of the metaphors of space was accompanied by a critical
evaluation of the prevailing metaphors for information processes, the conduit
and pathway metaphors, which led to the emergence of an alternative, resonance
metaphor. Whereas the dominant metaphors emphasized information as object
and the movement of objects and people through networks and other limitless
information spaces, the resonance metaphor suggests the existence of multiple
centers in dynamic proximity relationships...
The federation of multiple autonomous problem-solving spaces, toward goals
such as establishing communities of questioners, has become an objective
of this work. Future work will aim at accomplishing this federation, most
likely by means of the IS0
Topic Maps standard or similar semantic networking
Schroeder made extensive use of the Axon
Idea Processor: a visualization tool for thinkers, as developed
by Chan Bok, in elaborating his proposed workspace and illustrating its
operation. It allowed total network views and management of relations in
the form of clusters as well as explicit links. It also allowed the workspace
to be organized in terms of concentric polyhedra -- a feature suggested
earlier. Uunlike Stella, Axon does
not have a virtual reality mode. Despite that, Schroeder argues that the
workspace so enabled is an autonomous, stand-alone environment that affords
the possibility of being federated with similar spaces through use of emerging
facilities such the IS0 Topic Maps standard.
In his primary focus on the tensegrity in a virtual environment (but not
in the virtual reality characteristic of Stella), Schroeder appropriately
It should be noted here that the tensegrity figure in this workspace is
only an image, and does not have the capacity to behave in the digital environment
as a physical tensegrity would. The figure included here was created based
on observation of an existing physical model. The great advantage of the
physical tensegrity structures is that the relationships among the forces
that determine the structure and the physical stability that results creates
an immediate understanding of the whole system. Realizing these characteristics
in the digital environment, rather than just representing them, is suggested
as an objective of future work.
Schroeder also provides a very helpful detailed summary (pp 199-207) of
the advantages of the tensegrity-based workspace, notably in terms of :
- "cognitive plausibility"
- a central point of cognitive reference: "as locus of accepted assumptions,
or negatively, as the place of ultimate unknown, the nave about which the
wheel of knowledge turns"
- provision for "undefined as well as definable spaces"
- highlighting the role of context in terms of a "context sphere"
- suggesting an arrangement for the structured display of certainty and
- consistent display of multiple frames of reference
- possibility of displaying objects "as single entities, or
they can be formally linked as networks, arrayed in clusters suggesting
fields, or arranged along vectors suggesting the directions of operation
of forces within the space. The meanings of the symbolic objects that are
managed in this space can be represented in several ways: explicitly, by
embedding definitional text within the objects, or by assigning values
to links across objects; or implicitly, through relational arrays, with
significance of the array determined through analysis of the object clusters".
- representation of networks "by the chords that connect
the vertices of the polyhedra. A graph representing 'small world' phenomena
can be seen in the tensegrity, with the tendons representing local 'strong
ties' and the cross structure compression elements representing the
long-distance 'weak ties'."
- manipulability and multiple location of objects / tokens making it a
workplace for cognitive learning and discovery.
- ready representation of containment and inside / outside relationships
- ability to infer structural dynamism
- placement or representation of concepts that involve dynamic change
and periodic events in time
- representation of relationships implying opposition and bi-polarity
- possibility of groupings in several different numeric
- potential for simultaneous display of cognitive and geographical maps
- capacity to represent relationships characterized by discontinuity
- metaphorical use of "gravity effects" understood as accounting for
stable proximity relationships when physical connections are not in place
-- as in the clustering of concepts
around categorical prototypes
- user control of the workplace environment, notably enabling different
cognitive learning styles
Clearly such explorations need to be related to the multi-actor situation
of organization emergence and self-organization. Of particular interest is
the author's approach to:
- representation of relationships implying opposition, bi-polarity, uncertainty
and discontinuity, usefully to be understood as appropriate separation
-- rather than a "unification", as tends to be the inappropriate
- the "central point of cognitive reference", which in the case
of a symmetrical tensegrity is quite empty and effectively "virtual".
From a philosophical perspective, even a spiritual one, this is especially
significant, in contrast to the conventional approach in which any such
central position is necessarily occupied by some organizational or conceptual
entity, or even a central value.
- polyhedral organization of the geographical globe which
includes research into "geodesic
discrete global grid systems" (K. Sahr, et al., 2003) and "planetary
polyhedral tesselation" (G. H. Dutton, 1991; 1999), namely the use
of global coordinate systems based on regular polyhedra, as a complement
to those based on traditional latitude and longitude. Notable
is the author's idea that global geographic polyhedral projections
could easily be incorporated into the proposed heuristic workspace.
- the challenge of cognitive embodiment associated with any workspace,
as extensively argued by George Lakoff and Mark
Johnson (Philosophy in
the Flesh: The Embodied Mind and Its Challenge to Western Thought,
Implicitly, combining the above points, is the sense in which the emptiness
around which globality is centred brings a special and necessary form of
integrative order to "global" networks that are otherwise unconstrained
of nothingness and emptiness, 2008). Arguably it is this centrally
referenced emptiness that creates a space, that is potentially isomorphic
with that of the proposed workplace of the mind. The approach creates a "context" within
which "global" discourse
takes place effectively (Future
Generation through Global Conversation: in quest of collective well-being
through conversation in the present moment, 1997).
In a polyhedral pattern language, each polyhedron may effectively be
understood as a representation of a "cognitive circuit diagram". This might
be considered implicit, even explicit, in Fuller's "geometry of thinking"
and intentions, although his insights are undermined and "denatured" by the
inability to take account of the cognitive issues of embodiment so ably explored
by Lakoff -- and close to Pask's conversation/interaction theories.
Operationalized and enabled as a tensegrity, the featurs and resonant dynamics
of the circuit start to become apparent in their relevance to psycho-social
organization. There are indeed analogues to the characteristic features of
electrical circuits (resistors, capacitors, etc) through which "energy"
is engendered, stored and redistributed (cf Electrical
Systems as a Guiding Metaphor for Stages of Group Dialogue, 2001).
But, in the sense explored by Francisco
Embodied Mind: cognitive science and human experience, MIT Press 1991,
with Evan Thompson and Eleanor Rosch) and enactivism,
such a circuit diagram has to be embodied to be enabled.
It is such cognitive circuits that sustain the patterns of behaviour on
which governance is dependent -- and which it endeavours so desperately to
seek to change. They constitute the sustaining tracery of communication
pathways and feedback loops.
PART C: Meta-patterning considerations from other cultural perspectives
The challenge of any pattern language lies in what makes the pattern meaningful.
For psycho-social organization, what is "goodness of fit" in a cognitive,
organizational and strategic context where comprehension is critical to communication,
credibility, coherence and viability?
A core issue is any limitation on the capacity of the human mind to "grasp"
sets of elements of any degree of complexity and how any such constraints
may be circumvented in the organization of principles, categories, organizations
or strategies as discussed elsewhere (Representation,
Comprehension and Communication of Sets: the role of number,
1978). Polyhedra represent an interesting way of bypassing the constraints
of hierarchical and networking metaphors -- combining their advantages and
compensating for their respective weaknesses.
Patterns as enabling emergence of a "quality without
With respect to the challenges of governance, much has necessarily been
made of issues relating to the tangibles (food, health, etc)
on which economists so readily focus, and to the intangibles manifest over
time (freedom of information, freedom of religion, etc) which are also a
focus of politics. And, in the attention given to the pattern language of
Christopher Alexander (discussed above), the focus has been on the process
of design that the methodology enables in whatever domain. Little attention
is given to his declared, and extensively described, purpose of using such
patterns to enable the emergence of what he describes as the "quality
without a name" (Timeless
Way of Building, 1979).
In A Pattern Language (1977), in that spirit, Alexander
has done much to clarify what would here be termed the elven pathways fundamental
to providing a subtle sense of a desirable "place to be" or a "sense of place" --
of feeling "at home".
There is a central quality which is the root criterion of life and spirit
in a man, a town, a building, or a wilderness. This quality is objective,
but it cannot be named... every place is given its character by certain
patterns of events that happen there. These patterns are always interlocked
with certain geometric patterns in the space... To reach the quality without
a name we must then build a living pattern language as a gate. (pp ix-xi)
Industrialized society has however come to recognize
aspects of its importance under the term "quality time" or in the increasing
difficulty for top corporations to retain valuable executives. But the point
was made long ago by the realization that "man cannot live by bread alone".
This perspective is further discussed elsewhere (Walking
Elven Pathways: enactivating the pattern that connects, 2006).
The merit of Alexander's achievement has been to create a qualitative bridge
between the technical considerations of architecture, so evident in discussion
of tensegrity, and the qualitative purpose of the spaces so created. This
might be said to go beyond the "heuristic" workspace of the mind which Schroeder's
work seeks to enable. Put succinctly, what is the quality characteristic
of the space associated with any particular pattern and the manner in which
it is embodied and lived?
Curiously, at best, the architectual aesthetic is very sensitive to the
qualities of space created. It is in this sense that the use of strategic
confifgurations of pillars can be fruitfully revisited. Associated with those
pillars, for example, are the spaces between those pillars and the tension
associated with the relation of those spaces to the pillars that define
them. It might be argued that it is the purpose of the strategic pillars
to create desirable "places to be". Were the spaces to be filled, extending
the bounding pillars into a wall, "sides" are then created in ways that were
noted as problematic in the earlier study.
Quality of space as a central challenge of governance
Seemingly quite dissociated from the explicit challenges of governance,
there is an extensive literature on the spirit
of place and psycho-social
attachment to the land:
- Edward S. Casey. Getting Back into Place: toward
a renewed understanding of the place-world. Indiana University Press, 1993.
- James A. Swan. The Power of Place: sacred ground
in natural and human environments. Quest Books, 1991
- Y-Fu Tuan. Space and Place: the perspective of experience. University
of Minnesota, 1977
- Darrell Addison Posey (Ed). Cultural and Spiritual
Values of Biodiversity.
London, UN Environmental Program (UNEP), Intermediate Technology, 1999.
It is quite clear that it is precisely such attachment which provides
a prime focus for major conflicts, notably the unresolved cycles of violence
in the Middle East focused on the symbolism of Jerusalem. Implicit, but unmentioned
in that context is the epistemological significance of more poetic understandings
of space, as exemplified by:
- Fernand Hallyn. The Poetic Structure of the World:
Copernicus and Kepler.
Zone Books, 1990
- Gaston Bachelard. The Poetics of Space. New York, Orion Press, 1958/1964
The question to be asked, as an extension of Schroeder's concern with a
workplace of the mind, is the nature of the quality associated with particular
enabling polyhedral configurations. The disciplines of architecture and
design claim sensitivity to the appropriateness of spaces for particular
functions. This is reflected in the design of parliaments, meeting rooms,
think tanks and retreat centres.
Beyond the concrete however, what are the patterns that
enable configurations of thought of relevance to the challenges of governance?
How does a pattern language provide appropriate cognitive scaffolding for
the emergence of viable strategy? How is engagement with such patterns enabled?
"Spirit of team": vibration and resonance
The sense of quality associated with space is also sensed to be associated
with psycho-social organization. Typically this quality is named in jargon
such as "vibrations". People refer to the degree of "resonance" they experience
(or do not) with particular initiatives and groups of people. The most frequent
recognition of such "spirit" is in the experience of "team spirit" in sports,
and its analogue in the military.
Various efforts have been made to elaborate such understanding:
- Harrison Owen (Spirit: transformation and developmenty
Abbot Publishing, 1987) agues that "we might recognize that organizations
in their essence are Spirit". He highlights expressions in organizations
such as: "The spirit around this place is terrible", or "Got to keep the
spirit up" or, "Our spirit is our most important asset. As he says, however,
" we apparently possess very l;itte in the way of appropriate technology
in order to do something for Spirit."
- Jon R. Katzenbach and Douglas K. Smith (The Wisdom
of Teams: creating the high performance organization, Harvard Business
School Press, 1993) stress that much of the wisdom of teams lies in the
disciplined pursuit of performance
- from the perspective of the OECD Centre for Educational Research and
Innovation (CERI), Simon Field (Does
team spirit make economic sense?, OECD
Observer, No 226/227,
Summer 2001) notes that teamwork is as vital for successful companies
as it is for successful football teams. He recognizes that little
attempt has been made to measure its contribution to the economy, or
the cost of its absence, and suggests the need to pay more attention
to this invisible asset. For Field, attention to such social capital
can suggest new policy solutions.
Insights from Chinese culture
This exploration was inspired by the use of "pillar" as the overriding European
strategic metaphor, as discussed in the earlier paper (Towards
Polyhedral Global Governance: complexifying oversimplistic strategic metaphors,
have been presented there as configurations of such pillars in any more coherent
approach to governance. With respect to global governance, involving a variety
of cultures, it is therefore useful to seek complementary insights from the
quite distinct Chinese culture -- especially if there is any tendency to
assume that Eurocentric strategic thinking is to be considered appropriate
Geometric elaborations of polyhedra, developed by the logic of
geometric transformation from Platonic polyhedra, can be understood as
patterns implicit in the Platonic forms --
as implied by the potential for such transformation. Corresponding elaborations
and implications may be found in the Chinese logical elaboration
of two classic coding systems, each a pattern language par
- the set of 64 hexagrams associated with the binary coding of the I
Their representation in relation to a hexhedron (a cube) has been extensively
presented by Z. D. Sung (The Symbols of the Yi King
or Symbols of the Chinese Logic of Changes, New York, Paragon, 1969)
- the 81 tetragrams associated with the ternary coding of the Tai
Xuan Jing, T'ai
Ching or Canon of Supreme Mystery (translated by Michael
Nylan, The Elemental Changes: the ancient Chinese companion to the
I Ching, State University of New York, 1994). An earlier commentary
by Derek Walters (The T'ai Hsüan Ching; the hidden classic,
Aquarian Press, 1983) includes a section on The T'ai Hsüan Ching and
Scientific Thought which highlights the set of numbers
that represent the balance between two opposing forces. This is presented
in relation to mappings of imaginary numbers.
There is a visual irony to the fact that the European "pillars", and the
"unfilled spaces" between them, can be fruitfully compared to the complete
and broken (yin) lines constituting any hexagram. It is of course
a fact that the I Ching was long used as tool of governance in classical
times -- and was required study for entry into the Chinese civil service.
These patterns are then qualitatively associated, through
their respective metaphorical representations, in
- the commentaries on the hexagrams of the I Ching
- the commentaries on the tetragrams of the T'ai Hsüan Ching
The set of patterns calls for exploration as a pattern language (Conditions
of Objective, Subjective and Embodied Cognition: mnemonic systems for memetic
coding of complexity, 2007; 9-fold
Higher Order Patterning of Tao Te Ching Insights: possibilities in the mathematics
of magic squares, cubes and hypercubes, 2007).
This of course raises the question of the qualitative implications
that may potentially be associated with the patterns of the other Platonic
forms, as developments of the less complex ones. Both the icosahedron and
the dodecahedron suggest mappings of:
- 12: the many 12-fold archetypes (Dodekatheon, Zodiac, Apostles, Arthurian
round table, etc) onto faces in the case of the dodecahedron and vertices
in the case of the icosahedron
such as the 30 Articles of the UN
Declaration of Human Rights onto edges in both cases
The integrative (global) nature of such sets is a real challenge to comprehension
in terms of how the parts play off against each other. It is for this reason
that the relationships are typically embodied in metaphor and stories, an
approach explicitly favoured by the authors of The Wisdom of Teams (1993).
There have been many exercises in interpreting the relevance of the I
Ching and the Tao
Te Ching to issues relating to organizational strategy and management.
Perhaps most relevant to this argument is the classical text of Cheng
Yi (1033-1107) as translated by Thomas Cleary (The Tao of Organization:
the I Ching for group dynamics, Shambhala, 1995), who comments:
The Tao of Organizations analyzes relationships and power configurations
within groups. Taking into account both the subjective and objective dimensions
of these structures, it is extraordinarily subtle and complex. The relationship
between interpersonal and intrapersonal forces... is the central focus
of the explanation.
Cleary adds an appendix on Cheng Yi's instigation of "inner design" (or
noumenalism) intended to bring out hidden dimensions in classical Chinese
works -- obscured because of the use of rigidly fixed interpretation schemes,
inappropriate in any context of transformation. He comments at length on
how such principles were consciously applied by the legendary Japanese industrialist Matsushita
More generally the challenge of comprehending the interrelationship between
seeming disparate facets of a pattern may be seen as a challenge of "correlative
thinking" of which the Chinese understanding of yin in relation
to yang offers
an example (A. C Graham, Yin-Yang and the nature of
Correlative Thinking, Institute of East Asian Philosophies, 1986). The
issue for governance is how credible is any degree of correspondence and
to what degree of confidence does it give rise in strategy development and
implementation (cf Theories
of Correspondences and potential equivalences between them in correlative
Pattern dynamics: change, alternation, resonance
As noted above, the further work of Christopher Alexander and his team has
been on The
Nature of Order (2003-2004) in which the the mostly static patterns
Pattern Language have been amended by more dynamic
sequences, which describe how to work towards patterns.
As a set of patterns in its own right, the I Ching is also known
through its translation as the Book of Changes -- namely the transformation
between conditions symbolized by particular patterns. This focus on
change is also evident in its companion classic, the T'ai
It is interesting that at the molecular level, the benzene molecule
fundamental to the structure of organic matter, is explicitly recognized
to be based on a pattern of resonance in the bonding arrangements between
its six constituent carbon atoms. As such it is known as a resonance hybrid
-- characterized by the fact that its enduring viability is based on the
alternation between bodning configuration. Such molecular resonance is
recognized when no single conventional model, using only even number of
electrons shared exclusively by two atoms, can actually represent the observed
molecule. It might be expected that some analogue would be operative at the
psycho-social level (cf Configuration
of modes as a resonance hybrid, 1986).
Curiously whilst healthy democracy and governance is understood to be based
on alternation of power between political parties or coalitions, there is
little attention to the need to explore this principle in relation to healthy
governance and the formulation of strategy. In certain forms of farming,
the value of crop rotation is recognized as essential to systatainable exploitation
of fields. It might be inferred that this offers learnings for alternation
between strategies (Sustainable
Cycles of Policies: crop rotation as a metaphor,
1988). More generally it might be inferred that sustainable governance is
dependent on alternation between patterns (Development
In the light of such arguments, using the pattern coding language of the I
the systemic relationships between various sets of patterns have been explored
as an experiment (Transformation
Metaphors -- derived experimentally from the Chinese Book of Changes (I Ching)
for sustainable dialogue, vision, conferencing, policy, network, community
and lifestyle, 1997).
Possibilities of "variable geometry" in psycho-social
Within the above context current use of the term "variable geometry" fails
to distinguish between different configurations, understood simply as alternatives,
and the dynamics of shifting between configurations in response to different
conditions. The latter is the essence of structural nimbleness (cf Wanted
- A New Social Entity: role of the potential association, 1971).
An excellent metaphor is the switch consciously made, according
to circumstances, between different tactical configurations in rugby and
other such team sports. These configurations may be named or numbered to
be called out by the captain during a game. They are termed formations
in association football, as distinct from the formations
in American football. They refer to the position players line up in before
engaging during the course of play. There are both offensive and defensive
formations with many in both categories.They also feature in computer
simulations (see Team
For purposes of governance,
"variable geometry" has been defined in a European context as follows:
'Variable-geometry' Europe is the term used to
describe the idea of a method of differentiated integration which acknowledges
that there are irreconcilable differences within the integration structure
and therefore allows for a permanent separation between a group of Member
States and a number of less developed integration units. (Europa
As noted by Warren Mason and Susan Penksa (The
Variable Geometry of Security Cooperation: a policy framework for European
integration. 2004), the development
in Europe of a vast array of new structures of cooperation -- both public and
private -- has left analysts reaching for conceptual tools with which to frame
these phenomena. Charles Grant develops the argument further (Can
Variable Geometry Save European Enlargement, 2005). Its relevance
operational relevance has been highlighted by Patrick Joachim Dunphy (Variable
Geometry Europe -- patching together what works in the fight against hard-core
cartels: carrots, sticks, custody and leniency, 2007). Mike Goldsmith
Geometry, Multilevel Governance: European integration and subnational government
in the new millennium, 2003) reviews the extent to which
concepts such as variable geometry and multilevel governance remain useful
in aiding understanding of the processes of change through which
EU territorial politics are passing.
Variable geometry has been notably recognized in relation to trade (Paolo
Guerrieri and Stephen S. Cohen, The
Variable Geometry of Asian Trade, 1994. The
approach has also been envisaged for the UN system (Alternation
between Variable Geometries: a brokership style for the United Nations as
a guarantee of its requisite variety, 1985) and within the UN system. As reviewed by C.
Undertaking: a straitjacket or variable geometry? 2003) and
discussed by Andrew Cornford (Variable
Geometry for fhe WTO: concept and precedents,
2004) who notes that the idea of was raised during the
Uruguay Round when the constitution of the new multilateral organization
(eventually leading to the WTO) was under consideration. Indeed, as noted
by the Swiss National Science Foundation,
World trade rules are not marked
by a uniform 'geometry'.
Exceptions are made to general principles for defined groups of nations,
for specific principles and specific issues. Regional trade arrangements
(RTAs) and Special and Differential Treatment (SDT) are the two most important
The relevance has been explored in relation to the "multilateral" trading
system, notably at a meeting of World Trade Institute (The
Single Undertaking After Cancun: diversity and variable geometry in the WTO
On the occasion of a multi-stakeholder dialogue
and networking event for addressing the challenge of making ambitious targets
of the world community a reality, the Helsinki
Process on Globalisation and Democracy (2005), Susan George (Variable
Geometry to Design Positive Outcomes, 2005) stated:
In my view, variable geometry is the most useful political concept to emerge
from the Helsinki Process. It is the recognition that no one institution,
or type of institution, can solve by itself the problems we confront today.
We need a cooperative framework in which various actors abandon their turf-wars
and work together.
The question is whether comprehension of the possibilities would be enhanced
by the software facilities outlined above through which a large repertoire
of configurations and relationships can be explored.
Curiously, with respect to the suggestion above regarding sports
with popular games), the pattern of numbers defining the formations
is reminiscent to that used to characterize polyhedra:
|Figure 9: Comparison of number
patterns in football formations and polyhedra
(possibly suggesting that one might be represented by the other)
|Examples of nomenclature in offensive
||Examples of polyhedral symmetry groups
(typically further extended in vertex arrangements)
- 4-3-4: Four-Three defense
- 3-4-4: Three-Four defense
- 5-2-4: Short Yardage defense
- 4-2-5: Nickel defense
- 4-1-6: Dime defense
- 3-1-7: Prevent defense
- 3-3-2: tetrahedral
- 4-3-2: octahedral
- 5-3-2: icosahedral
- 3-6-6: tetrahedral truncated
- 4-6-6: octahedral truncated
- 5-6-6: icosahedral truncated
If there proves to be a useful mapping from football tactics to polyhedra,
given the extensive repertoire of the latter, this would then raise the possibility
of unforeseen tactics in football -- as envisaged with respect to the emergence
of unforeseen governance strategies. It would also offer a means to render
credible more complex strategies of governance in response to the problematique
-- a form of Rosetta Stone for strategy.
Given the variety of ways in which polyhedra can be represented, notably
to foresee possibilities of transformation between them, it may be useful
to note the manner in which Stella allows for the display of the cell diagram
of any polyhedron -- typically in the form of an inverted hierarchy:
A cell diagram is a graph indicating how stellation cells relate to each
other. The layers of cells are shown as layers of nodes, each node representing
one cell type. Edges of the graph connect nodes from one layer to nodes of
the next layer if the two cell types share a common face, so the cell type
at the bottom of the edge supports the cell type at the top of the edge.
Understanding of polyhedra may thus be usefully framed as providing
a conceptual interface between hierarchy and network -- typically problematic
in psycho-social organization portrayed in 2D -- using forms in 3D with degrees
of symmetry that render complexity comprehensible. Such understanding also
connects with traditions of "sacred geometry", even through "faceting diagrams".
In this context it is appropriate to note the many comments in the literature
on the polyhedral structure of a football, notably in relation to the fullerene
molecules (see also Understanding
Sustainable Dialogue: the secret within Bucky's Ball? 1996).
Comprehension of strategically appropriate patterns
through the fourth dimension
It is repeatedly noted that the strategic challenges of the times now call
urgently for extraordinary thinking -- beyond the conventional
continue to exacerbate those challenges. As a prime advocate, Edward de Bono
is instigating a World
Council for New Thinking. As noted
earlier, mathematician Ron Atkin asks whether man can indeed live in three
Man; can man live in 3-dimensional space? 1981). Another mathematican,
Marcus du Sautoy (Finding
Moonshine: a mathematician's journey through symmetry, 2007) makes
For centuries composers, writers, artists, choreographers and architects
have pludered the mathematical world in search of new structures to stimulate
them creatively. (Creative Calculations, The Guardian, 29 April 2008)
In also enabling the exploration of fourth dimensional polyhedral patterns
(regular polytopes), Stella might
then be said to act as a kind of bridging psychopomp.
It traces virtual pathways through the unknown and the uncertain to facilitate Walking
Elven Pathways -- enactivating the pattern that connects (2006).
The appropriateness and relevance of such exploration of the paradoxical
order of the hyperreality of the emerging knowledge society has been highlighted
through the subtle aesthetics of such as semiotician Umberto
Eco (Travels in
Hyperreality, 1973) -- effectively
calling for hypercomprehension (Hyperaction
through Hypercomprehension and Hyperdrive: necessary complement to proliferation
of hypermedia in hypersociety,
As a mathematician, Marcus du Sautoy has worked
with musicians and dancers to explore how new ideas of mathematics can be
woven into a piece of theatre pushing all boundaries (The
19th Step, 2008) -- inspired
by a work of Jorge
Luis Borges, author
of the Library
of Babel (1941), a knowledge-edifice of hexagonal-shaped rooms
in a four-dimensional context.
For governance the challenge might indeed be framed as the Comprehension
of Appropriateness (1986) -- for which a polyhedral pattern language
is a vital "revolutionary" cognitive support (Metaphoric
Revolution: in quest of a manifesto for governance through metaphor,
1988). The essence of this challenge is making the subtlety of appropriate
connectivity credible. The mathematician's response to "moonshine" usefully
frames one approach to this challenge (Potential
Psychosocial Significance of Monstrous Moonshine: an exceptional form of
symmetry as a Rosetta stone for cognitive frameworks, 2007).
Homeostatic equilibrium: necessary "human
The dynamic equilibrium characteristic of
tensegrity structures makes evident the challenge of the sustainability of
psycho-social systems through what can be mapped onto them. In the earlier
paper, it was argued that the deities of any pantheon can be usefully associated
with the implicit polyhedra for mnemonic purposes (Re-membering
the Dodekatheon). The self-stabilizing processes of a tensegrity,
through the manner of interaction of its parts under stress, could then be
understood as the manner in which the particular "gods" of which it is composed
require appropriate "sacrifice" -- to be appropriately "honoured" -- to ensure
the continuing integrity of the system as a whole.
How should such "gods" then be understood?
- in terms of natural systems,
these are the interrelated systems that ensure the viability of the human
environment -- water, air, etc. -- each appropriately linked through a
pantheon to a particular deity, that may have specific relationships
with several other deities.. Such relationships are fruitfully held by
stories, myths and legends about the gods -- in ways that engage many of
the governed beyond the communication capacities of governance. These have
been a concern of Joseph Campbell (The
Power of Myth, 1988) and Karen
Armstrong (A Short History of Myth, 2005). As discussed elsewhere
Fusion through Myth and Symbol Making, 2006), Armstrong makes
the point with respect to industrialized societies that:
- Another peculiar
characteristic of the human mind is its ability to have ideas and experiences
that we cannot explain rationally.... imagination is the faculty that
produces religion and mythology. Today mythical thinking has fallen
into disrepute; we often dismiss it as irrational and self-indulgent.
But the imagination is also the faculty that has enabled scientists
to bring new knowledge to light and to invent technology that has made
us immeasurably more effective.... Mythology and science both extend
the scope of human beings. Like science and technology, mythology...is
not about opting out of this world, but about enabling us to live more
intensely within it.
- in terms of psycho-social systems, these are the objective
systems with which governance is variously and more explicitly concerned.
They are the systemic "issues" that appear as major points on
international governance agendas.
- in terms of personal subjective systems, these might
be understood as the archetypal "deities within" that frame behaviour
under particular circumstances, as envisaged by Marsilio
the Present Moment: celebrating the insights of Marsilio Ficino interpreted
by Thomas Moore, 2001). They might also be associated with the
interacting sub-personalities highlighted by disciplines such as psychosynthesis.
For some this is mnemonically held by systems of psychological typing,
such as astrology.
It is the interplay of any set of "deities" that is then fundamental to
the integrity and identity of the system mapped by the tensegrity used. Any
such sense of integrity is typically much challenged in the current context,
whether with respect to natural, psycho-social or subjective systems. Of
great potential interest is then the nature and "appropriateness" of the
"sacrifice" that must be made within that framework to particular deities
"ruling" any of its parts. In tensegrity terms, this is the manner in which
particular parts must necessarily be constrained in response to the equilibrating
functions of the local (partial) systems within the tensegrity as a global
Use of the metaphor "human sacrifice" in this context provides a useful
systemic context for the "sacrifices" that humans, collectively or individually,
are currently being challenged to make in the interests of sustainable governance.
It is of course useful to note the association to the mortal sacrifices that
individuals were called upon to make in the past -- and which government
may continue to expect of them to protect "the motherland" (but not "the
planet?). As with the ritual sacrifices of the past, whether of animals or
humans, it is unfortunate that their systemic significance has been lost
with the rejection of the abhorrent characteristics that presumably were
then considered necessary to render such significance memorable. Ironically,
however, few regulatory measures, including legislation, are now introduced
through modern governance without some form of preliminary mortal sacrifice
to justify them.
On a personal level, how sacrifices are variously made may continue
to be an issue in response to the different challenges of living in a resource
constrained society. It is perhaps from this perspective that the seeming
rigidity of systems of values, such as the Confucian, should be revisited
in terms of the systemic significance attached to calls to "honour". The
same applies to the promotion of "family values" whether by government or
religion. These could be fruitfully positioned in relation to the "freedoms"
(from such values) that tensegrities may also be seen as encoding. The relevance
of such an argument may be seen in the analogous role played by calls for
"respect" -- and the dgree of importance attached to it -- within the seemingly
most alienated sectors of society.
A tensegrity based on a Platonic or Archimedean polyhedron is especially
valuable in highlighting the interlocking cycles underlying its structure
-- the "great circles" around it in geometrical terms -- in contrast to those
associated with the "cognitive circuits" (discussed above). Elsewhere it
has been argued that these fruitfully point to a cyclic understanding of
identity in dynamic rather than static terms (Emergence
of Cyclical Psycho-social Identity: sustainability as "psyclically" defined,
It is in this sense that traditional articulations of sets of values and
prescriptions with which many identify through religions can be fruitfully
seen as offering indications of systemic relevance (Navigating
Alternative Conceptual Realities: clues to the dynamics of enacting new paradigms
through movement, 2002). The work of Alexander on dynamics in relation to pattern
emergence is clearly relevant.
|Challenge of a new language for governance?
|"Why do we put so much emphasis on audio-visual means of portraying
goal, trend, condition, projection, and alternative? Partly because so
many valuable participants in decision-making have dramatizing imaginations...
They are not enamoured of numbers or of analytic abstractions. They are
at their best in deliberations that encourage contextuality by a varied
repertory of means, and where an immediate sense of time, space, and
figure is retained".
(Harold Lasswell, The transition towards more
sophisticated procedures. In: D. B. Bobrow and J. L. Schwartz (Ed.). Computers
and the Policy-making Community, 1968, pp. 307-314)
viability and comprehensibility
The key question is whether the possibilities of representation on a form
-- whose integrity only fully emerges virtually in 3D --
augments the range of possibilities of negotiating necessary constraints
in practice in order
to achieve such integration. A crude experiential metaphor is whether a game
of bridge is more feasible, interesting and sustainable where there is
a recognized need for 2 pairs of players such that, if only 3 are immediately
available, ensuring the presence of a fourth is desirable. A related illustration
is the (arbitrary) statutory restriction on numbers of members of some elite
The simplest regular polyhedra may be considered the least "global"
-- as exemplified by "spherical" -- in that, compared to more complex
Platonic or Archimedean polyhedra, the facets are most distant
from the circumsphere through the vertices. "Globality" is therefore
essentially implicit in these simpler and most readily comprehensible cases.
It is however the simplest that are the most easiest to construct in practice
and are the most stable.
The ease of representation of the more complex polyhedra in Stella lies
in the many advantages of a virtual environment. Ironically it might be argued
that articulation of any complex sets of values -- as virtues -- is also
much easier in a "virtual environment", unconstrained by the challenge of
implementation in practice.
The structural viability of the more complex polyhedra relies
on tensional integrity in practice -- namely an artful balance
between compression and tension elements ("checks and balances") that is
the focus of tensegrity architecture. The "art" of achieving this lies in
the requisite variety of the multiplicity of differently oriented facets
of such polyhedra -- that together, in psycho-social terms, reflect the sustaining
culture of the whole.
It should be stressed however that, in the case of psycho-social organization,
"in practice" is concerned with the necessary patterns of communication
between the parts of the whole -- the necessary feedback loops. In a society
constructed on information flows through cyberspace, viable "virtual
therefore dependent on how these communication pathways get designed into
the structure and reflected in e-mail exchanges, for example.
This is the
significance of the tensegrity "operationalization"
of polyhedra. It provides a map of both the requisite communication patheways
and the necessary separators (or insulators) in order for a new degree of
order to emerge -- with sufficient robustness to redistribute stresses globally,
thus dynamically resisting any tendency of its constitutive network to
collapse. It may be fruitful to consider the "insulators" as regulators (as
provided by governance through directives and regulatory authorities),
with the flexible communication pathways as exemplifying the "freedom" essential
to resilience and the aspirations of the governed.
The challenge indeed
lies in "bridging the chasm" between the simple and
the complex, the "virtual" and the "concrete". This
is a generalization of the challenge of "speaking across the chasm of
frame conflict" in human communication (fruitfully discussed by Schroeder)
-- to which the different orientations of the faces of polyhedra draw attention.
It is also recognized as the two-culture chasm between the "sciences" and
the "arts" -- exemplified in the realm of governance by the cognitive
challenge of heads of state inspired by poetry (Poetry-making
and Policy-making: arranging a marriage between Beauty and the Beast, 1993).
More provocatively and self-reflexively, this is also
the challenge of interrelating the various threads (architectural, cognitive,
and otherwise) of the above argument -- whose proponents might be variously
seen as living on different faces or planes of a polyhedron as yet to be
It is these principles that need to be embodied in tensegrity psycho-social
organization and strategy -- if viable coherent "global" governance
"integrity" is to be achieved, whether at the global, regional
or personal scale. In this context, the set of polyhedra offer a range of
explicit articulations of "global" -- especially through the dynamics of
their tensegrity variants.
It is important to recognize that the above focus is on enabling
exploration of possibilities and interpretations. The concern
is not with closure on any particular set of definitive
interpretations or understandings. In the application of such a "pattern
language" to governance in uncertain times, it is the capacity to
be cognitively sustained in the exploration of possibility and potential
that is most to be valued in the quest for "sustainable development" and "quality
of life". The art of global governance may turn out to be well illustrated
by the capacity to explore and promote more integrative metaphors -- possibly
mapped onto the transformational potentials of the set of spherically symmetrical
The possibilities of a polyhedral pattern language therefore lie in its
capacity to trigger alternative and complementary ways of thinking about
intractable governance issues -- eliciti9ng creativity appropriate to the
much sought "paradigm shift".
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