24th October 2009 | Draft
Geometry of Thinking for Sustainable Global Governance
Cognitive Implication of Synergetics
- / -
Produced in relation to
The Buckminster Fuller Challenge
2010, organized by
The Buckminster Fuller Institute,
in support of the development and implementation of a strategy that has significant
potential to solve humanity's most pressing problems.
Systems as polyhedra
Challenge to comprehension
"Uprightness" and global geometry
Matrix representation of psychological types and their styles of categorization
Epistemological "body odour"
Self-reflexivity in global modelling
Integrating disagreement and dissent
Requisite variety of perspectives
Self-reflexivity through a "shadowy" dual
Keys to global governance "embedded" in synergetics
as a meta-model
Implications for a "meta-model"
Cognitive engagement with globality
Challenge of cognitive geometry
Existential and experiential engagement with globality
Geometry as a metaphorical magic mirror of thinking
The secret within "Bucky's Ball"?
Fuller (1895-1983) is renowned for his innovations as designer, inventor
and futurist. He is most widely known for his invention of the seemingly improbable geodesic
dome. One of his key initiatives was the elaboration (in collaboration with
E.J. Applewhite) of an understanding of synergetics (Synergetics: Explorations
in the Geometry of Thinking, 1975; and Synergetics
2: Explorations in the Geometry of Thinking, 1979). With his particular
use of language and neologisms, he defined this
A system of mensuration employing 60-degree vectorial coordination comprehensive
to both physics and chemistry, and to both arithmetic and geometry, in rational
whole numbers... Synergetics explains much that has not been previously illuminated...
Synergetics follows the cosmic logic of the structural mathematics strategies
of nature, which employ the paired sets of the six angular degrees of freedom,
frequences, and vectorially economical actions and their multialternative,
equieconomical action options... Synergetics discloses the excruciating awkwardness
characterizing present-day mathematical treatment of the interrelationships
of the independent scientific disciplines as originally occasioned by their
mutual and separate lacks of awareness of the existence of a comprehensive,
rational, coordinating system inherent in nature.
He was instrumental in encouraging a systemic global approach to use of energy
and resources (Operating
Manual for Spaceship Earth, 1969) and the educational World
Game which has now been developed into the Global
Simulation Workshop (Thomas T. K. Zung, Buckminster
Fuller Anthology for the New Millennium, 2002).
In what follows a distinction is made between Fuller's focus
- geometric and design innovations
- implications for use of energy and conservation of resources
in a global context in the light of a systemic worldview underlying current
approaches to sustainability
- cognitive implications associated with his philosophy
- existential implications
It is the last two emphases that are explored here, especially in the
light of the expression "geometry of thinking" in the title of the
two volumes of his magnum opus. Whilst his own interpretation of these may
indeed be held to be implicit in that work and in other writings (I Seem
to Be a Verb,
1970), most reference to his work focuses on the first and second emphases.
It is the second emphasis that is typically the inspiration for proposals submitted
to the annual Buckminster Fuller Challenge of
the The Buckminster Fuller Institute "in
support of the development and implementation of a strategy that has significant
potential to solve humanity's most pressing problems".
The argument in what follows is that it is the cognitive and existential
implications from which the more tangible, material proposals emerge -- however
much their understanding is conditioned by evident design constraints.
It is these intangible factors that hold the key to understanding
why psychosocial systems have proven to be more than inadequate in designing
viable global responses to global challenges -- sustainable in their
own right rather than as idealistic proposals for global sustainability. In
this sense the more tangible preoccupations are secondary and derivative -- however
viable and successful they may be as isolated initiatives, typically
presented together as a list, rather than systemically configured.
therefore a case for exploring Fuller's Synergetics: Explorations
in the Geometry of Thinking as though it might indeed concern what
the words imply -- but in the light of richer understandings of psychology,
epistemology and ecological philosophy than are evident in his writings. What
"geometry of thinking" then imply if understood in this way?
The argument here follows from a long-term interest in the psychosocial implications
of the design principle developed by Fuller and underlying the geodesic
dome, namely that of tensional
integrity (tensegrity). This permits the construction of structures with
an integrity based on a synergy between
balanced tension and compression components.
These implications are discussed in a set
of documents, most notably From
Networking to Tensegrity Organization (1984). A particular interest
is the possibility of enabling virtual organizations and conceptual structures
through web technology ***. Such possibilities have been explored to
some degree by management cybernetician Stafford
Beer (Beyond Dispute: the invention of team syntegrity, 1994).
Systems as polyhedra
As previously cited in
reviewing Fuller's understanding (Synergetics:
Examples of Integrated, Multi-set Concept Schemes, 1984, referring
to sections in his two volumes):
- Synergetics is the geometry of thinking. How we think is
epistemology, and epistemology is modelable; which is to say that knowledge
organizes itself geometrically... (I, 905.01)
- Any conceptual thought is a system and is structured
is because all conceptuality is polyhedral. (I, 501.101). By tetrahedron,
we mean the minimum thinkable set that would subdivide Universe and have
inter- connectedness where it comes back upon itself. (I, 620.03)
- All systems are polyhedra: All polyhedra are systems. (II, 400.56)
- Human thoughts are always conceptually and definitively
confined to system considerablility and comprehension....All systems are
subject to comprehension (I, 400.07-20)
- Initial comprehension is holistic. The second stage is detailing
differentiation. In the next stage the edges of the tetrahedron converge
like petals through the vector-equilibrium stage. The transition stage
of the icosahedron alone permits individuality in progression to the omni-triangulated
spherical phase. (I, 1005.63)
- Dimension begins at four. Four-dimensionality is primitive
and exclusively within the primitive system's relative topological abundances
and relative interangular proportionment. Four-dimensionality is
eternal, generalized, sizeless, unfrequenced. (II, 1033.611)
- All conceptually thinkable, exclusively metaphysical
experlencings are fourfoldedly characterized...(systematically, topologically,
angularly, numerically). All generalized principles are conceptually thinkable
and fourfoldedly definable. Generalization is conceptually (i.e. systematically)
imaginable independent of (5) frequency. (II, 1072.22)
- By tetrahedron, we mean the minimum thinkable set that
would subdivide Universe and have interconnectedness where it comes back
upon itself. (I,
For Fuller's collaborator (Synergetics
as defined by E.J. Applewhite):
Synergetics is Fuller's name for the geometry he advanced based on the patterns
of energy that he saw in nature.... Fuller felt that the old classic approaches
did not describe the way nature actually behaves. For instance, Euclid's
lines were thought to go off to infinity. Fuller says lines are vectors of
energy and he rejected the notion that anything physical could be extended
indefinitely.... His geometry hinges on the tetrahedron, the simplest
structural system within insideness and outsideness: he advances it as the
most economical way to measure space and to account all physical (and metaphysical!)
experience. This is what he calls synergetics: an empirical mathematical
system in which geometry and number mesh without fractions. It gains its
validity not from classic abstractions but from the results of individual
It is clear that Fuller himself strongly related geometry with epistemology
and the thinking process, even implying that this accorded with a sense of
energy processes in thinking.
Challenge to comprehension
Fuller's use of language
and neologisms (exemplified above) is notorious for its impenetrability,
even by those sympathetic to his initiative and appreciative of its tangible
outcomes. But this challenge to comprehension is in fact central to any "geometry
and it can be argued that he does not address this adequately with respect
to the fundamentals of his approach. This is not to deny his attention to
education with respect to global allocations of resources and the like --
or his very lengthy seminars endeavouring to communicate his understanding.
It could be argued that the failure to address this dimension adequately
-- within the framework of any "geometry of thinking " -- is fundamental
to the limited consideration of his insights at the level at which they might
prove most relevant to his demonstrated global concerns.
Whilst it may indeed be the case that some have the intellectual facility,
or particular intelligence, which enables them to engage fruitfully with geometrical
abstractions, this is not common. The tangible products of these abstractions
in the form of the regular
polyhedra and semi-regular
polyhedra do indeed offer
a kind of illusion of comprehension -- perhaps an intuition of its implications.
Their symmetry naturally facilitates this.
There is the intriguing possibility that the increasing complexity of polyhedra
may be understood as a form of representation of increasing dimensionality
-- and therefore the challenges and possibilities of their comprehension through
The mathematician who has best addressed the challenge of comprehension is
Ron Atkin (Multidimensional
Man: can man live in 3-dimensional space?, 1981). He illustrates this
by the challenge of comprehension in relation to experience "within" the
geometry of a triangle -- especially with regard to the perspective necessary
to comprehend the triangle as a whole. Hence the subtitle of his book. It is
this "fourth" perspective which offers a link to what amounts to
of departure" for Fuller, namely the tetrahedron (Threshold
of Comprehensibility: a fourfold minimal system? 1983).
Other mathematicians have
explored the challenges of shifting perspective from 1, though 2, to 3 dimensions.
The cognitive challenge has long been delightfully articulated in such
mathematical fiction as Edwin
A. Abbott's Flatland:
a romance of many dimensions (1884), Charles
Howard Hinton's An Episode on Flatland: or how a plain folk discovered
the third dimension (1907), A.
K. Dewdney's The
Planiverse (1984), Ian
Stewart's Flatterland (2001),
and Rudy Rucker's Spaceland (2002).
The 1884 novel has recently taken the form of an animated version (Flatland,
2007) to highlight the challenges otherwise.
The concern with comprehension is also central to the study of multi-term
systems by John
G. Bennett (General
Systematics, Systematics, 1, 1, June 1963) who, like Atkin,
represented them using polygonal (rather than polyhedral) configurations.
His related interest in the "energy" associated with such systems
was consistent with his professional responsibility for research on coal,
as discussed elsewhere (Reframing
Sustainable Sources of Energy for the Future: the vital role of psychosocial
variants, 2006). The insights have been further developed by Anthony
Supreme Art of Dialogue: structures of meaning, 2008).
A degree of concern with comprehension
is evident in the adaptation to (psycho)social organization by Stafford Beer
Dispute: the invention of team syntegrity, 1994) of Fuller's
work on tensegrity -- and the subsequent development of syntegrity (Allenna
D. Leonard, Team
Syntegrity Background. 2002; J. Truss, et al. The
Coherent Architecture of Team Syntegrity: from small to mega forms,
The point to be stressed however is that Fuller's more general arguments
in terms of the tetrahedron and polyhedra fail to address the capacity to comprehend
such structures. The need to do so is seemingly bypassed by the evident ability
to represent and to construct them -- implying that this achieves the degree
of comprehension of any cognitive challenge they represent -- if his basic
argument is to be taken seriously. It is not clear who can claim the capacity
to think in dimensions appropriately articulated by even the simplest regular
polyhedra -- the icosahedron or the dodecahedron, for example. Exploration
of syntegrity focuses primarily on the icosahedron.
This point may seem to be irrelevant if the
degree of comprehension is indeed adequate to the design and construction of
complex geodesic domes -- effectively very complex polyhedra. The point may
seem to be even more irrelevant with the proven capacity of mathematicians
to detect ever more complex symmetry groups (of which polyhedra are the simplest
form). For example:
However it could be argued that the ability to develop formalizations concerning
many dimensions involves a degree of "kidding oneself" (or others)
regarding the capacity to understand the "systems" and wholes they
are thereby held to represent. Operationally the assumption of success is achieved
through engaging in a
"concrete" iterative process over time -- a succession of operations
or procedures in which the parameters are slightly changed. A geodesic dome
may, for example, be constructed in this way -- as with elaborating an "ex-planation" from
which some kind of overview (of the plane) is obtained.
The argument is exemplified
by the fact that mathematicians exploring high orders of symmetry now
accept that any coherent "proof" of a theorem relating to them may
be hundreds of pages in length. That for the so-called "enormous
theorem", depends on many distinct contributions, totalling some 15,000
pages in length -- and far beyond the capacity of any single individual, however
specialized or dedicated. Mathematicians do not seek to comprehend the many
"dimensions" in such theories. They are merely letters or numbers in equations.
For someone (like the writer) challenged by even "four dimensions",
the elegance of any visual representation (such as those above) implies the
possibility of a form of comprehension which is as elusive as any harmony sought
in the reconciliation of disciplines, faiths or ideologies in response to the
challenges of global governance. If, as is implied, the challenges
of global governance call upon more than three dimensions, clearly how people
are empowered to engage with such complexity merits insights which may indeed
benefit from Fuller's "geometry
of thinking". In the case of the above structures, for example,
the challenge has been (naively) considered elsewhere (Potential
Psychosocial Significance of Monstrous Moonshine: an exceptional form of
symmetry as a Rosetta stone for cognitive frameworks, 2007; Dynamics
of Symmetry Group Theorizing: comprehension of psychosocial implication,
The assumption made here is that the tangible emphases of
Fuller (and of those who assume them to be adequate to the challenges of global
governance) are overly simplistic and inadequate precisely because they ignore
insight implied by Fuller's own analysis -- and possibly the source
of his own conscious creativity. If indeed a viable system can only be understood
in terms of four dimensions, represented minimally by a tetrahedron, then attention
is required to comprehension of more complex polyhedra. What kinds of thinking
do they imply -- as they increase in complexity?
"Uprightness" and global geometry
The relevance of the challenge of comprehension to global governance is evident
in the fact that many people, if not most, consider that they are "right" --
whether individually or through the groups and belief systems with which they
are associated. The problem is that they each tend to disagree with each other,
often violently -- namely with others who also perceive themselves to be "right" (Jonathan Haidt, The Righteous Mind: why good people are divided by politics and religion, 2012).
It is from the dynamics of this "system" that some form of
coherence is expected to emerge for effective global governance -- perhaps
through the hypersimplification that any democratic majority is "right" and
that the minority is then "not-right", or possibly when some elite
considers itselfs "right", irrespective of the understanding of a democratic
The question is how any "geometry
of thinking" can assist
in enabling coherence under such circumstances. Many have assumed that it
is possible to present or impose a particular pattern of order -- with whom
all are expected to agree and to consider "right" -- although it
is readily apparent that such agreement is not forthcoming (despite current
unprecedented use of forms of individual and collective violence, deemed "right"
in their turn).
In the metaphorical spirit of the cognitive
linguistics of George
Lakoff and Mark
We Live By, 1980), the sense of being right can be interpreted as the
sense of being "upright" on the surface on which one stands -- being "upstanding",
holding a "standpoint" in relation to what one "understands".
The challenge of any global perspective is that being upright is what each
of the 6 billion people on the world can do anywhere on the surface of the
globe, provided it is recognized that people are then variously angled relative
to each other, with some on the other side of the globe even being "upside
down" -- although
not from their own perspective.
The metaphor offers ways of understanding why those distant from where I am "upright" appear
smaller -- and may even disappear over the horizon into invisibility, insignificance
and irrelevance, whatever their perspective. This perspective, compared to
their understanding of what is held to be "normal",
may appear to justify their being labelled from elsewhere as "abnormal" and "extremist",
off the edge of the map".
Curiously an effort has been made to claim that
globalization is effectively a flattening of the Earth (Thomas
World Is Flat, 2005). The problematic aspect of this perspective, recognized
as a "flat earth mentality", has been criticized
Dependence on a Flat Earth Mentality-- in response to global governance challenges,
2008). However, if each perceives themselves to be upright on a plane -- "normal"
with respect to that plane -- then these planes are all effectively tangential
to the surface of a "globe" -- whatever the cognitive significance
and "globe". The "plane" might be considered what is readily
comprehensible, with "ex-planation" offering a measure of non-planar
understanding, whether or not this is indeed comprehensive and "global".
As noted above, Fuller appropriately challenges the notion that anything physical
could be extended indefinitely to infinity -- whether a line or a plane.
If the perspectives of all those variously upright in this way are to be honoured,
somehow they need to be positioned around the globe -- irrespective
of how unusual their orientation may be from my own position. The plane with
respect to which I am right and normal, as a tangent to the globe, may then
be understood as intersecting other tangential planes of different orientation
-- which collectively are configured as approximations to the surface of the
globe. Together they are a polyhedron of 6 billion faces, with fewer faces
to the extent that more agree with one another on what is right -- "democracy
with a human face"?
If each such plane is understood to be like the piece of a jig saw puzzle,
the challenge might then be how to fit all the pieces together. In the plane
this is studied as tiling
patterns or tesselation. Here the implication is the need for a
spherical tiling -- a spherical jig saw, as suggested by the famous Rubik's
This geometry is relatively comprehensible, even if the implication of different
orientations is not -- as reflected in clashing disciplines, religions and
civilizations. It is however possible that if humanity does indeed live in
more than three dimensions -- Atkin's question -- that only even more
complex surfaces can appropriately reconcile the differences in orientation
and the associated paradoxes. Arguably it is more than clear that simple tilings,
plane or spherical, are not adequate to the challenge of global governance
-- or answers would already have been found long ago. Claims that a sphere
are adequately indicative of global representation are then clearly inadequate,
if not extremely naive.
Other surfaces of great interest, on which people could be variously "right"
and "normal", are the torus, the Mobius strip and the Klein bottle
-- before even considering the multidimensional shapes considered of such fundamentaL
significance by mathematicians and physicists. These also point to the question
of whether everyone being "right" together could be better represented
by them standing on the inner surface of a globe -- and therefore with a convergent
orientation towards the centre, rather than the divergent orientation associated
with standing on the outer surface. This is of course not consistent with physical
experience, to the extent that is relevant.
The argument here is that Fuller's "geometry of thinking" is extremely
useful to the discovery of configurations of adequate complexity to the cognitive
challenges of global governance -- starting with the simpler polyhedra, or the
tensegrities based on them. It has not been mined to that end. The issue is
how to "decode" the geometry as a means of holding comprehension
of distinct perspectives and interrelating them -- and the challenge of understanding
another apparently strange perspective, namely any other way of being "right".
Matrix representation of psychological types and their styles of categorization
One common approach to avoiding the challenges of multidimensional
geometry is through clustering styles of thinking, whether as lists
or in simple tables. The sense of being "right" is then associated
with a particular cluster having a shared mode of thinking or engagement with
reality. This is most evident in lists of psychological types or forms of intelligence
(Systems of Categories Distinguishing Cultural Biases, 1993).
Differences of appreciation may then be "ex-planed" by associating
people or groups with different types. To the extent that such typing
is reframed as "profiling" or "stereotyping", such "ex-planation" does not
effectively address the dramatic dynamics of the relationship of one type to
another in practice.
Lists of clusters may however be configured into a two dimensional table or
matrix, as with the Myers-Briggs
Consideration may be given to the complexification of such representation into
a periodic table (Periodic
Pattern of Human Knowing: implication of the Periodic Table as metaphor of
elementary order, 2009) . Classical approaches, such as the organization
of the hexagrams of the I
Ching, may also
be understood in this light. Also of interest is the configuration of types
into a circular form, as with astrological types, or with the Chinese Ba
Any such tabular representation may itself be subject to geometrical transformation
to introduce the possibility of other integrative implications. The table may
be rolled into a cylinder, with the ends joined to form a torus
-- with its own significance. Two tori may also be linked (Comprehension
of Requisite Variety for Sustainable Psychosocial Dynamics Transforming a matrix
classification onto intertwined tori, 2006). Geometrically a torus
is closely related to the sphere which is Fuller's primary focus. Types and
categories may also be configured spherically, even at the most basic level
of accounting (Spherical
Configuration of Categories to Reflect Systemic Patterns of Environmental Checks
and Balances, 1994; Spherical
Accounting: using geometry to embody developmental integrity, 2004).
Epistemological "body odour"
There is however a related challenge of comprehension which needs to be considered.
Whilst the metaphorical geometry of the previous paragraphs offers a way of
understanding in principle the issue of different ways of being right, it
does not address the curious phenomenon that the creative thinkers
inspired by geometry typically cannot "stand" each
other and find each other's efforts irrelevant or worse. This is a classic,
well-documented problem in the development of mathematics but is evident in
any other comprehensive approach, most notably that of religions (even where
they attach fundamental significance to geometric symbols).
The argument is confirmed by Fuller
himself who seldom, if ever, cites others who have ventured into that domain
-- or preceded his own ventures. The disagreements he had about priority in
the discovery of "tensegrity" are
only one indication. The phenomenon has been discussed elsewhere using the
metaphor of "body odour" (Epistemological
Challenge of Cognitive Body Odour: exploring the underside of dialogue,
2006). It has been specifically explored by contrasting two approaches to "integral
futures", that of Ken Wilber and that of David Lorimer (Self-reflexive
Challenges of Integrative Futures, 2008).
A natural consequence of a creative vision of an integrative framework is
to see it as all-encompassing, rendering other considerations irrelevant or
misleading, whether or not they are explicitly subsumed. This is of course
typical of belief systems, ideologies and of many disciplines -- and of "scientific
revolution" as discussed by T
S Kuhn and Karl
Rather than the mutual citation
pacts characteristic of some academic endeavour -- potentially questionable
as "incestuous" --
it is effectively a case of mutual non-citation pacts, deliberate marginalization
and the like (Considering
All the Strategic Options -- whilst ignoring alternatives and disclaiming cognitive
2009). The possibility of coherent global strategies emerging from such a context,
and attracting widespread support, is clearly problematic, whether or not they
are of requisite variety to be sustainable in cybernetic terms.
Self-reflexivity in global modelling
Fuller is clearly exceptionally conscious of the place of the "self" in
any global system, as illustrated by the following:
- Instead of starting with parts -- points, straight
lines, and planes -- and then attempting to develop these inadequately
definable parts into omnidirectional experience identities, we start with
the whole system in which the initial "point" turned out to be self, which
inherently embraced all of its parameters wrapped tightly in that initial
underdeveloped, self-focused aspect of self... (I, 488.00)
- The fourness of self and the fourness of otherness comprehension.
Comprehension involves tuned-in octave resonance as well as omnidirectional
and local angular integrity. (II. 268.02)
- Experience is inherently omnidirectional; ergo, there
is always a minimum of 12 "others" in respect to the nuclear observing self. The
24-positive and 24-negative-vectored vector equilibrium demonstrates an
initially frequenced, tetrahedrally quantized unity of 20, ergo, the Universe,
as an aggregate of all humanity's apprehended and comprehended experiences
is at a minimum a plurality of 24 vectors. (II, 537.131)
It is however quite unclear that these cognitive insights have been explored
in subsequent development of his work. In part this is a consequence of his
special jargon -- a typical characteristic of innovators with respect to modes
Fuller's reference to 12 "others" is clearly of potentially fundamental
significance to the common symbolism of the unreconciled Abrahamic religions
that are at the root of so much global discord in a context of faith-based
Irresponsibility for Major World Problems: the unexamined role of Abrahamic
faiths in sustaining unrestrained population growth, 2007; Generic
Reframing of the 12 Tribes of "Israel": "We have met the Zionists
and them is us", 2009).
Is this a failure of cognitive geometry? If the issues of archetypal symbolic
and spiritual 12-foldness have
yet to be effectively addressed, why is there any expectation that secular
analogues, in the form of roundtables and jury panels, should operate effectively
in support of global governance? How is it that the exceptional genius, William
Sidis (1898-1844) is widely quoted as saying: I attach
great value in the working out of my theories to the help given by polyhedral
angles of the dodecahedron which enter into many of the problems. Is
there a cognitively unexplored implicit heritage from the Greek
dodekatheon (and its
Roman analogues) -- now primarily embodied in the trade marks on luxury
goods? Is there an important sense in which cognition is dependent on a "dodecameral
of Intelligible Associations: remembering dynamic identity through a dodecameral
mind, 2005)? Curiously one of the shapes hypothesized for the universe
is a Poincaré dodecahedral
The challenge is that each such innovator has somehow arrived at a unique
insight from which claims are made with regard to its capacity to encompass
the whole. This is necessarily an "inconvenient truth" for others
exposed to it, or other innovators who may follow (An
Inconvenient Truth -- about any inconvenient truth, 2008). The problem
is central to the challenge of any new global strategy which purports to render
obsolete, or subsume, any previous strategy. The question is "where" is
any such insight positioned within a "geometry of thinking", and
how is it configured in relation to other such insights?
The question is therefore how to render explicit such paradoxical
reflexivity and how to embody it in the light of the arguments of Francisco
Varela (Laying Down a Path in Walking: essays on enactive
The Embodied Mind: cognitive science
and human experience, 1991) and George Lakoff and Mark Johnson (Philosophy
In The Flesh: the embodied mind and its challenge to western thought, 1999).
approaches have perhaps been most succinctly summarized by Jennifer Gidley
Evolution of Consciousness as a Planetary Imperative: an integration of integral
views. Integral Review, 5, 2007) to the effect that:
However, the growing awareness of a potential planetary crisis has highlighted
the significance of finding new ways of thinking, if humankind is to move
through our current complex challenges. This critical imperative appears
to be mobilizing researchers from a wide range of disciplines to broaden
the notion of evolution of consciousness beyond its biological bounds.
Integrating disagreement and dissent
The international community
makes a case for "tolerance" with little articulation of any practical
utility. In the aftermath of the financial crisis of 2008, it was argued
that the inequality created by huge bankers salaries is a price worth paying
for greater prosperity (Public
must learn to 'tolerate the inequality' of bonuses, says Goldman Sachs vice-chairman,
The Guardian, 22 October 2009). This is reminiscent of the tolerance
expected by a US
Ambassador to the United Nations, Madeleine
Albright when questioned on whether the sanctions against Iraq (killing
more children than at Hiroshima) was appropriate. Albright replied: "I
think this is a very hard choice, but the price -- we think the price
is worth it." (We
Think the Price is Worth It, Fair, 2001).
The simple question in terms of any creatively elaborated "geometry of
is how does it allow for those who do not think in the same way -- who disagree?
This is the core challenge of global governance -- and of democracy. How can
allowance be made for disagreement in such a geometry? However "tolerance"
is also a design term fundamental to construction of all kinds. But how is "tolerance" to
be understood in a "geometry of thinking"?
There is no map of how the unique "cognitive odours" are positioned
in relation to one another -- of how the mutually offensive "stinks" ensure
distance between innovators. In effect there is no effort to process or
represent disagreement -- except in efforts to facilitate its elimination through
reconciliation in agreement. Is this text itself an invitation to agreement?
And yet again, Fuller's articulation of tensegrity offers insights into how
disagreement might be configured, namely how perspectives of different orientation
might be configured without seeking to ensure that there is only one orientation
for Superordinate Frame Configuration, 1992).
Interestingly, tensegrity structures are robust precisely because of their
dynamic "tolerance" to destabilization. But how might that translate
into any cognitive configuration?
Requisite variety of perspectives
There is a curious implicit assumption that if everyone agreed with what is
presented by some as being "right", then all global strategic challenges
could be resolved. There is relatively little recognition that differences
of perspective are vital to the sustainability and survival of any system.
In cybernetic terms this has been expressed as the requisite
variety, or requisite complexity, to
manage a complex system. In psychosocial systems, however, this variety may
often be framed as anathema -- as a recognition of those who are not "on
or "singing from the same hymn sheet", having failed to grasp
the message. In some belief systems they may simply be framed as "unbelievers"
against whom any sanction is appropriate. How is this perspective to be integrated?
Consistent with Fuller's focus on three and four in constituting a viable
system as described geometrically, others have struggled with the articulation
of psychosocial systems in the light of three and four categories, in various
combinations. The work of Carl
Jung has been especially significant,
notably through his efforts to interpret a range of symbol systems from a variety
of cultures in this light -- some with geometrical representations. This
work was more specifically developed by Marie-Louise
von Franz (Number and Time, 1974). Typically
however any associated representations have been in two dimensions through
polygons. This is also the case of the AQAL system of the Integral
Movement with its focus on four quadrants of a circle.
Fuller has done much to extend the representation into three dimensions but
in doing so has essentially focused on the geometry and its tangible significance
and has rendered implicit the psychosocial implications. It is Stafford Beer
and his collaborators who endeavoured to give functional significance to polyhedral
representation of psychosocial systems -- with his focus on the icosahedron
through syntegrity. Associated with this work has been the further development
of his management cybernetics into the elaboration of a viable
system model (VSM). However the psychosocial implications of this are much
diluted, except in the extension into knowledge cybernetics by
Maurice Yolles (Knowledge
Cybernetics: a new metaphor for social collectives, Organisational
Transformation and Social Change, 2006; Exploring
Cultures Through Knowledge Cybernetics, Journal of Cross-Cultural
Competence and Management, 2007).
Such ventures are a long way from any recognition of the psychosocial significance
of more complex polyhedra in more than three dimensions (Potential
Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry
as a Rosetta stone for cognitive frameworks, 2007). Given the level
of disagreement which prevails in the global system, the question is how complex
might a polyhedron need to be to be able to map such complexity and the many
orientations it implies? And how then to comprehend it?
The consequence of such failure is well illustrated by the traditional Eastern
tale and image of the seven
blind men and the elephant. How many perspectives are required for a global
understanding? How to determine how many may be lacking for such a perspective?
The simpler example of the two perspectives necessary for stereoscopic vision
makes clear the nature of the challenge described by as the need for "poly-ocular
vision" by Magoroh
Maruyama (Polyocular Vision or Subunderstanding, Organization Studies,
2004). However this focus on the vision metaphor
obscures the more general challenge of the need for quite different modes of
knowing as exemplified by the challenge of integrating a set of polysensorial
Challenge of Polysensorial Knowledge: bringing the "elephant" into "focus",
2008). This is consistent with the argument of Chris
Lucas that generally
multiple objectives or parameters have to be met or optimised before any 'master'
or 'holistic' solution is considered adequate (Practical
The cognitive challenge may be clarified through nuclear fusion as a metaphor
-- where the technical challenge is to configure magnets so as to confine and
contain plasma such that it does not touch the walls of its container when
heated to extreme operational temperatures. The question is what is the configuration
of perspectives necessary to contain collective attention globally without
it becoming inappropriately attached to the forms by which it is contained
-- if such containment is to be transformative (Enactivating
a Cognitive Fusion Reactor Imaginal Transformation of Energy Resourcing (ITER-8),
This same challenge of cognitive fusion might also be described from an Eastern
perspective in terms of a configuration of an appropriate variety of perspectives
adequate to the containment of ch'i.
The complete set of 64 conditions encoded by the hexagrams of the I
might be understood in this light. Both understandings offer insights
into the challenge of global governance.
In each such case it is not simply the structural configuration
-- as is clear from tensegrity. It is a question of the dynamics of the structure.
It is the contrast between inadequate assumptions regarding the adequacy of
"genetics" as a source of comprehensive explanation and the recent
recognition of the importance of the dynamics of epigenetics.
It is a question of how the different modes of understanding "dance" together.
The question may be what is the epigenomic
map (Ian Sample, Epigenome
Decoded: 'A new frontier for genetics', The Guardian, 15
October 2009). Or perhaps the challenge is an "epimemetic map"?
Again this recognition is partly represented through Fuller's detailed articulation
of the transformation between different configurations, notably in terms of
the vector equilibrium (Vector
Equilibrium and its Transformation Pathways,
1980). But again there is almost no trace of the psychosocial implications
of this dynamic in the subsequent development of his work.
Self-reflexivity through a "shadowy" dual
Although Fuller's work is seemingly based on a cognitive understanding of
self, as mentioned above, the dramatic challenge in any psychosocial system
between subjectivity and objectivity is apparently absent. And yet it could
be argued that its articulation is present in a most insightful manner through
his extensive discussion of the geometry of the relationship between polyhedral
However its potential psychosocial significance is again "buried".
The images below indicate how duality might be encoded in the objectivity
of "points", interrelated by "lines" of argument triangulating
them into a configuration -- thereby creating "sides". But subjectively,
the "sides" may
be held to be "points", interrelated by a different pattern of "lines" --
thereby creating a different set of "sides". One mode of understanding
is the invert of the other. In Jungian terms it might be understood as an implicit
shadow or one
"hidden" within an "other".
Representation of such images by software enables the transformation of one
to the other to be followed -- in geometrical terms (Stella:
There is a real challenge to ensuring any cognitive continuity between subjectivity
and objectivity, especially collectively in a psychosocial system. In drama
it is described as the process of enantiodromia,
whereby one is transformed into its opposite. This may be observed on a larger
scale where a political system hostile to the values of another
progressively acquires the values of the other. On the occasion of the UK Tory
and Labour annual conferences in 2009, much was made of the Tories taking on
the "red" values of Labour and of Labour taking
on the "blue" values of the Tories. It might be argued that the US
has adopted the level of invasive surveillance of its population that it previously
disparaged in USSR society -- whilst the latter has taken on a range of dubious
capitalist values it previously disparaged.
The geometric representation highlights the sense in which if one of the pair
is an "objective" system, the other is an anti-system associated
with the "subjectivity"
whereby that objectivity is called into question. This might be said to be
the nature of the relationship between "mainstream" global initiatives
lauded for their "objectivity" and "alternatives" disparaged
for their lack of objective coherence. However, even in the case of any "objective" system,
perspectives emerge amongst those who perceive the system not to be what it
is claimed to be -- recognizing underlying dynamics, etc. This is most obviously
evident in "objective" efforts to rationalize complex organizations
-- possibly resulting in disaffection amongst personnel who experience matters
otherwise (an extreme example being the staff
suicides in France Telecom, a major scandal in 2009).
A "geometry of thinking: must necessarily
encompass these extremes and the dynamics between them.
Keys to global governance "embedded" in synergetics as a meta-model
The argument above uses the richness of Fuller's synergetics to stress that
attention is required as much to what is not elicited
from that work, by himself and those who have followed, as to what is evident
and a widely appreciated inspiration. In that sense, as a comprehensive model,
the more general argument is that it does indeed model integrative thinking
through the geometry -- but some (if not a greater proportion) is effectively
"hidden" or "buried" within the model. The model embeds
or embodies that of which it is not conscious. It effectively implies a (cognitive)
dual which is implicit and to that extent absent.
Like each comprehensive endeavour, it is its own metaphor -- using the phrase
of biologist Gregory
Catherine Bateson, Our Own Metaphor;
a personal account of a conference on the effects of conscious purpose on human
1972). In explaining why "we are our own metaphor", Bateson
One reason why poetry is important for finding out about the world is
because in poetry a set of relationships get mapped onto a level of diversity
in us that we don't ordinarily have access to. We bring it out in poetry.
We can give to each other in poetry the access to a set of relationships
in the other person and in the world that we're not usually conscious of
in ourselves. So we need poetry as knowledge about the world and about ourselves,
because of this mapping from complexity to complexity. (pp. 288-289)
In this sense a model is not what it seems. Its hidden dual holds a complementary
pattern of insight. It is only together that they are effectively as comprehensive
as is claimed for the objective interpretation. But comprehending what has
not been rendered explicit is a challenge because it is "about" the process
of comprehension -- of "thinking about the geometry".
Due to the progressive interlocking of accumulated patterns into nested meta-patterns,
as a solution to human processing capacity limitations, there is a form
of directed, convergence onto a progressively clarified ultimate meta-pattern,
towards which learning tends asymptotically, in that final (en)closure is never
achieved (except possibly as an essentially transient, private, transcendental
experience). Bateson describes this ultimate pattern as:
The pattern which connects (all living creatures) is a meta-pattern.
It is a pattern of patterns. It is that meta-pattern which defines the vast
generalization that, indeed, it is patterns which connect." (Mind
and Nature; a necessary unity, 1979, p. 11)
Of possible relevance in terms of poetic sensibilities, in the light of Bateson's
comment, is the concept of a clinamen.
This is a constraint that guarantees an enormous flexibility of meaning and
is an act of memory.
Model builders have a marked tendency to set cognitive processes in definitional
"stone" -- to reify and to petrify (Reorganizing
Knowledge and Unfreezing Categories, 2009). Matters are in fact worse
when it is "the
other" who gets set in stone and petrified -- by whom one is then "petrified"
in turn, hence "terrorism". Any dynamic engagement with such a "stone"
-- dialogue -- is then ridiculous. Some of the challenges are delightfully
highlighted by the following points.
|The Hazards of System Building
Matthew Melko, System Builder
(Presented at the Foundation
for Integrative Education Conference, Oswego, New York, 1969;
reproduced in Main Currents in Modern Thought, vol. 269 no.
- You identify with your system. It cost you blood to build it, and
if it is attacked, it is your blood that is being shed.
- You cannot tolerate tentativeness, suspension of judgment, or anything
that does not fit the system.
- You cannot apprehend anyone else's system unless it supports yours.
- You believe that other systems are based on selected data.
- Commitment to systems other than your own is fanaticism.
- You come to believe that your system entitles you to proprietorship
of the entities within it.
- Since humour involves incongruity and. your system explains all
seeming incongruities, you lose your sense of humour.
- You lose your humility.
- You accept all these points -- insofar as they apply to builders
of other systems.
- So do I. (P.S. I hope I believe in the cult of fallibility)
Implications for a "meta-model"
Summarizing points made above, any model that claims to be comprehensive
-- a cognitive Theory of Everything -- would seem to require or imply in some
- designing in the potential
for disagreement, the incommensurable and the intractable, rather than
designing them out (Using
Disagreements for Superordinate Frame Configuration, 1992)
- self-reflexivity (Consciously
Self-reflexive Global Initiatives: Renaissance zones, complex adaptive
systems, and third order organizations, 2007)
- a paradoxically conscious approach to ignorance, incomprehension, uncertainty,
Undoing: challenge of incomprehensibility of systemic neglect, 2008; Being
What You Want: problematic kataphatic identity vs. potential of apophatic
identity? 2008), providing for development/evolution into what may
be unknown and allowing for the development/evolution of those who do not
understand (thereby legitimating traditional perspectives)
- flexibility in opening and closing to new information and perspectives,
whether of higher or lower dimensionality (Orrin
E Klapp, Opening
and Closing; strategies of information adaptation in society, 1978;
between Variable Geometries: a brokership style for the United Nations as
a guarantee of its requisite variety, 1985)
- flexibility in alternating between a subjective and an objective perspective
(Max Deutscher, Subjecting and Objecting: an essay
in objectivity, 1983), the essential dynamic of
a holomovement between explicitation and implicitation (David
and the Implicate Order, 1980)
- openness to humour (Humour and Play-Fullness: essential
integrative processes in governance, religion and transdisciplinarity, 2005)
- engagement with understandings of complexity, and the dynamics of complex
systems, as exemplified by the Mandelbrot
through the Dynamics of Strategic Dilemmas -- in the light of the coherence
and visual form of the Mandelbrot set, 2005)
- a creative engagement with questions that emerge in response to comprehension
of the apparent contradictions intimately associated with the paradoxes of
globality (Conformality of 7 WH-questions to 7 Elementary
Catastrophes: an exploration of potential psychosocial implications,
These may be fruitfully related to criteria emerging from other ways of looking
at the challenge of a meta-model.
One approach is to distinguish any criteria by a succession of patterns, as
in the following exploration of articulations governed in terms of from
1 to 20 factors variously challenging to comprehension. These are derived
of Integrated, Multi-set Concept Schemes (1984) as explained in Patterns
of N-foldness; comparison of integrated multi-set concept schemes as forms
of presentation (1984).
As the primary discipline of relationships, the wide range of mathematical
disciplines might be mined for the underlying or generative
which they each emerged (Towards
a Periodic Table of Ways of Knowing -- in the light of metaphors of mathematics,
as to how to think about the emergent insight of anything "meta" may
be sought in a variety of "disciplines" and "ways of knowing".
The particular focus of that paper and its sections (listed
above) is on the possibility of "re-reading" the clues from spiritual
traditions, in the light of the disciplines of movement, as epistemological
clues. The core argument is that whilst spiritual traditions point
to a better, essentially static, condition to be achieved through following
their guidelines, the injunctions in their guidelines are do's and don'ts that
give no sense of the dynamics of the experiential reality that their practice
is claimed to enable. As a
result they appear essentially static and moralistic, and disconnected from
the patterns of movement that people find meaningful -- setting up, through
misapplication of those guidelines, a somewhat antiquated moral barrier that
prevents interpretation of those guidelines in ways that would be highly valued
by those who seek a richer and more dynamic reality. The dynamic is likely
to be essential to the viability of the emergent pattern.
Whilst such guidelines may well be vital to what might be understood
as "attitude control" and coordination, the latter can be usefully understood
as prerequisites to any process of shifting attitude into subtler perceptions
-- described metaphorically through somewhat misleading terms such as "ascent" or "escape".
The distinction between attitude control and ascent for an individual may then
be compared with the various highly elaborated challenges of launching any
vehicle into planetary orbit -- into orbit around the globe (Entering
Alternative Realities -- Astronautics vs Noonautics: isomorphism between launching
aerospace vehicles and launching vehicles of awareness, 2002; Noonautics:
four modes of travelling and navigating the knowledge "universe"? 2006).
Hence the cognitive challenge of "launching" a credible global strategy.
But it is curious that this tends to take the form of launching a single
"pillar" -- only too reminiscent of rocket, missile and projectile
Missives, Missions and Memetic Warfare: navigation of strategic interfaces
in multidimensional knowledge space, 2001).
Especially interesting in relation to model building of any kind is the extent
to which elements of "attitude control", typical of spiritual disciplines
(such as the "humility" highlighted above by Melko), are in fact
vital to the construction and comprehension of any more subtle meta-model --
to the epistemology which it necessitates.
The role of a dynamic is also central to the study of Arthur
of Meaning, 1976), notably in relation to learning/action cycles, and
tentatively adapted elsewhere (Characteristics
of phases in 12-phase learning-action cycle, 1998; Typology
of 12 complementary strategies essential to sustainable development,
1998). Of particular interest is the possibility that seemingly incommensurable
cultural symbols should be reconciled through movement (Dynamic
Exploration of Value Configurations: interrelating traditional cultural symbols
through animation, 2008).
The cognitive challenges have also been variously highlighted through the
Cognitive engagement with globality
Fuller's "geometry of thinking" may be understood as implying a progressive
engagement with globality which he indeed understood to be fundamental to
the global management of resources of "Spaceship
Earth" -- a term which he
Manual for Spaceship Earth, 1969). But it might be said that it is
precisely the instrumental "rationality" of his understanding, and those inspired
by it, which has failed to reflect the psychosocial processes which undermine
such rationality in response to the dramatic challenge of world crises. The
failure of rationality associated with the global financial crisis of 2008,
and its aftermath, is but one indication.
And yet the elements of cognitive geometry are implicit, if not evident, in
the metaphorical geometry through which the attempt is made to develop global
Such examples are developed in more detail elsewhere (Metaphorical
Geometry in Quest of Globality -- in response to global governance challenges,
of Organizations, Policies and Programmes, 1992).
Of particular interest is the continuing reliance on the simplest forms
of geometry in strategic construction, notably the "pillar".
Where Hammurabi (ca.
1728-1686 BC) and Ashoka (304-232
BC) both used
one to articulate their historic principles, the "four pillars" of Barack
Obama were announced in 2009 as: non-proliferation and disarmament;
the promotion of peace and security; the preservation of our planet; and
a global economy that advances opportunity for all people. Other strategic
concerns may be articulated in terms of "axes" or "poles" at
the global level, with a focus on "stakes"
at other levels of society. There is a degree of irony to the fact that T.
E. Lawrence (1888-1935) considered a larger number of "pillars" to
be appropriate (Seven
Pillars of Wisdom, 1922) with respect to the Middle East arena
-- which continues to be strategically problematic.
institutions articulate their basic strategies in terms of sets of pillars
Value Frameworks: pillar-ization, polarization and polyhedral frames of
reference, 2008). There is a metaphorical irony to the fact that "pillars" on
their own do not constitute any form of shelter -- even if "stakes" may
be configured to form a protective stockade. Curiously it is sacred architecture
that tends to configure pillars to enable arches to be constructed to sustain
vaults -- thus creating a form of cognitive shelter.
In a secular society, with respect to the earlier comment on "uprightness",
it is curious that claims are "staked" for a protective set of "rights" which
are merely presented as a list (Universal
Declaration of Human Rights, 1948). The facility with which they may
be configured as a system is not considered (Dynamic
Exploration of Value Configurations: polyhedral animation of conventional value
Whilst pillars are of course basic to any design, such
geometric elements are of the simplest kind in relation to the range of
configurations explored by Fuller. A tensegrity may be fruitfully understood
as a configuration of interlinked pillars in three dimensions. An effort was
made to configure as a tensegrity a set of strategic dilemmas (as paradoxical
forms of pillar) emerging from considerations at the 1992 United
Nations Conference on Environment and Development (Configuring
Strategic Dilemmas in Intersectoral Dialogue, 1992; Spherical
Representation of Icosidodecahedral Net of Strategies, 1992).
Clearly of deep concern is the extent
to which reliance is currently placed on elements so simplistic that they
are incapable of encompassing the strategic challenge, for lack of requisite
complexity. This is notably indicated by the challenge of "polarization" and
"sides" in any current political discourse from which global strategies
are expected to emerge. It is also indicative of the inability to elaborate
sustainable configurations of points or parties -- requiring more complex geometry
-- capable of holding higher orders of consensus. The question is how to move
cognitively beyond "points" and "linearity", as discussed
with Globality -- through cognitive lines, circlets, crowns or holes,
In the light of Fuller's geometrical argument, this suggests the merit of
exploring the role of polyhedra in more effective strategic engagement with
Polyhedral Global Governance complexifying oversimplistic strategic metaphors,
Global Governance Groups: experimental visualization of possible integrative
relationships, 2008; Polyhedral
Empowerment of Networks through Symmetry: psychosocial implications for organization
and global governance, 2008).
Challenge of cognitive geometry
But, despite Young's argument for learning cycles, little effort has been
made to integrate cognitive cycles with the great
circle geometry so fundamental
to systemic viability in Fuller's terms (Emergence
of Cyclical psychosocial Identity: sustainability as "psyclically" defined,
of Interlocking Elements for a Sustainable Global System: configuring strategic
dilemmas in intersectoral dialogue, 1992; Spherical
Configuration of Interlocking Roundtables: internet enhancement of global self-organization
through patterns of dialogue, 1998).
At issue is the nature of "cognitive geometry" (cf Harada Toshinobu,
of "Cognitive Geometry" and
the application to primitive, Bulletin of Japanese Society
for Science of Design, 2000; Rashi Glazer and Kent Nakamot, Cognitive
Geometry: an analysis of structure underlying representations of similarity, Marketing
Science, 1991). This may be explored through the extension beyond linearity
Circlets (2009) and Cognitive
Use is as yet seldom made of available software to support non-linear integrative
Pattern Language Software: facilitation of emergence, representation and transformation
of psychosocial organization, 2009). In theory web technology should
provide communication protocols that are highly appropriate to enabling the
emergence of such forms. This has been recognized in the case of the Team Syntegrity
Initiative as described by J. Truss, et al. (The
Coherent Architecture of Team Syntegrity: from small to mega forms,
2003), where it is noted that:
TSI has not had the resources to simultaneously develop electronic applications,
though many exciting Syntegrity-based designs are awaiting the right opportunity
and resources. Our task for the future ranges from providing the ability
for groups to conduct some or all of the Syntegration process online, to
applying the geometric design principles underlying the architecture of the
Syntegrity forms, and the cybernetic principles underlying the protocols,
to support the evolution of and connections among groups and communities.
Insight into cyclic geometry may in fact be most readily
understood through music (Carol L. Krumhansl, The
Geometry of Musical Structure: a brief introduction and history, Computers
2005). Hence the potential merit of musical representation of strategic challenges
of Global Hot Air Emissions to Music, 2009). This may relate to
transforming "vicious" social cycles and feedback loops (Vicious
cycles and loops, 1995; Dysfunctional
Cycles and Spirals: web resources on "breaking the cycle", 2002).
Given the efforts of Stafford Beer to design and implement a cybernetically
informed management system at corporate level and at the national level (in
Project Cybersyn), it is
curious that so little of that research continues with respect to the challenge
of global governance. In contrast, however, it might be considered amazing
the amount of effort and investment devoted over deacdes to the design of the
Large Hadron Collider in
pursuit of the so-called "God
Particle" -- faith-based science at its best (Robin McKie, Second
chance for Large Hadron Collider to deliver universe's secrets, The
November 2009). At an estimated cost of 4 billion euros, it is funded by and
built in collaboration with over 10,000 scientists and engineers from over
100 countries as well as hundreds of universities and laboratories. Projet
Cybersyn was of course destroyed at the instigation of Nobel Peace Laureate
Henry Kissinger, due to inability to tolerate any alternative models or experiments
in governance in the western hemisphere. The contrast
is all the more astonishing in comparing the geometry of the two images below
-- and what they imply for the underlying cognitive geometry.
|Logic diagram of a cybernetic
factory by Stafford Beer
[from Andrew Pickering,
Science of the Unknowable:
Stafford Beer's cybernetic informatics,
2006, Fig 4]
|Cross-section of the 27km circular tunnel of the
Large Hadron Collider
|The diagram which
merits display here derives from a document by Beer (1962). Reproduction
of the diagram is however indicated as subject to the
permission of John Wiley and Sons
and Allenna Leonard. Similarly, although the CERN device has been developed
entirely with taxpayer funds, that image is also subject to copyright.
Such antiquated constraints on the rapid dissemination of ideas for non-commercial
purposes is indicative of a more fundamental problem in interrelating any
insights of potential value to global governance (as discussed
in the Conclusion). Given their common focus on
the integrative power of rings, such dysfunctional possessiveness may be
well-caricatured by the role of the Gollum in The
Lord of the Rings.
Existential and experiential engagement with globality
The cognitive challenge, and its implication for more appropriate psychosocial
organization, might be said to be a legitimate preoccupation of mainstream
behavioural approaches -- to the extent that the psychological dimension is
considered to be of any significance. Such approaches might however be seen
as insensitive, if not hostile, to the degree of subjectivity implied by existential
and experiential approaches. It is questionable whether such dimensions were
considered meaningful by Fuller.
The global strategic challenge, and the question of a collective political
will to change, would seem however to lie beyond the realm of behavioural psychology,
notably as it is deployed to "motivate" people in conventional marketing
of products and services, including the promotion of global social change strategies.
The missing factor is a degree of existential engagement, whatever that may
be held to be (Psychology
of Sustainability Embodying: cyclic environmental processes, 2002).
The "geometry of thinking" might be understood as one approach to a "pattern
language". But, as with other languages, a vital question is how people experience
their identity as expressed and carried by any language. The exercise mentioned
above (Patterns of N-foldness, 1984) presents various pattern languages. That
Pattern Language, 1977) has constituted an exemplar for other approaches
to pattern language and experimental adaptations of it (5-fold
As a metaphor, however, the point might be made that the visible
stars have long been configured into patterns of named constellations with
which legendary meanings have been associated. Such interpretations are however
meaningless from an astronomical or astrophysical perspective. The patterns
of constellations might be said to be as meaningless as the process of "joining
up the dots"
which led the intelligence communities to assert the existence of weapons of
mass destruction in Iraq.
Crucially Alexander moves beyond the patterns he identifies, framing their
significance in a new way, in an interpretive volume (The
Timeless Way of Building, 1979):
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
and precise, but it cannot be named,
The search, which we make for this quality, in our own lives, is the
central search of any person, and the crux of any individual person's story.
It is the search for those moments and situations when we are most alive.
In order to define this quality in buildings and in towns, we must
begin by understanding that every place is given its character by certain
patterns of events that keep on happening there.
These patterns of events are always interlocked with certain geometric
patterns in the space. Indeed, as we shall see, each building and each town
is ultimately made out of these patterns in the space, and out of nothing
else: they are the atoms and the molecules from which a building or a town
The specific patterns out of which a building or a town is made may
be alive or dead. To the extent they are alive, they let our inner forces
loose, and set us free; but when they are dead, they keep us locked in inner
The more living patterns there are in a place -- a room, a building,
or a town -- the more it comes to life as an entirety, the more it glows,
the more it has that self-maintaining fire which is the quality without a
As he notes, the patterns are always interlocked with certain
geometric patterns. Beyond human construction, Alexander has also explored
these patterns in nature (Christopher Alexander, The
Nature of Order, 2004). Arguably it is through this
existential engagement with the geometric patterns that any meaning associated
with globality emerges, on whatever scale. It is specifically this factor that
is absent, or ineffectually present, in current efforts to engage people with
global strategies, however urgent they are claimed to be -- as with climate
Although it is not the case, the term "pattern" is readily assumed
to imply some configuration that can be meaningfully represented in two dimensions.
Of far greater interest is the possibility of patterns in three or more dimensions,
as suggested by the elaboration of Fuller's "geometry of thinking".
A more appropriate term is then topology, especially because of the psychological
significance of "topos" as place, as notably articulated by Frances
Art of Memory, 1966) with respect to the mnemotechnical method
of loci. This is also fundamental to the philosophy of Martin
Heidegger as described by J. E. Malpas (Heidegger's
topology: being, place, world, 2006):
Almost all of Heidegger's language... is "iridescent" in the sense of constantly
shining and showing different facets. The attempt to delineate the topology
of thinking and the topology of being will always carry a certain "iridescence"
of this sort. It is an iridescence that may also be compared to the "backwards
or forwards" relatedness that is found in hermeneutical thinking and that
is also tied to the topological. It is the reflection of the iridescent,
the multiple, shifting character of place as such. (p. 37)
The configuration of any pattern in three dimensions then offers
a new kind of template for identity and the dynamics of its engagement with
encompassing cognitive reality, and any embodiment of it (Topology
of Valuing: psychodynamics of collective engagement with polyhedral value
2008). It is through the potential of such topological configurations that
as yet unexplored possibilities are to be found (In
Quest of a Strategic Pattern Language: a new architecture of values,
2008). Being more generic, topology includes forms that are more paradoxical
and less intuitively obvious, as already explored by some schools of psychoanalysis
R. D. Laing). The simpler examples of great potential significance are the Möbius
strip and the Klein
bottle, as discussed elsewhere with respect to self-reflexivity
with Globality through Enacting a Klein bottle: cognitive implication in
a polysensorial "lens", 2009). Jacques
Lacan and his followers, informed by topology and knot theory, focused on
the significance of the manner in which the surface of the
Klein bottle appears to be intersected by a portion of itself.
Again the argument here is that, whether in Fuller's work or those of other
initiatives of comprehensive ambition, the challenge is one of "decoding"
what is clearly there. But the challenge, as with a Rosetta stone, is that
the code is effectively "lost" because it lies "beneath" or "within" the
geometry that is so visible. In Maruyama's terms the existential significance
has been "subunderstood". A degree of cognitive closure has set
in through the manner in which geometry is conventionally apprehended. However,
in principle at least, Fuller's work is not about closure but about degrees
of openness -- which the satisfaction with premature cognitive closure has
Such openness is evident in the tensegrity structures and principles
which underlie the viability of geodesic domes. The question is whether those
principles are of relevance to the design of a new order of psychosocial organizations
and strategies capable of configuring a higher degree of incommensurability
Self-reflexive Global Initiatives: Renaissance zones, complex adaptive systems,
and third order organizations, 2007).
A quite distinct approach to cognitive geometry may be found in the patterns
in sacred architecture, notably as assiduously explored by Keith
Critchlow (Order in Space: a design source book, 1969; Islamic
Patterns, 1976; Islamic Art and Architecture: system of geometric
design, 1999). Of relevance is the contrast between the Western attitude
(and its concentration on the external look of a building) and the traditional
Islamic concern with the feel of space within. As argued by Geeti
of an exhibition entitled Kham Space and the Art of Space, New Delhi,
The geometry of architecture is clearly based on an elaborate symbolism.
In Islam, the dome, the minaret, the arch, the quindi vaults and pendentives
do not stand for themselves, as invented forms. based at times on engineering
feats; but for another, supra-reality which cannot be depicted in any other
way but pure geometry. The dome for instance, is associated with the Spirit
which pervades all beings, as indeed the vault of the sky embraces its enclosed
space. The dome unifies space and encompasses it. The arch expresses the
human soul, repeated ad infinitum soaring and aspiring towards the heavens.
The iwan, the arched doorway or corridor, is viewed as the locus
of the soul, moving between the room, seen as the body, and the garden or
courtyard which is taken as the spirit.
The nature of what tends to be lost in conventional abstraction -- in the
geometry on its own -- has been highlighted by Steven
M. Rosen (Topologies
of the Flesh: a multidimensional exploration of the lifeworld,
of Apeiron: a topological phenomenology of space, time, and individuation,
Value Inquiry Book Series, 2004). He notes the manner in
which the richness of psychosocial engagement with the world has been completely
undermined by formal discourse -- an "eclipse of the lifeworld" in his
terms. Ironically, in a period of sensitivity to the challenges of "resources" and "energy",
this view is echoed by other authors, notably arguing for the desirable
potential of a participatory encounter with reality:
Geometry as a metaphorical magic mirror of thinking
It is curious that there is widespread recognition of the function of aerial
arrays. especially radio telescopes, to resolve distinct signals into a coherent
image or message. The metaphor has been developed to detect cognitively "distant" or "larger" systems
de Rosnay (The
Macroscope: a book on the systems approach, 1979) who subsequently
prefaced a sequel by Luc de Brabandère (Le Latéroscope: systemes
et creativite, 1989). The latter noted that, as the basic tool of creativity,
the latéroscope is necessarily impossible to construct. Such
endeavours raise the question of the nature of the cognitive instrument by
which meaning can be reflected. The suggestion is that like the telescope
it has a particular geometry, but that its mirroring capacity has a "magical"
quality to it, perhaps as in many mirrors of legend. The instrumental nature
of the geometry is necessarily complemented and reframed by metaphor, most
probably an array of complementary metaphors.
Metaphor: There is now a considerable body of literature
regarding the cognitive role of metaphor, notably with respect to policy formation.
The question is what are the productive metaphors, or sets of complementary
metaphors, that might be a key to a new geometry of global governance (Metaphors
as Transdisciplinary Vehicles of the Future, 1991). More challengingly,
with respect to any enterprise as noted above by Bateson: We
are our own metaphor.
With respect to comprehension through personification, Kenneth
Boulding (Ecodynamics; a new theory of societal evolution, 1978)
helpfully cautions against rejecting such metaphors in the following terms:
Our consciousness of the unity of the self in the middle of a vast complexity
of images or material structures is at least a suitable metaphor for the
unity of a group, organization, department, discipline, or science. If personification
is only a metaphor, let us not despise metaphors -- we might be one ourselves.
More of a challenge is the extent (whether individually or collectively)
to which cognitively one may become (in any integrative sense) a caricature
of oneself, a mockery of oneself, or a shadow of one's former self -- or that
a civilization may turn into a parody of what it believes it coherently represents.
This is typically echoed in political
satire and more concretely in the burning
of an effigy by opponents.
Magic: The last of the three
laws of Arthur
Clarke suggests that: Any sufficiently advanced
technology is indistinguishable from magic. However the "technologies"
of the future are as likely to be cognitive as what is now conventionally
recognized as technology -- as already implied by Robert
as Symptom and Dream, 1989). What might be the nature of the cognitive
technology that would constitute a "magical" breakthrough in global
governance -- given the optimistic dependence on future human ingenuity to
circumvent foreseen and unforeseen crises (Thomas Homer-Dixon, The Ingenuity
Gap: how can we solve the problems of the future? 2000).
The nature of the "requisite" cognitive surprise is well indicated
by the much-quoted
statement by physicist Niels
Bohr in response to Wolfgang
"We are all agreed that your theory is crazy. The question which divides
us is whether it is crazy enough to have a chance of being correct. My
own feeling is that it is not crazy enough."
To that Freeman
Dyson added: "When a great innovation appears, it will almost
certainly be in a muddled, incomplete and confusing form. To the discoverer,
himself, it will be only half understood; to everyone else, it will be
a mystery. For any speculation which does not at first glance look crazy,
there is no hope!" (Innovation in Physics, Scientific American,
199, 3, September 1958)
Decades later string
theory, as the amazing new "craziness", is now the great
hope for a unifying theory of the material universe. It endeavours to reconcile
quantum mechanics with relativity by arguing that subatomic particles are strings
vibrating through space
and time, differing merely in the ways in which they vibrate -- through 10
or 11 dimensions (as in M-theory). This possibility has progressed so far
beyond experimental provability that the only guide to the adequacy of a
solution is its unifying beauty and elegance.
What might this imply for a form of global governance
appropriate to the challenge of the 21st century? Pointers towards understanding
this challenge are discussed elsewhere (Imagining
the Real Challenge and Realizing the Imaginal Pathway of Sustainable Transformation,
Quest of Mnemonic Catalysts for comprehension of complex psychosocial dynamics,
The extreme forms of symmetry (represented above), detected by mathematicians
and claimed to be of fundamental significance, emerge from an extraordinary
appreciation of unusual connectivity, which they themselves have nicknamed
du Sautoy, Finding Moonshine: a mathematician's
journey through symmetry, 2008). The question might be the
challenging nature of the "moonshine"
that would be of value to future understandings of global governance
Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry
as a Rosetta stone for cognitive frameworks, 2007).
Geometry itself has been framed as "magic" (Siobhan Roberts, The
King of Infinite Space: Donald Coxeter and the Magic of Geometry,
2006).There are indeed many references
to the "magic" of Fuller, most typically from an architectural perspective
(R J Evans, Geodesic
No Place Like Dome, Architecture,
July 2009). The thinking of Fuller has been related to the "magic
of M. C. Escher (Victor
Time with M. C. Escher and R. Buckminster Fuller, 2003). In describing
the "magic" of the operation of the open source community, Eric
S. Raymond (The
Magic Cauldron, 1999) acknowledges the relationship
with "ephemeralisation" (doing more with less) through the knowledge of synergy
promoted by Fuller.
"Magic" is of cognitive significance in another respect, namely through the
"magic numbers" that are the focus of extensive literature. Their relation
to the geometry of thinking is discussed in Fuller's Synergetics (995.00:
Vector Models of Magic Numbers, 1997). Of particular interest are
the patterns of association of numbers characteristic of magic
squares, notably recognized as fundamental to sacred geometry in various
Higher Order Patterning of Tao Te Ching Insights: possibilities in the mathematics
of magic squares, cubes and hypercubes, 2003). Fascination with such
patterns is evident in the widespread interest in sudoku.
Such "magic" raises the question of the relevance of such connectivity to governance
(Governance through Patterning Language: creative cognitive
engagement contrasted with abdication of responsibility, 2006).
relevance to such tenuous connectivity and coherence are various understandings
of correspondence (Theories
of Correspondences -- and potential equivalences between them in correlative
thinking, 2007). Curiously some of these recall the cognitive implications
of traditional understandings of the cognitive role of the image, whether
in magic (Magic,
Miracles and Image-building: Poetry-making and Policy-making, 1993),
or as highlighted by Kenneth Boulding (The Image:
knowledge in life and society, 1956). The role of such correspondences
in relation to traditional cognitive engagement with the environment has
been extensively documented by Darrell
A. Posey (Cultural and Spiritual
Values of Biodiversity: a complementary contribution to Global Biodiversity
Mirror: The paradoxical nature of the cognitive challenge
has been extensively explored by Douglas
Escher, Bach: an Eternal Golden Braid, 1979; Metamagical
Themas, 1985; I
Am a Strange Loop, 2007).
A mirror has been used
metaphorically in many cultures to facilitate comprehension of that challenge.
Use of magical mirrors for scrying and
"speculation" has been traced back to Euclid as the first geometer.
It was the subject of a papal bull (Super Illius Specula, 1326)
threatening excommunication of those confining demons in mirrors
so as to foretell the future. Brian Dillon (Disc
24 October 2009) comments on the fascination for artist and magus of
the black mirror as being actually and allegorically
a portal between arcane practices and mainstream
painting and sculpture. The use of mirrors, notably in the form of a jade
bi disc, has been associated with the representation of cosmological
principles in Chinese culture (Robert Dickter, The
Ya Shape and: Bronze Mirrors, The Ming Tang, The Jade Bi Disc, The Mayan
Calendar In: Number, Time and Archetype).
Of particular interest
to any global strategy is the extent to which the patterns of order in nature
Nature of Order, 2004) themselves constitute a mirror (Stepping
into, or through, the Mirror: embodying alternative scenario patterns,
Embodiment of Transdisciplinary Integration (SETI): the universal criterion
of species maturity? 2008). The "cognitively transformative" interaction
with a mirror might be usefully understood through a conflation, "con-fusion"
or "con-volution" of the implication of a simple mirror reflection,
a torus, a Mobius strip and a Klein bottle (Engaging
with Globality through Knowing Thyself, 2009). Rather than any form
of "revolution", the new paradigm so widely sought may in fact
require a paradoxical degree of cognitive "convolution". As with
looking into any mirror, what is then seen may be terrifying -- readily to
be condemned from a conventional papal perspective, as with the non-geocentric
model of the universe (Thinking
in Terror: refocusing the interreligious challenge from "Thinking after
The cognitive implications
of the hole in the bi disc (with its two sides to be understood
as cognitively twisted together) is reminiscent of the Eygyptian all-seeing Eye
of Horus, as well the distorted projection of the two-sided hole into
the traditional two-dimensional symbol of the Tao, as discussed previously
of The Other a politically relevant psycho-spiritual metaphor? 2006).
Curiously the hypothesized dodecahedral form of the space-time universe has
an inherent mirroring property as described by Jean-Pierre
Cosmic Hall of Mirrors, Physics World, September 2005;
Finite Dodecahedral Universe, Nature, 9 October 2003; Mirror,
Mirror up above, Unesco Courier, May 2001).
for any "cognitive
light leaving that dodecahedron through a given face immediately re-enters
through the opposite face, such that any observer whose line-of-sight intercepts
one face has the illusion of seeing a slightly rotated copy of their own
dodecahedron. Luminet asks whether we could be living deep in a cosmic mirage,
where rays of light multiply and distort our perceptions of space. Instead
of being flat and infinite, might space not in fact be folded up -- and
our sense of the universe's vastness just an illusion? How might this
apply to any "universe of knowledge"?
A prudent approach suggests that the pattern of understanding held to be
most appropriate to the unification of the material universe should be
considered of greater probability with regard to comprehension of the unification
of the intangible universe. Adapting the above statement with respect to string
theory, the future unifying theory of psychosocial relations might endeavour
to reconcile the cognitive engagement with locality and with globality by arguing
that the disparate cognitive senses of individual identity are strings vibrating
through cultural space and comprehension time, differing merely in the ways
in which they vibrate -- through 10 or 11 dimensions.
It would be an amazing
irony to discover a correspondence (as
understood above) between the cognitive capacity to envisage a unifying physical
theory (through the variety of string
theories) and the
capacity to imagine various representations of individual variety and integrity
(with their different mappings, whether traditional or modern). The ultimate
provocation to conventional thinking would be any recognition that the traditional
a crude intuitive 2-dimensional mapping of some form of 12-dimensional integrity
intimately associated with comprehension of number
theory -- however this may
be understood in the future (Representation,
Comprehension and Communication of Sets: the role of number, 1978).
Any cognitive unification would also require integration of the sense of
identity with intellectual property and the competitive derivation of energy
from it -- of continuing fundamental concern to the institutionalization of
synergetics, syntegrity and analogous endeavours (Einstein's
Implicit Theory of Relativity -- of Cognitive Property? Unexamined influence
of patenting procedures, 2007).
A pattern corresponding to Wolfgang Pauli's
Principle is suggested by the challenge of epistemological antipathy. Also
of interest is the extent to which the reflective, refractive and mirroring
properties of the facet configuration of precious stones -- typically
associated with "magic" -- offers a mirror indicative of the geometry
of possible unification (Patterning
Archetypal Templates of Emergent Order: implications of diamond faceting for
enlightening dialogue, 2002).
However, just as the guide to the adequacy of a string theory is to be found
primarily in its aesthetic elegance, that of any emergent theory of psychosocial
relations in "10 or 11 dimensions" may also depend on its aesthetics and symmetry.
It is in this sense that music, poetry and song offer a form of cognitive mirror,
as argued by Gregory Bateson (repeating the quote above):
One reason why poetry is important for finding out about the world is because
in poetry a set of relationships get mapped onto a level of diversity in us
that we don't ordinarily have access to. We bring it out in poetry. We can
give to each other in poetry the access to a set of relationships in the other
person and in the world that we're not usually conscious of in ourselves. So
we need poetry as knowledge about the world and about ourselves, because of
this mapping from complexity to complexity.
Given the widespread engagement with aesthetic resonances (and an explicit
recognition of "vibrations" and "vibes"), the challenge is how to engage that
understanding to reframe global governance and the appreciation of the global
problematique as previously discussed (A
Singable Earth Charter, EU Constitution or Global Ethic? 2006; Poetry-making
and Policy-making: arranging a marriage between Beauty and the Beast,
This has the potential of reframing current strategic challenges (Poetic
Engagement with Afghanistan, Caucasus and Iran: an unexplored strategic opportunity? 2009; Conversion of Global Hot Air Emissions to Music: aesthetic
transformation and instrumentalization of vaporware, 2009).
The secret within "Bucky's Ball"?
There is a curious mirroring, potentially of great significance, between the
worldwide (popular) fascination with fooball and the dramatic global challenges
of the future with which the world is believed (by an elite minority) to be
faced. This is evident in the tragic complementarity between:
- the engagement worldwide with football -- evocative of belief in the
"spirit of the game" -- as having a unique coherence that is collectively
significant and might be said to transcend and encompass ordinary modes of
cognition as well as national and cultural boundaries (Nick Green, The
Spirit of Football in an Image and a Poem, 100 Percent Soccer,
18 March 2009)
- the focus on globality and globalization which might well be
described in terms of "kicking the globe around", with relatively
little concern for its condition and with only an (often token) aspiration
to global coherence and engagement; topics of global significance might be
fruitfully understood as "kicked around" like a football -- typically with
respect to a polarized arena over which two competing factions compete.
The cognitive entanglement between a "micro ball" (within a "macro context")
and the "micro treatment" (of that macro global context) may be
explored in terms of geometric commonalities:
- the stitching of
leather patches on a soccer ball follows the pattern of a polyhedron -- a truncated
icosahedron, one of 12 semi-regular solids central to Fuller's preoccupation
with regard to the "geometry of thinking".
- the planetary globe was mapped by Fuller onto the surface of a polyhedron
(such as an icosahedron or
which can then be unfolded to a net in many different ways and flattened
to form a two-dimensional map which retains most of the relative proportional
integrity of the global map. It is known, and patented by Fuller (unfortunately)
as a Dymaxion
map. Unlike most other projections, it is intended only for
representations of the globe in its entirety.
In a period of intense concern with regard to climate change, a further geometric
association may be added, namely the discovery in 1985 of buckminsterfullerene (C-60
or buckyball). This is an unusual spherical molecule composed entirely of carbon
-- resembling a geodesic dome in appearance, and hence the name. It is the
fullerene molecule in
which no two pentagons share an edge -- the most common fullerene in
terms of natural occurrence, as it can often be found in soot. Most ironically,
the chemists researching it had to be informed by mathematicians that what
they were looking for was indeed commonly represented by the stitching of leather
patches on a soccer ball.
As noted above, one of the shapes hypothesized for the universe
is a Poincaré dodecahedral
space, a positively curved space, colloquially described as "soccer ball
shaped" (Jean-Pierre Luminet, A
Finite Dodecahedral Universe, Nature,
2003; John Whitfield, Universe
could be football-shaped, Nature,
might this imply for any "cognitive
universe"? Perhaps, with apologies to William
Blake (Auguries of
To see the universe in a football game and heaven
in a ball ?
in awareness now and eternity in a mall ?
Geometrically the buckyball and the football are more complex than those
structures discussed above (such as the icosahedron), where there is a modicum
of attention to their psychosocial significance. As previously explored in
relation to dialogue (Understanding
Sustainable Dialogue: the Secret within Bucky's Ball? 1996).
Maybe the "ball" that gets kicked around between positions in any dialogue
-- the topic -- needs to be understood as more complex. It is not just a "point".
It is only this complexity that accounts for its resilience and ability to
bounce back. Who would want a dialogue with a "ball" that did not bounce, but
just stuck where it landed? Would a dialogue then be possible? What is the
difference between games with a bouncing and a non-bouncing "ball"? C-60
is remarkable for its resilience. Like a manufactured football, it is a satisfactory
approximation to a perfect sphere.
When we observe a soccer game, the ball moves unambiguously all over the
field -- shifted onwards, or blocked and deflected, by players at different
positions. Runs and plays can be watched and remembered as a whole -- but
even then with some difficulty. For the game as a whole, the moves of the
ball -- and the corresponding positions -- could only be remembered by those
with photographic memory, or the mnemonic skills of a particular form of
autism. The ball is explicit, whilst the context -- the whole within which
it is set -- is implicit. We all have difficulty in understanding what is
going on in a dialogue. How come it took people so long to understand the
significance of C-60, having been exposed so long to footballs? What is so
well known to us in the psychosocial realm that is of similar significance?
In subsequent consideration of engagement with globality (Engaging
with Globality through Cognitive Circlets, 2009) reference was made
to how astounding it was that greater sophistication is applied
to the analysis of patterns of interaction in various sports -- passing
patterns -- than is applied to the patterns of dialogue at vital strategic
gatherings (Mark Weston, Passing
Patterns, 2006; Athalie Redwood-Brown, Passing
patterns before and after goal scoring in FA Premier League Soccer, International
Journal of Performance Analysis in Sport, 2008; Association for Soccer
Education and Teaching, Passing
Patterns and Small Sided Games, 2008; Alan Reifman, Network
Analysis of Basketball Passing Patterns II, 2006; ).
The approach has been adapted to message passing in complex organizational
networks. With respect to global dialogue, the situation is all the more
curious given the widespread metaphoric use of "ball" in strategic dialogue
-- as in the "ball
is in their court".
Given the constant pressure for higher quality performance in such contexts,
how is the quality of dialogue regarding the current crisis to be evaluated?
The movement of a ball, or a set of clubs, has long been tracked and visualized
to improve performance (Daniel A. Reed, Matthew J. Gardner and Evgenia Smirni, Performance
Visualization: 2-D, 3-D, and Beyond). How is it that no effort is
made to do so for strategic dialogue -- especially widely publicized panel
Generation through Global Conversation: in quest of collective well-being through
conversation in the present moment, 1997).
The question here is whether there is a degree of credible "moonshine" connectivity
possible between the universal engagement with football, its well-recognized
geometric form, and its potential as a patterning template for new forms of
global psychosocial dialogue and organization -- beyond current conventions?
Might the panels of stitching of a football be fruitfully understood as indicative
of the desirable configurations of the panels in a global conference
Configuration of Interlocking Roundtables: internet enhancement of global self-organization
through patterns of dialogue, 1998)? Might the viability of sustainable
global governance depend on the credibility of isomorphism with the familiar
patterns of of a football?
Is the very dynamic of the game essential to the viability
of such an emergent structure (Playfully
Changing the Prevailing Climate of Opinion: climate change as focal metaphor
of effective global governance, 2005)? Perhaps as a form of resonance
of Modes as a Resonance Hybrid, 1986; Patterns
of Alternation: cycles of dissonance and resonance, 1995)?
More challenging is the paradoxically mirrored cognitive relationship between
the (micro) football and the (macro) globe. Is there a form of cognitive inversion
associated with that mirroring, perhaps usefully to be captured by the Mobius
strip as previously discussed (Psychosocial
Energy from Polarization within a Cyclic Pattern of Enantiodromia,
2007)? Might football be as important as climate change to global governance?
There is the possibility that buckminsterfullerene may indeed be of requisite
cognitive complexity such that the panels of any corresponding football could
be used to explore in a learning environment the configuration of global issues
or those of climate change -- labelling each panel with one topic. Footballs
could even be distributed with such topic maps as a guide to multi-panel conferences.
This would be something tangible for delegates to being home from conferences
to their family and friends. However it is also possible that such a configuration
might be fundamental to any viable global arrangement transcending conventional
patterns of agreement and disagreement. In this sense a football would be a
vital means of rendering comprehensible its underlying complexity. As remarked
by Chris Lucas: An interesting analogy in terms of a labeled
football, is that if any
panel is eliminated the ball goes flat, if any are seriously changed in
size the distortion of the ball makes it impossible to play with.
The explicit or implicit antipathy between those undertaking any consideration
of the "geometry of thinking", or any cognitive Theory of Everything, necessitates
the search for frameworks of greater complexity to encompass
such divergent perspectives. Astrophysics may offer pointers (Towards
an Astrophysics of the Knowledge Universe: from astronautics to noonautics? 2006).
Are the cognitive wormholes -- through which each is able to "wriggle"
from one "universal framework" to another -- configured in some special way,
perhaps forming a polyhedral cognitive metaverse.
The notion of a metaverse has been explored from an artificial intelligence
perspective by Ben
Goertzel and also in science fiction. Given the efficiencies of a polyhedral
organization of computer (memory) systems, what might then be the appropriate
geometry of any future global
brain? How might its emergence be comprehended, given the challenge
Ass argued above, however, a "cognitive
inverse" may also be implied through mirroring. Hence the cognitive value
of the Stella Polyhedron
developed by Robert Webb, notably Stella4D which
enables exploration of 4D polytopes -- with 4D models projected into 3D,
offering visualizations of their 3D cross-sections and nets in real-time. As
in Stella4D, Chris Lucas also uses the partial mirroring of stereoscopic
images to enable a sense of four dimensions (Four Dimensional
Strange Attractors in Stereogram form, 2002)
Both in the case of Fuller's innovations and those of Beer, it is much to
be regretted the extent to which these remain subject to constraints of intellectual
copyright -- inconsistent with their purported global significance in a period
of global crisis. Such constraints might be understood as an appropriate metaphor
of the flaws inhibiting effective global initiatives (Future
Coping Strategies: beyond the constraints of proprietary metaphors,
It is perhaps to be expected that every comprehensive initiative should have
a central flaw -- fundamental in some aesthetic schemes to its appropriateness.
As discussed with respect to lipostrategies the challenge is how to incorporate
this constraint into a tragic poetic epic, a civilizational magnum
opus, as a commemorative mnemonic for the future (Lipoproblems:
Developing a Strategy Omitting a Key Problem -- the systemic challenge of climate
change and resource issues, 2009). This might offer a framing corresponding
to that of the mysterious wound of the Fisher King in the epic poem Parzival (cf
Richard Sanderson, Wounded
Masculinity: Parsifal and The Fisher King Wound) which inspired the
opera Parisfal by Richard
In the case of Buckminster Fuller, despite his uniquely global engagement,
one aspect of this tragic flaw is the manner in which his inventions of potentially
fundamental significance are subject to copyright -- inhibiting
their development by others, contrary to the spirit through which resources
are shared in an open source
community. As with others discovering geometric applications
of potential value to remedial global strategies, this might be held to be
the collective equivalent of "shooting oneself in the foot", or shooting
an own goal in a football metaphor -- or friendly
fire in military terms.
As with the Fisher King, Fuller's
"wound" may be essentially a topological "subunderstanding" resulting
from failure to appropriately embody the four-dimensionality exemplified by
the paradox of the Klein bottle -- a perspective on knots notably explored
in Lacanaian psychoanalysis. This has been a theme of the recent work of Melanie
Purcell (Towards A New
E.R.A.: Epistemological Resolution Analysis By Through and From Klein-Bottle
Wholeness and Transdisciplinary Education) who explicitly
recognizes the inadequacy of platonic
geometry and the need for higher-dimensional
topologies. In this sense the seeming flaw in in any comprhensive "geometry
of thinking" is a consequence of inappropriate self-reference (even "self"
destructive) which is corrected in an appropriate "topology of thinking".
Curiously the dissemination of most key insights relevant to the challenges
of global civilization is already severely constrained by copyright. Is the
pattern such that global civilization will be held to ransom by a future inventor
of the ultimate remedial technology for its ills? Is distribution of the swine
flu vaccine in 2009 an indication of that model? Will some geo-engineering
technology follow that pattern? This mindset may be the key to the question
posed by Jared M. Diamond (Collapse:
how societies choose to fail or succeed, 2005).
A similar phenomenon is evident in the probability that the most legally
binding constraints to emerge from the United
Nations Climate Change Conference (Copenhagen,
2009) may well be those relating to wider
use of any documents presented to it to clarify the global challenge -- and,
perhaps most significantly, that governing the copyright of the symbol
of the Copenhagen event. In contrast to other such UN symbols, this is
a valuable effort to reflect that
challenge in spherical geometry (reminiscent of Fuller's own endeavours).
representation of section headings of this document (indicative)
(made with Stella Polyhedron
In both images, the 18 section headings are on the square faces of a rhombicuboctahedron
set within the framework of its dual, a deltoidal
icositetrahedron (with the section
headings on its corresponding vertices). The great circles of both structures
are individually coloured.
(click each image for enlarged versions; gif
animation of rotation not included)
|The attribution of section headings
to faces and vertices is of course arbitrary, suggesting contiguity adjustments
(as with Rubiki's Cube). It is however indicative of a possible future
approach to the introduction of greater cognitive coherence into the organization
of a linear text. The software used permits the addition of many other
geometrical features (symmetry axes, reflection planes) as well various
possibilities of morphing the configuration into its dual or unfolding
the polyhedron into a net. In interactive use, or by generation of animations,
a more dynamic overview is necessarily obtained.
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