Challenges to Comprehension Implied by the Logo
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13th November 2008 | Draft

Unexplored Potential of Mathematics and Geometry

in reframing psycho-social challenges

- / -


Introduction
Polyhedra and tensegrity
Complex system dynamics and self-organization
Strange attractors and the Mandelbrot set
Integration, synthesis, system unification
Cycles
Sets, numbers, patterns, symmetry group theory
Sets: number-based
Polarization, duality
Matrices and classification
Methodology and formalization
Catastrophe theory
Hyperspace
Simulation and modelling
Geometry, configuration, complementarity
Systems analysis, network analysis, mapping
Simplicial complexes and q-analysis
Uncertainty and probability


Introduction

The papers grouped below are those accessible on this website. They correspond to explorations over a number of decades which have sought to highlight the wider potential of particular themes in mathematics and geometry -- or loosely associated with such themes. The explorations are necessarily speculative -- raising questions and imagining answers. The themes may notably be used metaphorically. The commitment has been primarily to stimulate imagination. Some documents have however focused on (and resulted in) software implementations. The papers listed therefore include those relating to systems analysis, notably with respect to information systems.

The concern that better use had not yet been made of such mathematical insights has been strongly articulated in one case (And When the Bombing Stops? Territorial conflict as a challenge to mathematicians, 2000; Reframing Relationships as a Mathematical Challenge: Jerusalem as a parody of current interfaith dialogue, 1997). This argument has been further developed with regard to insights from symmetry group theory (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008).

Papers grouped by mathematical theme

Polyhedra Complex system dynamics

Integration

Sets

Strange attractors

Matrices and classification
Sets: number-based Cycles Methodology and formalization
Polarization, duality Catastrophe theory Simulation and modelling
Hyperspace Simplicial complexes and q-analysis Systems analysis
Geometry, configuration Self-organization Synthesis
Number Mandelbrot set System unification
Tensegrity   Network analysis
Patterns   Mapping, visualization
Symmetry group theory    
Complementarity    

Polyhedra and tensegrity

Complex system dynamics and self-organization

Strange attractors and the Mandelbrot set

Integration, synthesis, system unification

Cycles

Sets, numbers, patterns, symmetry group theory

Sets: number-based

Polarization, duality

Matrices and classification

Methodology and formalization

Catastrophe theory

Hyperspace

Simulation and modelling

Geometry, configuration, complementarity

Systems analysis, network analysis, mapping

Simplicial complexes and q-analysis

Uncertainty and probability

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