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The Geometries of Situation and Emotion and the Calculus of Change in Negotiation and Mediation Valparaiso University Law Review Volume 29 Number 1 Fall 1994 pp.1-120 Fall 1994 The Geometries of Situation and Emotion and the Calculus of Change in Negotiation and Mediation John W. Cooley Follow this and additional works at: https://scholar.valpo.edu/vulr Part of the Law Commons Recommended Citation John W. Cooley, The Geometries of Situation and Emotion and the Calculus of Change in Negotiation and Mediation, 29 Val. U. L. Rev. 1 (1994). Available at: https://scholar.valpo.edu/vulr/vol29/iss1/1 This Article is brought to you for free and open access by the Valparaiso University Law School at ValpoScholar. It has been accepted for inclusion in Valparaiso University Law Review by an authorized administrator of ValpoScholar. For more information, please contact a ValpoScholar staff member at [email protected]. Cooley: The Geometries of Situation and Emotion and the Calculus of Chang VALPARAISO UNIVERSITY LAW REVIEW Volume 29 Fall 1994 Number 1 Articles THE GEOMETRIES OF SITUATION AND EMOTIONS AND THE CALCULUS OF CHANGE IN NEGOTIATION AND MEDIATION JOHN W. COOLEY* I. Introduction .................................. 3 II. Leibniz-The Person; The Lawyer; The Problem Solver ...... 5 A. Leibniz-The Person .......................... 5 B. Leibniz-The Lawyer ......................... 12 C. Leibniz-The Problem Solver .................... 15 1. Solver of Mathematical Problems .................16 2. Solver of People Problems ................... 18 III. Leibniz's Geometry of Situation .................... 19 A. Problem Solving-General ...................... 19 B. The Origin of Geometry of Situation .. ..............20 John W. Cooley is a former United States Magistrate, Assistant United States Attorney, Senior Staff Attorney for the United States Court of Appeals for the Seventh Circuit, and a partner in a Chicago law firm. He is a past Chairman of the Chicago Bar Association's Arbitration and ADR Committee. In private practice in the Chicago area, he currently serves as a mediator, arbitrator, and consultant in dispute resolution systems, and he is an Associate of the Dispute Resolution Colloquium, Dispute Resolution Research Center, Kellogg Graduate School of Management, Northwestern University. An Adjunct Professor of Law at Loyola University of Chicago School of Law, he has co-designed and co-taught an innovative course on Alternatives to Litigation. He is the author of The Appellate Advocacy Manual and numerous articles on litigation, judicial, and ADR topics. He is a graduate of the United States Military Academy at West Point and the University of Notre Dame Law School. This article is the fifth in a series authored by Mr. Cooley that describe a new approach to interpersonal problem solving called 'Pracademics"-the application of classical methods to achieve practical solutions in negotiation and mediation. Citations to the other four articles appear in infra notes 1, 27, 185, and 336. Produced by The Berkeley Electronic Press, 1994 Valparaiso University Law Review, Vol. 29, No. 1 [1994], Art. 1 2 VALPARAISO UNIVERSITY LAW REVIEW [Vol. 29 C. Leibniz's Theory of Relations .................... 26 D. Geometric Imagineering of an Interpersonal Relationship .............................. 31 1. Nominal Relations ........................ 31 2. Analysis of a Particular Relationship .............. 32 a. Structure of Relationship .................. 34 b. Substance of Relationship .................... 35 E. Geometry of Situation and Modem General System Theory ............................. 39 1. The Satir Model: Assessment of Family System ...... 41 2. The Circumplex Model: Assessment of Family System . 45 IV. The Geometry of Emotions ....................... 50 A. Spinoza's Euclidean Structure of Emotions ............. 50 1. Spinoza-The Person ....................... 51 2. Overview of the Ethics ..................... 51 3. Spinoza's Definitions of Emotions ............... 53 4. Spinoza's Propositions on Intensity of Emotions ...... 59 5. Spinoza's Axioms and Propositions on the Control of Emotions ............................ 60 B. A Modem Theory of the Structure of Emotions .......... 61 V. The Calculus of Change in Negotiation and Mediation ....... 68 A. Calculus-An Instrument for Visualizing and Measuring Change ................................. 69 1. Differential Calculus-Visualization Techniques ...... 73 2. Integral Calculus-Visualization Techniques .......... 80 B. Psycho-Geometric Models for Effecting Behavioral Change ................................. 84 1. The Satir Model: Calculus for Change ............. 85 a. Congruence .......................... 85 b. Process of Change ...................... 86 2. The Circumplex Model: Calculus for Change ....... 87 C. Geometric Imagineering and Behavioral Change ........ 88 1. A Two-Dimensional Method for Visualizing Behavioral Change ........................ 88 a. Notational Method of Situational Analysis ......... 91 b. Geometrical Analysis of Balance in Relations ...... 97 2. A Multi-Dimensional Method for Visualizing Behavioral Change ....................... 101 a. Basic Tenets of the Catastrophe Theory ......... 102 b. Catastrophe Theory and Conflict Behavior ....... 109 VI. Conclusion ................................ 113 Appendix A. Leibniz's Metaphysical Foundations of Mathematics . 114 Appendix B. Graphical Examples of Types of Change ......... 120 https://scholar.valpo.edu/vulr/vol29/iss1/1 Cooley: The Geometries of Situation and Emotion and the Calculus of Chang 1994] GEOMETRY OF SITUATION AND EMOTIONS 3 I. INTRODUCTION This Article is a sequel to Descartes' Analytic Method and the Art of Geometric Imagineering in Negotiation and Mediation, published in Volume 28 of the Valparaiso University Law Review in the Fall of 1993.' While a review of that article may be helpful in more quickly grasping the ideas'presented below, it is not absolutely necessary. As in the Descartes article, definitions of mathematical terms and expressions are liberally provided throughout this article to enlighten the reader as to the simple essences of the pertinent mathematical concepts. Every effort has again been made to minimize the pure mathematics aspects of the discussion, to simplify mathematical concepts actually discussed, and to analogize, in an uncomplicated way, those aspects of the concepts which have direct or indirect application to solving real-life problems presented in transactions or in disputes. Most everyone having a basic understanding of high school level mathematics and of the psychology of visual perception should have no trouble understanding the material presented here. Every dispute or transaction has two principal elements which must be addressed by a negotiator or mediator: (1) the substance of the dispute or transaction and (2) the relationship between or among the parties. 2 The Descartes article presented an analytical and geometric imagineering paradigm for use in addressing the substance of a dispute or transaction in the context of collaborative negotiation.3 This Article presents an analytical and geometric imagineering paradigm for use in addressing the relationship element of a dispute or transaction. The primary distinction between the two paradigms exists in the timing and sequence of their use in relation to collaborative negotiation. The Descartes paradigm is normally used during the course of collaborative negotiation to 1. The word "imagineering" here means the mental and/or graphical construction and use of visual images in problem solving. The expression "geometric imagineering" connotesvisual images that are in the shape, form, or nature of geometric figures, lines, curves, or constructs. This article is a sequel to the Descartes article in the same sense that D. Burger's book, SPHERELAND: A FANTASY ABOUT CURVED SPACES AND AN EXPANDING UNIVERSE (1965) is a sequel to Edwin Abbott's book, published originally in 1880, entitled FLATLAND: A ROMANCE OF MANY DIMENSIONS (5th ed. 1967). See John W. Cooley, Descartes' Analytic Method and the Art of Geometric Imagineering in Negotiation and Mediation, 28 VAL. U. L. REV. 83, 130 n.122 (1993). The present article and SphereLand each venture into a new dimension of imagination. 2. ROGER FISHER ET AL., GETTING TO YES: NEGOTIATING AGREEMENT WITHOUT GIVING IN 19-21 (2d ed. 1991). 3. For purposes of the Deseartes article and the present one, "collaborative negotiation" means group decisionmaking in which emotional issues are not present (non-existent or already dissipated) and positional bargaining (right vs. wrong; rights vs. duties) is not present or has been concluded, and the parties are focusing on their interests (or needs) and resources to satisfy those interests with the goal of achieving a mutually acceptable solution. Produced by The Berkeley Electronic Press, 1994 Valparaiso University Law Review, Vol. 29, No. 1 [1994], Art. 1 4 VALPARAISO UNIVERSITY LAW REVIEW [Vol. 29 facilitate group decisionmaking; the paradigm described in this Article, hereinafter referred to as the Leibniz paradigm, is normally used preliminarily by a negotiator or mediator to perceive ways to prepare and to acclimate the parties to collaborative negotiation. In short, this Article will ultimately explore the geometric and calculus-based visualization techniques to be used preliminar- ily by negotiators and mediators to address issues pertaining to the relationship between or among parties in dispute and transaction settings. This Article will make this journey in four exploratory segments, Sections II through V. In Section II, this
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