3 June 2009
Transformation of Global Governance through Bullfighting
Visual symbols and geometric metaphors
- / -
(in main paper)
Annex 2 of Viable Global Governance through Bullfighting: challenge of transcendence
tauromachy) is considered by many to be a flagrant example of glorified indulgence
in abhorent human cruelty to animals and a highly problematic reflection
on those who appreciate it. It is also considered by some to exemplify some
of the highest values of humanity, notably courage, skill and elegance in
the face of the immediate possibility of personal fatality. A bull is seen
as the epitome of animal strength and courage, and much to be admired.
What follows is an exploration of how the challenges of global governance
might be fruitfully represented through visual symbols and geometric metaphors
through the lens of bullfighting, articulated in the main paper (Viable
Global Governance through Bullfighting: challenge of transcendence).
A valuable context for any such exploration is to be found in the cultural,
even archetypal, significance of the bull over millenia. Bull
mythology was widespread in the ancient world where it had been the subject
of various cultural and religious incarnations -- now partly reflected in
some neopagan cultures. Bullfighting traces its roots to prehistoric
bull worship and sacrifice.
The visual experiments here follow from earlier exercises in relating fundamental
symbol systems (Dynamic
Exploration of Value Configurations: interrelating traditional cultural symbols
through animation, 2008;
Interrelationship of Symbols of Coherent Experiential Representation of Nonduality,
Quest of a Strategic Pattern Language: a new architecture of values,
The relevance of a metaphorical approach to geometrical representation has
been explored separately (Metaphorical
Geometry in Quest of Globality: in response to global governance challenges,
Relevant to the approach taken there
is the account of formal mathematics of Edmund
Husserl as summarized by Kenny
Conceptions of Formal Mathematics, 2004) in relation to the thinking
of Kurt Gödel:
Edmund Husserl’s conception of mathematics was a unique blend of
Platonist and formalist ideas. He believed that mathematics had reached
a mixed state combining Platonic and formal elements and that both were
important for the pursuit of the sciences, as well as for each other. However,
he seemed to believe that only the Platonic aspects had significance for
his science of phenomenology
Citing Husserl, he notes
"If analogy can be any guide to method, it will act most powerfully if
we restrict ourselves to material mathematical disciplines like, for example,
geometry and accordingly ask more specifically whether a phenomenology
must be, or can be, constituted as a [material] “geometry” of
mental processes.” This usage of the word “geometry” implies
that it is still being used to describe the science of physical space.
The metaphorical ‘geometry of mental processes’ would similarly
be a science of existing objects that we can access directly through intuition
(Wesensschau), and not formally through reasoning and axioms.
Given the role of geometric forms in indicating a number of the above processes
and distinctions, there is a case for the elaboration of a sequence of phases
illustrated by bullfighting in an effort to relate this more succinctly to
the challenge of global governance. In the light of the focus
of cybernetics on generic understanding of control systems, there is the possibility
that such a geometric articulation may interrelate a number of threads.
In the three "storyboard" experiments that follow, the effort
is to weave together various threads highlighted by the commentary on the
significance of bullfighting to an understanding of appropriate governance.
The concern is to provide a succinct pattern of mnemonic cues, as previously
Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial
dynamics, 2007). As an experimental format, the storyboard is
partly inspired by the classic Zen Buddhist Ten
Ox Herding Pictures and
by the comparable, but less significant, exercise of Pablo Picasso (Picasso's
The threads can be understood as different languages describing the same
generic pattern -- to the extent that the particular lanugage lends itself
to description of parts of the any connecting story. The concern is to seek
ways of combining logical and systemic relationships with geometrical and
aesthetic correspondences. The issue of course is whether the connectivity
variously woven into the story include:
- bullring as circlet (womb/matrix): feminine principle engenders the man-bull
- a degree of geometric development (more evident in Storyboard B and
- playing to some degree on the traditions of sacred geometry
- including the topological challenges of the Möbius
- including implications of representation in three dimensions
- symbolism, including associations to:
- Greek and Egyptian cultures
- continuing value-related significance of "pillars" for
- continuing masonic reference to Egyptian
- use of the laurel leaf as emblematic of global governance in various
institutional logos (discussed in main
- the systemic contrasts, from a general systems perspective, of:
- micro-level: dynamics of biological cell division, considered
as a system in which traits from different genetic stock are combined
** cell mitosis
- macro-level: the challenges of global management and globalization
- cognitive approaches to system dynamics through:
- dynamics of complex systems
in the light of:
- implications for decision-making options and blockages
It should be stressed that these "storyboards" are
purely exercises. The
question is whether they are fruitfully suggestive of a succession of important
challenges and opportunities. Each might have had more panels and
the contents of any of the panels could be improved or replaced -- as with
the commentaries. Notably with respect to the first, rows of panels
could be removed to simplify the story.
The sequences of the storyboards are not independent. They tell the same
story. Storyboard C is a highly schematic geometric version of portions of
Storyboard A. Storyboard B reinforces the multidimensionality of what is
represented in two dimensions by drawing attention to the possibility of
seeing the other images in three dimensions (where any circle is understood
as a sphere) or from a plan perspective.
|The three following panels create the arena for those
that follow. It is within this arena that the matador confronts the bull,
as with any confrontation with otherness or between polar opposites
(right/wrong, positive/negative, female/male, etc). Contrasting colours
are used to indicate such incommensurable differences. *** alchemy
||surrounding/within larger circle?
||nose to nose confrontation
The apparent simplicity of the laurel leaf theme above is presented in the three
following panels as having a hidden degree of complexity characteristic of
lived reality. Each of the two laurel branches might be understood as ordered
in its own terms, but an order incommensurable (or chaotic) with respect
to the other. The images derive from zooming in on the fractal boundary
between order and chaos evident in the visual rendering of the Mandelbrot
***below (selection from Image
gallery of a zoom sequence in Wikipedia).
In terms of the symbolic theme of the ***abyrinth (as the realm of the Minotaur),
it is in this complexity that it is easily possible to be lost. The infinite
range of such "attractive"
images therefore constitutes a form of barrier.
|Labyrinthine boundary (Step
||Labyrinthine boundary (Step
||Labyrinthine boundary (Step
| Seeing through and beyond the labyrinthine
complexity above, calls for an understanding of the underlying dynamics.
The images also evoke a relationship to genetic reproduction through cell
division. ** alchemical analogues
|A degree of ordered response
to the complex dynamics of the challenging relationship between matador
and bull is evident in the sequence of passes controlled by the matador's
cape. The above rendering of minimal orbits within that set alludes aesthetically
to how the set of cape movements might be displayed statically.
||This image and the following
highlight stages in what is described as cross-fertilization, notably
between disciplines. Models of this are to be found in the process
of meiosis replication
in biological cells. A form of "cognitive
meiosis" has been
decribed, now reframed in terms of memetics.
||This implies a form of "inter-species
learning" in which fundamental opposites (such as matador and bull)
acquire insights from their dance (with one partner killing the other
after that transfer, as in some species)
|The following panels highlight an emergent (principled)
order through mirroring, reflection and inversion -- a process of enantiodromia,
perhaps to be understood as linking local and global, specific and
general, or mundane and transcendent. Such emergence may also be understood
as a distillation according to the alchemical metaphor -- from the lower
"vessel" to the upper. The mirroring is however to a degree illusory as
indicated by the use of the single-sided Möbius
strip to relate the inversion
between the two levels (Psychosocial
Energy from Polarization within a Cyclic Pattern of Enantiodromia,
2007). Visually, the Möbius theme
may also be understood as introducing the implications of 8-fold organization
-- fundamental to the Ba
Gua concept of Chinese symbolism. These panels
frame the challenge of executive decision through which possibility is understood
as excluded, neglected or transcended -- an imposition of binary logic
(A and not-A), excluding
the challenge of other possibilities (A
and not-A and neither-A-nor-not-A)
of the quadrilemma characteristic of many real-world choices. *** defines
|Frames the relationship
in Greek symbolism between Europa (in
the upper half) who "rode off on the back of Zeus"
in the form of a bull (with the lower half representing
the realm of that bull).
||Frames the relationship
in Greek symbolism with the labrys (doubleheaded
axe) notably used in the sacrifice of bulls -- through cutting the spinal
chord. It is associated with thunder deities, a form of Zeus. The illlusory
complex cross-over of the Möbius
strip may be understood as a knot -- the Gordian
a 2-wheeled "ox cart"). Both symbols anticipate the sacrificial
||An indication of the sacrifice
resulting from killing the bull, and symbolically cutting off the relationship
(or influence) of that realm or transcending it. It is indicative of
the nature of any simplifying "executive" decision in response to complexity
and an attitude of detachment. Examples might include focusing on positive
(vs negative), conscious (vs unconscious), rational (vs arational),
male (vs female).
As a result of a simplifying "executive" decision, the emergent order
on its own (the remaining "upper half"), readily lends itself to the simplistic
representation of the following panels -- with a consequent difficulty
in encompassing the "excised" complexity implicit in the representation.
|The challenge of any "other"
(epitomized by the bull) having been overcome, the victor (the matador)
now "rests on the laurels" -- emblematic of that victory. Differences
have been eliminated, or can be ignored, as a result of that achievement
-- or so it may be assumed. Harmony is implied.
||From a global perspective,
the laurel branches now frame an understanding of globality and integrity.
Global differences are assumed to have been indistinguishably harmonized
in an ordered world of higher values. Underlying discordant dynamics
can be ignored -- having been cut out as a disassociation from the
Dionysian -- identifying Zeus with Apollonian values.
||Reverts to explicit colouring
of the laurel branches indicative of the reality of the dynamics between
unresolved fundamental differences and associated strategic dilemmas.
Global order is not adequately or sustainably "held". The "voices" of
the "higher values" (of the image on the left) readily resemble
those of castrati --
lacking the "base" which emerges as "bull" within
that supposedly transcendent arena (now a context for renewed "bullfighting").
|The following panels clarify the kind of continuing
illusory oscillation or alternation between the "upper" and "lower" focus
of attention following the sacrifice of the lower half.
|Focus on "higher" values and
dynamics; ignoring "lower" values and dynamics
||Focus on "lowerr" values
and dynamics; ignoring "upper" values and dynamics
||Focus on "higher" values
and dynamics; ignoring "lower" values and dynamics
The following panels highlight the dynamic nature of the
ordered complexity encompassing that which is recognized and accepted
for consideration (as "known") together with that which
is otherise ignored, unpredictable or incomprehensible (the "unknown").
The "lower" half of the earlier 8-fold pattern (fundamental to the Ba
Gua understanding of decision-naking in complex situations
of change) is now specifically re-integrated into the frame (cf Animation
of Classical BaGua Arrangements: a dynamic representation of Neti Neti).
|Whereas the conventional laurel-leaved symbolism
implies a form of closure -- a succesful encompassing of the world,
despite its complex dynamics -- the following panels explore the implications
of "openness", effectively "releasing" reality from the grasp of cognitive
closure (a possibility implied by initiatives towards "open governance").
The "realm of the bull" is then potentially reintegrated into the representation.
|The ends of the laurel branches
are opened to "release" global understanding in both its planetary and
integrative senses. It can now be understood as finite but unbounded
rather than constrained by a grid. As such it is now associated symbolically
with a range of Sun god symbolism. "Winged" in this way, this resonates
with the symbolism of the Egyptian deity Horus and
the Eye of Horus.
||It is the opening "above" that
enables appropriate reconnection to the previously ignored "lower values".
This is the challenge for governance of reconnecting with the real world
of the masses and relating to the environment.
||It is through the reconnection
that the grounded, physical world can be appropriately managed as a "greener"
future -- dependent on a form of cognitive "recycling" between "upper"
and "lower" values (implied by the 8-fold representations of earlier images)
|Using the laurel wreath
||Rendering of the Mandelbrot
set mapped onto the complex
plane (real axis, vertical; imaginary axis,
||Image of the head of the
Hathor, otherwise commonly
depicted as a cow goddess with head horns in which
is set a sun disk -- effectively housing or enclosing Horus as
a sun god
This reinforces the multidimensionality of what is represented
above in two dimensions by drawing attention to the possibility of
seeing the other images there in three dimensions (eg where any circle
is understood as a sphere). The following
panels relate parabola, ellipse and hyperbola, together juxtaposed with
a classical chalice.
This image offers another way of summarizing succinctly the above story
especially in that it suggests a view from above into the chalice. Such
view (from the top) is an orthographic projection of the chalice representation
as a 3-dimensional object through
it from above. This possibility is of interest because of the nature
of the three curves constituting it. These would not be readily
distinguishable. All would be effectively set within a circle -- usefully
suggesting the complexity implicitly embedded within the circle as a
culminating image in the story above.
Also of interest is the implication that the functionality of the chalice
is not complete without a hand to grasp its lower portion. It is this
engagement which reflects that of the lower portion of the images above
-- the grounded "realm of the bull". Rather than a simplistic
understanding of detachment, it thereby emphasizes concerns with embodied
cognition as discussed
by various authors (George
Lakoff and Mark
In The Flesh: the embodied mind and its challenge to western thought,
J. Varela, Evan T. Thompson, and Eleanor Rosch,
The Embodied Mind: cognitive science and human experience, 1992).
The cognitive response to a chalice considered sacred might therefore
fruitfully be extended to what is implied by the hand that grasps it
by the stem, as suggested by Mudras:
an embodied pattern language for sustainability? (in Handing
Over Handy: metaphors for the communication of intent, 2006).
The three curves are also interesting in terms of their significance with
regard to the dynamics of the three more complex forms of the seven elementary
catastrophes of catastrophe
theory -- of which the simpler forms are even more closely related to
The implications of catastrophe theory for new understanding of human
dialogue have been explored separately using the chalice (Interrelating
Cognitive Catastrophes in a Grail-chalice Proto-model: implications of
WH-questions for self-reflexivity and dialogue, 2006).
The following is a highly schematic geometric version
of portions of Storyboard A
||Confrontation between matador and bull
|Dancing relationship between
and bull enabled by
|Emergence of transcendent principles
||Sacrifice of the bull
||Laurel wreath of victory
|Typical wreath-enclosed globe of international
illusory separation from "real economy")
|Wreath branches "open"
||Reintegration of bull