It does, even in print; pardon some publicity! You may start at the end with the table of contents, then, here, the book epilogue:
Epilogue: Enthusiast E and Skeptic S: Dialogue at a Higher Level
E: Well, where are we now? How do you feel?
S: A little exhausted. But greatly relieved at one major point.
E: Any particular chapter, branch, part of peace theory?
S: No, the whole thing. I worried that you would put something belonging to all of us, peace, into a big machine with parameters and then the machine would produce outputs about what to do. Like economists do with something belonging to us, our own livelihood. I liked your distinction between equations and formulas, between mathematics and mathematese.
E: Is your worry that reality is so complex that no set of equations can ever mirror it? Like linear equations being inadequate, non-linear equations being more promising?
S: No. I am actually more afraid of the perfect model. OK, maybe I could give in to some part, like a model of which lane to drive in a traffic jam–some people have found the slow lane to pay off. But to surrender our ultimate command of peace and livelihood to a model is like submitting to a bunch of planners running a planned economy, or to a bunch of speculators running a “free” finance market economy. Or to a dictator, presumably with an overview and insight beyond all of us. I prefer autonomy.
E: Great. But do you agree that we can identify in mathematics ways of thinking and concepts that can inspire us to deepen and broaden our thinking about peace?
S: I was struck by transcendence of number systems. By Möbius. By what you got out of the empty cell in a product set. And the use of the attributes of relations to build peace communities and subvert domination and polarization. And by feedbacks, indeed!
E: How about applying the ideas of self-similarity and iteration from chaos theory to normative theory, and from there to a theory of human evolution that we can steer ourselves, not having to wait for gene mutations due to cosmic particles-radiation and natural selection? Or, using the inhuman suffering of violence to decide who is the fittest by who suffers most and least casualties? And that in a human-made world increasingly based on our mind, and spirit, and decreasingly on our bodies? Brain more than brawn?
S: Too new for me. But I am struck by evolution as complexity. Humans are complex structures of cells connected by neurons in tissues woven together in bodies. Persons-nations-worlds; atoms-molecules-supermolecules; acts-norms-loci-societies-worlds.
E: There is something here if we can identify formulas that when iterated deliver a complexity similar to nature and society. One formula for peace was actually presented in the text:
P = +PosP/-NegP = (Equity x Harmony)/(Traumata x Incompatibility)
Build equity, harmony, clear traumata, resolve incompatibilities.
S: I found catastrophe theory very true to life in that respect. The idea of zones of stability with quantitative change, and then some tipping edge where small moves have huge qualitative consequences. And then the careful balance between stability and ultra-stability. Maybe we need catastrophes now and then? The whole catastrophe narrative reminds me of two lovers—
E: A little move, or the wrong word, having huge consequences?
S: Precisely. And giving more depth to the relation by testing the limits. And, exploring new equilibria, from one to the next.
E: You said the catastrophe narrative? Or system narrative?
S: 12 chapters, 12 sets of concepts woven into 12 narratives told in mathematese, of, by and for peace? Isn’t that about it?
E: You said the last word, my friend.
Johan Galtung
12 March 2012
PEACE MATHEMATICS
Johan Galtung and Dietrich Fischer:
TRANSCEND University Press, 2012; Table of Contents:
Preface
Prologue: Peace, Mathematics, and Peace Mathematics
Introduction: A Dialogue between Enthusiast E and Skeptic S
[1] NUMBERS
Math: Transcendence Primes Goldbach conjecture Zero Infinity
Peace: Camel conflict Transcendence Dilemma-tetralemma Möbius
[2] SETS
Math: Intension-Extension Zero & Product-sets Combinatorics
Peace: Commission-Omission DPT Polities Economies Mediation
[3] PROBABILITY
Math: Laplace-von Mises Stochasticity Parameters Errors Type I&II
Peace: Equality concepts and measures Peace as disorder Entropy
[4] LOGIC
Math: Implication Heuristics using zero-sets and product-sets
Peace: Approaches to political-economic equality Transformation
[5] RELATIONS
Math: Attributes vs Relations Types Structure Isomorphism
Peace: Building equivalence Subverting dominance Balance Equity
[6] MATRICES
Math: Representation of relations Stochastic relation matrices
Peace: Sociograms Representations of structures Dynamics
[7] GRAPHS
Math: Representation of relations (Im)balance Harary theorem
Peace: Graphs of direct and structural peace and violence Change
[8] GAMES
Math: Game Logic Saddle points Pareto optimum Nash equilibria Peace: Prisoner’s Dilemma Axelrod-Rapoport Discourse problems
[9] CHANGE
Math: Calculus Differential equations Stability-instability
Peace: Richardson’s arms races Common security Defensive defense
[10] SYSTEMS
Math: Control Feedbacks positive, negative, both
Peace: Feedbacks for peace and violence processes Examples
[11] CHAOS
Math: Fractal vs euclidean geometry Self-similarity Iteration
Peace: Normative reality layers Evolution as normative development
[12] CATASTROPHE
Math: Discontinuous-qualitative change Dialectics Ruptures Peace: Change of structure Structure of change Evolution
Epilogue: Enthusiast E and Skeptic S: Dialogue at a Higher Level
Endnotes Literature
