Geometry: implications for thinking and identity

Implication of Toroidal Transformation of the Crown of Thorns: Design challenge to enable integrative comprehension (Part #4)

The previous remarks focus on formal, mechanistic issues. The question that merits attention is their implication for psychological engagement with the geometry. Especially intriguing is the integrative significance to be attached to "globality" -- and how that is experienced and intimately associated, if only through metaphor, with particular geometric forms and patterns.

This has been extensively discussed separately -- notably with respect to the geometric progression from points, to lines (of argument), to fields (of study), to more complex forms -- including those implying a degree of (fruitful) paradox, as with the Mobius strip and the Klein bottle (Metaphorical Geometry in Quest of Globality, 2009; Engaging with Globality -- through cognitive lines, circlets, crowns or holes, 2009). The implications in support of a sense of identity have also been explored (Geometry, Topology and Dynamics of Identity, 2009).

Especially significant to this exploration is the work of:

Christopher Alexander (Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole, International Journal for Unconventional Computing (IJUC), 2009) as discussed in Harmony-Comprehension and Wholeness-Engendering eliciting psychosocial transformational principles from design (2010)
Ron Atkin (Multidimensional Man; can man live in 3-dimensional space? 1981; Combinatorial Connectivities in Social Systems; an application of simplicial complex structures to the study of large organizations, 1977) as summarized in Comprehension: Social organization determined by incommunicability of insights (1995)
Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994) as discussed in Spherical Configuration of Interlocking Roundtables: Internet enhancement of global self-organization through patterns of dialogue (1998)
R. Buckminster Fuller (Synergetics: explorations in the geometry of thinking 1975) as discussed in Geometry of Thinking for Sustainable Global Governance(2009)
Arthur M. Young (The Geometry of Meaning, 1984) as discussed in Characteristics of phases in 12-phase learning / action cycles (1998) and Typology of 12 complementary strategies essential to sustainable development (1998) and Typology of 12 complementary dialogue modes essential to sustainable dialogue (1998)
Michael Schiltz (Form and Medium: a mathematical reconstruction, Image [&] Narrative, 6, 2003) as discussed in Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori (2006)

A very helpful summary of relevant possibilities is provided by Eileen Clegg and Bonnie DeVarco (What is the Shape of Thought? The Intersection of Nature, Geometry, and Communication, Shape of Thought Approach, 26 July 2010). More comprehensive are the works by John D. Barrow (Cosmic Imagery: key images in the history of science, 2008) and Michel Random (L'Art Visionnaire, 1991)

This argument has necessarily worked with the simplest geometric forms, seeking to relate a flat surface with a sphere through a torus. Each is understood as offering a kind of template over which the dynamics of daily life are variously organized and played out. Board games, as template of choice for competitive sport and (collective) strategy of every kind, are however a challenge to relate comprehensibly to any concern with globality and its governance. The dynamics of games illustrate the manner in which one can be placed at a disadvantage, or gain advantage, by any ability for non-linearity, unpredictability or creativity.

Some of the cognitive surprises in changing from a flat template to one inspired by the sphere have been delightfully explored in a special form of fiction by mathematicians (Edwin A Abbott, Flatland: a romance of many dimensions, 1884; Dionys Burger, Sphereland: a fantasy about curved spaces and an expanding universe, 1965; A.K. Dewdney, The Planiverse, 1984; Ian Stewart, Flatterland, 2001; Rudy Rucker, Spaceland, 2002). These are all designed to give a sense of the multi-dimensionality that people lose when trapped in a space of lower dimensionality. Game developers have now envisaged a "torusland":

Flatland need not be entirely "flat"! It could be Sphereland, for instance, where our (non-Euclidean) Square is restricted to the surface of a sphere. Or Rubberland (as one might call it), which can be stretched and distorted easily in three dimensions. Or Torusland where such well-known characters as Pacman reside (Flatland: the videogame, gamedev.net, January 2010).

The merits of such geometry is that it is typically within a cognitive "grasp" as compared for the far richer patterns otherwise available from mathematics. It is the nature of this comprehensive grasp which can be rendered more consciously explicit through accessible geometry. Excessive complexity effectively creates a horizon effect -- forcing significance "over the horizon" beyond immediate ken and out of range of behaviours dependent on familiarity.

The objective geometry as a template then gives a degree of expression to subjective experience and its organization. This might include the experiential:

sense of centre
sense of focus
sense of place
sense of "making" a point -- or "getting" or "taking" a point
sense of placement and organization -- putting things in their place, or giving them a place
sense of proximity and distance
sense of orientation

Main menu

Directions

You are here

Main menu

Search form

Directions

You are here

Geometry: implications for thinking and identity