{"id":17874,"date":"2012-03-12T12:00:37","date_gmt":"2012-03-12T12:00:37","guid":{"rendered":"http:\/\/www.transcend.org\/tms\/?p=17874"},"modified":"2012-03-11T17:59:48","modified_gmt":"2012-03-11T17:59:48","slug":"peace-mathematics-does-it-exist","status":"publish","type":"post","link":"https:\/\/www.transcend.org\/tms\/2012\/03\/peace-mathematics-does-it-exist\/","title":{"rendered":"Peace Mathematics – Does It Exist?"},"content":{"rendered":"
\n

It does, even in print; pardon some publicity!\u00a0 You may start at the end with the table of contents, then, here, the book epilogue:<\/p>\n

Epilogue: Enthusiast E and Skeptic S: Dialogue at a Higher Level<\/em><\/p>\n

E:\u00a0 Well, where are we now?\u00a0 How do you feel?<\/p>\n

S:\u00a0 A little exhausted.\u00a0 But greatly relieved at one major point.<\/p>\n

E:\u00a0 Any particular chapter, branch, part of peace theory?<\/p>\n

S:\u00a0 No, the whole thing.\u00a0 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.\u00a0 Like economists do with something belonging to us, our own livelihood.\u00a0 I liked your distinction between equations and formulas, between mathematics and mathematese.<\/p>\n

E:\u00a0\u00a0 Is your worry that reality is so complex that no set of equations can ever mirror it?\u00a0 Like linear equations being inadequate, non-linear equations being more promising?<\/p>\n

S:\u00a0 No.\u00a0 I am actually more afraid of the perfect model.\u00a0 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.\u00a0 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.\u00a0 I prefer autonomy.<\/p>\n

E:\u00a0 Great.\u00a0 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?<\/p>\n

S:\u00a0 I was struck by transcendence of number systems.\u00a0 By M\u00f6bius. By what you got out of the empty cell in a product set.\u00a0 And the use of the attributes of relations to build peace communities and subvert domination and polarization.\u00a0 And by feedbacks, indeed!<\/p>\n

E:\u00a0 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?\u00a0 Or, using the inhuman suffering of violence to decide who is the fittest by who suffers most and least casualties?\u00a0 And that in a human-made world increasingly based on our mind, and spirit, and decreasingly on our bodies?\u00a0 Brain more than brawn?<\/p>\n

S:\u00a0 Too new for me.\u00a0 But I am struck by evolution as complexity.\u00a0 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.<\/p>\n

E:\u00a0 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>\n

P = +PosP\/-NegP = (Equity x Harmony)\/(Traumata x Incompatibility)<\/strong><\/p>\n

Build equity, harmony, clear traumata, resolve incompatibilities.<\/p>\n

S:\u00a0 I found catastrophe theory very true to life in that respect.\u00a0 The idea of zones of stability with quantitative change, and then some tipping edge where small moves have huge qualitative consequences.\u00a0 And then the careful balance between stability and ultra-stability. Maybe we need catastrophes now and then?\u00a0 The whole catastrophe narrative reminds me of two lovers—<\/p>\n

E:\u00a0 A little move, or the wrong word, having huge consequences?<\/p>\n

S:\u00a0 Precisely.\u00a0 And giving more depth to the relation by testing the limits.\u00a0 And, exploring new equilibria, from one to the next.<\/p>\n

E:\u00a0 You said the catastrophe narrative<\/em>?\u00a0 Or system narrative<\/span>?<\/p>\n

S: 12 chapters, 12 sets of concepts woven into 12 narratives told in mathematese, of, by and for peace?\u00a0 Isn’t that about it?<\/p>\n

E:\u00a0 You said the last word, my friend.<\/p>\n

 <\/p>\n

Johan Galtung and Dietrich Fischer: PEACE MATHEMATICS<\/em><\/p>\n

TRANSCEND University Press, 2012; Table of Contents:<\/p>\n

Preface<\/em><\/p>\n

Prologue<\/em>:\u00a0 Peace, Mathematics, and Peace Mathematics<\/p>\n

Introduction<\/em>: A Dialogue between Enthusiast E and Skeptic S<\/p>\n

[1]\u00a0 NUMBERS<\/p>\n

Math:\u00a0 Transcendence Primes Goldbach conjecture Zero Infinity<\/p>\n

Peace: Camel conflict Transcendence Dilemma-tetralemma M\u00f6bius<\/p>\n

[2]\u00a0 SETS<\/p>\n

Math:\u00a0 Intension-Extension Zero & Product-sets Combinatorics<\/p>\n

Peace: Commission-Omission DPT Polities Economies Mediation<\/p>\n

[3]\u00a0 PROBABILITY<\/p>\n

Math: \u00a0Laplace-von Mises Stochasticity Parameters Errors Type I&II<\/p>\n

Peace: Equality concepts and measures\u00a0 Peace as disorder Entropy<\/p>\n

[4]\u00a0 LOGIC<\/p>\n

Math:\u00a0 Implication Heuristics using zero-sets and product-sets<\/p>\n

Peace: Approaches to political-economic equality\u00a0 Transformation<\/p>\n

[5]\u00a0 RELATIONS<\/p>\n

Math:\u00a0 Attributes vs Relations Types Structure Isomorphism<\/p>\n

Peace: Building equivalence Subverting dominance Balance Equity<\/p>\n

[6]\u00a0 MATRICES<\/p>\n

Math:\u00a0 Representation of relations\u00a0 Stochastic relation matrices<\/p>\n

Peace: Sociograms\u00a0 Representations of structures Dynamics<\/p>\n

[7]\u00a0 GRAPHS<\/p>\n

Math:\u00a0 Representation of relations\u00a0 (Im)balance\u00a0 Harary theorem<\/p>\n

Peace: Graphs of direct and structural peace and violence\u00a0 Change<\/p>\n

[8]\u00a0 GAMES<\/p>\n

Math:\u00a0 Game Logic\u00a0 Saddle points\u00a0 Pareto optimum\u00a0 Nash equilibria Peace: Prisoner’s Dilemma\u00a0 Axelrod-Rapoport\u00a0 Discourse problems<\/p>\n

[9]\u00a0 CHANGE<\/p>\n

Math:\u00a0 Calculus\u00a0 Differential equations\u00a0 Stability-instability<\/p>\n

Peace: Richardson’s arms races Common security Defensive defense<\/p>\n

[10] SYSTEMS<\/p>\n

Math:\u00a0 Control\u00a0 Feedbacks positive, negative, both<\/p>\n

Peace: Feedbacks for peace and violence processes\u00a0 Examples<\/p>\n

[11] CHAOS<\/p>\n

Math:\u00a0 Fractal vs euclidean geometry\u00a0 Self-similarity\u00a0 Iteration<\/p>\n

Peace: Normative reality layers Evolution as normative development<\/p>\n

[12] CATASTROPHE<\/p>\n

Math:\u00a0 Discontinuous-qualitative change\u00a0 Dialectics\u00a0 Ruptures Peace: Change of structure\u00a0 Structure of change\u00a0 Evolution<\/p>\n

Epilogue<\/em>: Enthusiast E and Skeptic S: Dialogue at a Higher Level<\/p>\n

Endnotes Literature<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

It does, even in print; pardon some publicity! You may start at the end with the table of contents, then, here, the book epilogue:<\/p>\n

Enthusiast E and Skeptic S: Dialogue at a Higher Level:
\nS: 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…<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[],"class_list":["post-17874","post","type-post","status-publish","format-standard","hentry","category-editorial"],"_links":{"self":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/posts\/17874","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/comments?post=17874"}],"version-history":[{"count":0,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/posts\/17874\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/media?parent=17874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/categories?post=17874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.transcend.org\/tms\/wp-json\/wp\/v2\/tags?post=17874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}