# Peace Mathematics – Does It Exist?

EDITORIAL, 12 March 2012

**#208 | Johan Galtung, 12 Mar 2012 - TRANSCEND Media Service**

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 and Dietrich Fischer: *PEACE MATHEMATICS*

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

This article originally appeared on Transcend Media Service (TMS) on 12 March 2012.

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There is no “peace mathematics” as there is no “war/violence/conflict mathematics”. Mathematics is neutral. It can be used for peace purposes as it can also be used for war/violence/conflict purposes. We have a choice.

Iron, for example, is neutral. It can be used for constructing a school for peace as it can also be used for producing military weapons. We have a choice.

If we have a choice, let’s use mathematics for peace. If we have a choice, let’s use any other things and materials for peace (as well as for wellbeing and happiness of the whole humanity).

May peace be with you.

Dear Satoschi, thank you for this profound contribution.

Mathematics, tool or ideology? Any conflict inside mathematics? No question about the polemics about the foundations of Mathematics, Brouwer and Weyl vs. Hilbert? No question about the birth, after two centuries of infinitesimal analysis, a much more elementary mathematics in computer science which is so relevant at present times? First the mathematics and after the ethics or viceversa, first the choices about the kind of mathematics and after the mathematics?

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Does violence mathematics exist? I think it does. It actually exists in societies where people are separated by unconcealed walls or electricity is produced by gigantic nuclear power plants.Such violence could not exist in societies where peace mathematics is alive in our brain and brawn. How can peace mathematics(PM) be invented? How about this formula?

PM=Skeptic in mathematics × Skeptic in peace

Anyway, thank you very much for giving us such a wonderful idea. It is very inspiring for me to deepen and broaden my thinking about peace. I like it very much.

I am teaching a course at the university of colorado denver department of mathematical and statistical sciences (3 semester hour graduate and undergraduate seminar – 40 students have enrolled) on the mathematics of peace. I am interested in mathematical materials for this course. I will look at your book Peace Mathematics. How do I order you book? Amazon does not show it. Weldon

Hello Mr. Lodwick, you may purchase the book through here:

http://www.transcend.org/tup/index.php?book=37

Thank you, best regards

Antonio C.S. Rosa, editor