18 March 2009 | Draft

Metaphorical Geometry in Quest of Globality

in response to global governance challenges

- / -

Produced on the occasion of the G20 Summit (London, 2009)
Summary of Engaging with Globality -- through cognitive lines, circlets, crowns or holes (2009) and its detailed discussion of the cognitive implications of Dimension 1: Cognitive Realignment: making points and aligning a target; Dimension 2: Cognitive Circlets: learning/action cycles; Dimension 3: Cognitive Crowns: all-encompassing, well-rounded experience; Dimension 4: Knowing Thyself: embodying engagement with otherness

Table of metaphors

There is a curious embodiment in common metaphorical phrases of seemingly fundamental intuitive understanding relating to globality -- expressed in terms of abstract geometrical forms. The current international focus of efforts to "fix" the global financial system is through an approach of dimensionality inadequate to the complexity it represents -- if only in terms of the metaphors used to communicate the challenge. The "initiatives", that are "targeted" on sectors, within a global "plan" are best described in terms of Dimension 1 and Dimension 2 in the table below. The "global" challenge is best understood in terms of Dimension 3. Unfortunately the kinds of initiatives currently conceived (whether of Dimension 1, Dimension 2 or Dimension 3) fail to take into account cumulative dynamic effects (typically vigorously denied). These can only be recognized in terms of Dimension 4.

"Higher" dimensions to the right are:

  • associated with greater, longer-term value/worth, but more amorphous/intangible,
  • less precisely measureable or communicable
  • more challenging to understanding and associated with greater metaporical impoverishment
  • only potentially implicit in those to the left (as the "sparkle" or "glow" associated with the latter)
Indicative array of geometrically-based metaphors
Presented as a tentative sketch, recognizing that distinctions made are not absolute.
Content might overlap between cells of the array
Each row could be split in two, indicative of functional and dysfunctional possibilities
. Dimension 1
point and line
Dimension 2
area and circle
Dimension 3
globe (and polyhedral approximations to a sphere)
Dimension 4
torus, etc

shooting a line, lining up support, bottom line, deadline, in line with our thinking, stepping over the line, holding the line
bullet points (aligned)
wrong end of stick
pillarization, stakeholders

planning, in the plan, according to plan
orbiting around an axis,
innovation (R&D) cycle
business cycles
fashion cycles
left-right politics
circling the wagons

-- feedback loops
-- metabolic pathways
-- ecosystemic cycles

dynamic systems
product making a point
scoring a goal, hitting the target
making a profit
balancing the budget package/portfolio of spread risk
dividend, share value,
strategy target/goal (development, or environment, or growth)
"you are with us or against us"
reconciliation of strategic dilemmas (sustainable development) recognition of constraints (resource overshoot, climate change) mirroring, self-reflexivity, "them is us"
bonding relationships, links, contacts, well-connected circle of contacts, peers, friends (trust, confidence)
hemicycle plenary debating chamber
community of peers (friends, etc)
"our world",
dynamically gated communities
self-community relationship
(school shootings, scapegoating, etc)
outcome globality as the light at the end of the tunnel (scoring, killing) action/initiative globality encircled by the process work/exploitative cycles
laurel leaf "clasp"
"self-regulation" unexpected consequences,
action initiative
career path
work/family (im)balance
experiential cycles (daily, weekly, annual, life), work/recreation (im)balance
health, maturity,
wisdom, psychological health,
senility, "screwed-up", perverted needs
conformity running around with sticks
(batons, rockets, skyscrapers)
ensuring submission to the plan (singing from the same hymn "sheet")
budget (spreadsheet), input-output analysis
grid planning
wrap into a concept "package"
image, label
communication text(ing) video(ing)
map, systems diagram
blogosphere, cyberspace, Facebook, YouTube meaning?
discourse comment
aphorism, truism
story/plot, narrative sets of folk tales (Nasrrudin, Aesop),
108 Upanishads
technology message (LinkedIn, Plaxo)
individual feedback in response to general message (asymmetric communication)
propaganda, televised "fireside chats"
message plus feedback (symmetric communication) resonance ("bell")
knowledge cybernetics
innovation idea, innovation property, copyright
body of knowledge ?
consume, excrete, greed, want, grasp, ambition, desire give and take
checks and balances
worth, respect, honour, dignity self-esteem, self-worth, self-respect, sense of (in)dignity
maths linear equation (providing for velocity and accelaration) along a line curves approximating to a circle (and velocity and accdelration around it) curves describing spherical volumes (and approximations to them) complex equations such as those on which the development of financial derivatives were based
references Getting to Yes (1981) Hannah B. Higgins (The Grid Book, 2009), Thomas L. Friedman's The World Is Flat (2005)
book? dymaxion map
unity in diversity?
wisdom literature?
brains "Brain 1" "Brain 2" "Brain 3" "Brain 4"
This table is itself an example of a Dimension 2 grid --
posing the challenge of how to comprehend it as a whole (globally), to enfold it, and embody it


Engaging with globality -- geometrically illustrated (tentatively)
Dimension 1
point and line
(linear initiatives shown as tangents, potentially encompassing a circle)
Dimension 2
area and circle
("global plans" shown as variously related to an interlinking circular process, or potentially as tangential to a sphere)
Dimension 3
(and polyhedral approximations to a sphere, requiring minimally three interlinking circles, illustrated by Dymaxion Map; discussion in Towards Polyhedral Global Governance)
Dimension 4
interlocking tori, etc
(discussed in Engaging with Globality through Dynamic Complexity)
Dymaxion Mao


Laurel leaf "clasp": the logos of the UN and its UN Specialized Agencies, for example, have a partially encircling laurel wreath -- "clasping" a sphere (necessarily in two dimensions, with one "side" hidden)

Plenary debating chamber: these frequently take the form of hemicycles, as in various parliaments. Geometrically, they lend themsleves to comparison with a torc (and, perhaps only as a mnemonic indicator, to "talk" as a homophone).

Brains: Antonio de Nicolas (Neurobiology, Communities, Religion: A Bio-Cultural Study, 1998) focuses on the biocultural implications of the five brains of humans: reptilian, limbic, right and left hemispheres, and the "interpreter module". These brains function either independently or in harmony, either as dictators or as balanced multiplicity, either as a democracy or as victims, and thus there is still room for further human development. They develop progressively and successively through childhood, although the development of any of them be inhibited and stunted. They also have their cultural counter-parts:

Thus we know of ancient cultures as being maia types, since the brain serving as the "pilot" was primarily the reptilian, as in the child after birth; or mythos types, since they primarily developed the limbic brain, as in children between the ages of one to eleven; or right brain mimetic, since they acted on the language of images of the right hemisphere of the neocortex, as in children between the age of four and fifteen (magicians, leaders, the demiurge); or left brain mimetic (theoreticians, ideologues, theologians, social scientists), since they acted primarily from the left hemisphere of the neocortex, as in children from the age of seven on; or logos types, those whose experiences are imageless, experts in the creation of substitution systems, not able to deal with any of the other forms of knowledge of the right brain hemisphere. These biocultural types are invariant in the sense that they represent individual and social possibilities of human realities and development, but unless these brains are exercised they do not develop in full, or if one is socially sanctioned over the others, then cultural imperialism and individual loss may follow.

The challenge for individuals and communities -- and notably faith-based communities interacting with one another -- is that they may find themselves to be using only one of the brains, or faced with others in that condition. In the case of the mimetic left-brain, this might give it the power of dictatorship or the arbitrariness of an emperor-king. As noted by de Nicolas: "Imperialism at its worst may be the result of arrested development in the culture of the individual".

Metaphorical geometry: Relevant to the approach taken here is the account of formal mathematics of Edmund Husserl as summarized by Kenny Easwaran (Husserl’s 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.


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