Systematic Political Science


Examining the Elasticity of Conflict Resolution Planes in Negotiations Between Inter- and Intra-Theological Groups Using the Tessellations of a Moral Abacus and Cellular Automata 

Dallas F. Bell, Jr. 

1. The Elasticity of Conflict Resolution Planes

Antoine A. Cournot (1801-1877) is often credited with informally introducing the idea of elasticity.  Elasticity can be explained as the ratio of proportional change in one variable to proportional change in another variable.  The elasticity of conflict ranges from a T1 choice of complying with all Natural Laws of Freewill (NLF) to a T3 choice of not complying with NLF.  Conflicts should generally be few for the T1 and the theological monads of forgiveness and mercy implemented as Alexis de Tocqueville commented on regarding the United States in the 1800's.  On the other hand, T2 has more conflicts and less forgiveness and mercy.  T3 would have the most potential conflicts with the least forgiveness and mercy applications.  This behavioral range of conflict produces a elastic plane of resolution possibilities.  The highest resolution potential for rapprochement (French meaning to bring together) is the T1 variable with the variable of fewest conflicts and most forgiveness and mercy ratio.  The lowest resolution potential is the T3 variable with the variable of the most conflicts and least forgiveness and mercy ratio. 

Thomas C. Schelling, recipient of the 2005 Nobel Prize for economics, published a book in 1960 titled The Strategy of Conflict.  Schelling described the game theory concept of a focal point (the Schelling point).  This is the point of each person's expectation of what they believe they are expected to do.  For example, two people are prevented from communicating with each other are each given a group A, consisting of five pennies and one nickel, and a group B, consisting of five nickels and one penny.  Each is told that they will receive a prize if they move the same type of coin from group A to group B and move the same type of coin from group B to group A.  It is most likely that each will move the one nickel from group A to group B and move the one penny from group B to group A. 

Schelling followed up on that human tendency to see groups and prefer order (see Gestalt laws of perceptions which can be exploited).  He wrote an article in 1971 called Dynamic Models of Segregation.  It used a checkerboard model to demonstrate his observations.  Pennies and nickels were placed on the checkerboard in different patterns and moved until it was perceived that the pennies and nickels had reached a state of happiness.  That meant the pennies metaphorically preferred to form one group of proximity and the nickels another.  Once that cycle of separation was begun, it had a self-sustaining momentum as witnessed in human group behavior.  Given the recent historical genocidal behavior of Nazis murdering Jews, Hutus murdering Tutsis and Muslims murdering non-Muslims, separation momentum would entail more than increased passive migration of T1 groups, but also include increases in aggressive and violent options of T2 and T3 groups.   

At the time of Schelling's writings, U.S. T3 lawmakers were already attempting to interfere with that natural process and force unnatural desegregation on its citizens in schools, businesses and government based on race.  They created an enormous amount of conflict.  Those same T3 lawmakers did not desegregate themselves. Whenever U.S. citizens had the freedom to choose their own associations they immediately deconstructed the artificial grouping and desegregated into peaceful like groupings.  Thus, interfering with Physical Natural Laws (NLP) will create conflict and accepting NLP will be more peaceful.  That further demonstrates the range of conflict resolution planes. 

2. Negotiations Between Inter- and Intra-Theological Groups

Conflict resolution results in an end to a conflict and conflict management results in an agreement for less conflict.  The most heavily studied approach to conflict resolution is negotiation.  Negotiation is to bring about an arrangement of agreement between opposing parties.  Conflict management uses the common business model of attempting to make compromise with the behavioral elements of competition, accommodation, collaboration and avoidance.  That model is largely adapted from Kenneth W. Thomas' 1976 book titled Conflict and Conflict Management: In the Handbook of Industrial and Organizational Psychology.  Robert Axelrod's 1984 book, The Evolution of Cooperation, presents the interaction of humans as largely having potentially opposing incentives for decision making into the context of dynamic and repeated interaction where cooperation may result. 

Axelrod implied that cooperation should not be very likely but oddly opposing forces often use a "tit-for-tat" strategy introduced by Анато́лий Бори́сович Рапопо́рт (Anatol Rapoport).  This strategy is to be nice, forgiving, retaliatory toward defection, and having clearly stated intentions.  He inadvertently reflected the NL strategy of T1 groups: to be nice by not paying back good with evil (Prov. 17:13) and seeking peace (Prov. 15:1; Ps. 34:14; II Tim. 2:22; I Peter 3:8-13); to be forgiving of repentant trespassers (Matt. 18:21-22; Luke 17:3-4 [see examples list in endnotes]); to be retaliatory as Solomon said that there is a time to kill and heal (Eccl. 3:3); to be clear and let your 'yes' be 'yes' and your 'no' be 'no', as Jesus taught (Matt. 5:37).  T1 groups are not perfectly compliant with all NLF--sinless.  Because they do what they would not (sin) and do not what they would do.  This is a witness for the existence of NLF and the sinful nature that wars against the mind (Rom. 7).  Conflict is then inevitable (James 4:1-3).  Moses was taught how to negotiate disputes by teaching NL so people know what to do (Ex. 18:13-26). 

Negotiating inter-theological conflicts are between theological groups which are either (T1, T2), (T1, T3) or (T2, T3) with the intellectual levels of abilities of gifted (gi), average (av) and lower (lo) which are (gi, av), (gi, lo) or (av, lo).  Negotiating intra-theological conflicts are between the same theological groups which are either (T1, T1), (T2, T2) or (T3, T3) with the intellectual levels of (gi, gi), (av, av) or (lo, lo).  The intra-theological negotiations would have the most common abilities and value proximities which are conducive to the resolution process.  

Conflict between individuals is different than it is for governments.  Behavior between individuals is to be kind (I Sam. 26:18-21), not involve cursing (Job 31:29-30), nourishing (Rom. 12:20), loving (Luke 6:27, 35), forgiving (Matt. 6:12-15), and prayerful (Luke 23:34).  Compromise is necessary between T1 believers (Prov. 6:1-5; Matt. 5:24-25; Gal. 2:7-9).  T1 believers are forbidden to make agreements with error (I John 4:1-6) and nonbelievers (Ex. 34:12-16; I Cor. 10:21).  T1 governments are forbidden to make compromises with the ungodly (Ps. 1:1), evil (Rom. 12:9), unbelievers (II Cor. 6:14-18), false teachers (Gal. 1:8-10; II John 7-11), and spiritual darkness (Eph. 5:11).  Some examples are Lot (Gen. 13:12-13; 19:1-29), Samson (Judg. 16:1-21), Solomon (I Kings 11:1-14), Asa (II Chr. 16:1-9; 18:1-3), and Jehoshaphat (IIChr. 19:1-2; 20:35-37).  When the head of Israel stabbed the oppressive enemy king to death, the Israelites had peace for eighty years (Judg. 3:12-30). In an earlier time, Israel did not justly use the sword (Rom. 13:3-4) but wrongly negotiated with evil by first enacting toleration, then assimilation, next imitation and lastly consolidation (Judg. 1-2).  Hugh Latimer (1485-1555) was burned to death for not compromising with evil.  John Milton (1608-1674) spoke for the NL of free presses in Areopagitica.  Milton cited that Adam had reason and so had freedom to choose--reason is but choosing. 

Conflict is sometimes used as a tool of God to induce His desired behavior (e.g. Esau chased Jacob away and Jacob, named Israel, then created his family and the twelve tribes that became the Israeli nation.  Later Israeli spies in Jericho were sought by enemy soldiers causing Rahab to intercede for them in exchange for sparing her life and from her linage came King David and Jesus [Josh. 2:1-24; 6:17-25].)  Ultimately, when a man's ways please the Lord, He makes even his enemies to be at peace with him (Prov. 16:7). 

It is often difficult to know whether theological and eschatological beliefs are given due consideration in negotiation strategies within nation-states.  (That sentiment was expressed by Thomas Schelling in a brief email exchange with Dallas F. Bell Jr. in April, 2008.)  Contemporary examples of glaring compromisers with evil are Neville Chamberlain, Jimmy Carter and Ariel Sharon where evil triumphed.  Contemporary examples where evil was not compromised with are Winston Churchill, Ronald Reagan and Benjamin Netanyahu and evil was defeated. 

3. Tessellations of a Moral Abacus and Cellular Automata

3.1. Tessellations

A tessellation (Latin, tessera means square tablet) is a collection of shapes that cover a plane with no gaps or overlaps.  A regular polygon has three or more sides and angles that are equal.  A regular tessellation is made up of congruent (having the same size and shape) regular polygons.  If there is a regular polygon tessellate made up of 4 squares that cover the plane, we may count from its vertex (where all the squares touch in the center) all 4 sides of the 4 polygons.  Its name would then be 

A semi-regular tessellation is formed by regular polygons and the vertex point is arranged identically.  An example would be 2 triangles and 2 squares called  Such a visualization tool for negotiations could be used to indicate 3 sides or offences of perceived violations of NLF-8 (not stealing) and 3 sides or offenses of the perceived violations of NLF-10 (not coveting) by the 2 triangles, and 4 sides or offenses for the perceived violations of NLF-6 (not murdering) and 4 sides or offenses of the NLF-9 (not lying).  Those 4 polygons of NLF shapes would cover the negotiation plane.  An abacus would indicate a count in the 8th and 10th rows of 3 each, and in the 6th and 9th rows of 4 each. 

3.2. Moral Abacus

A moral abacus would have 10 rows (one for each NLF) with 5 buttons, each with a '0' side and a '1' side.  The first binary button could equal 1.  The second could equal 2.  The third button could equal 4.  The fourth could equal 8.  The fifth button could equal 16.  A maximum number of offences would be 11111 (or 31) beyond which tallying additional violations would not be constructive until the first offenses were adequately addressed.      Using the example at the end of the previous section of this paper, rows 8 and 10 would reflect the button arrangement of 00011 (or 3) and rows 6 and 9 would be 00100 (or 4).  Forgiveness, mercy (I Sam. 24:10-17), and grace (I Peter 4:10) could be allowed to negate the shown abacus math or logic of that example's sum. 

In act 1, scene 1 of William Shakespeare's Much Ado About Nothing (c. 1600), Benedick's shifting loyalties causes Beatrice to say that, "He wears his faith but as the fashion of a hat; it changes with the next block."  The moral abacus value of loyalty would show a deficit for Benedick since the appropriate loyalty is to God and His immutable laws (NL).  King David often reflected that value correctly (II Sam. 1:13-16; 4:4-12).  People with less beliefs may act as a friend after having their lives saved until they have, in their perception, repaid the act at which time they are free to become an enemy if they so choose.   The 2004 book, The Chinese Machiavelli: 3,000 Years of Statecraft, describes how loyalty or chung is derived from the theologies of Taoism, Buddhism and Confucianism.  Those T beliefs create a 'this-for-that' self-loyal abacus void of the morals of forgiveness and mercy etc.  That paradox causes a dilemma because there is a reality of truth to divide the choice of possibilities.  

3.3. Cellular Automata

Cellular automata (plural of automaton) consist of a lattice of cells, each in one of a finite number of states.  The type of agent at a position is updated according to the fixed rule that depends on both the present value and the corresponding immediate neighbors.  The cellular automata approach has been used for Schelling's dynamic model of segregation. 

The rule for our purposes would be to meet the needs of those involved by seeking efficient like T believers.  The tessellation plane would be like the squares on a checkerboard or environment of cells where T1, T2 and T3 believers interact and segregate.  That state, common to all healthy organisms, would attempt to heal itself by the T1 criminal prosecution of T2 and T3 violations of NLF until the T2 and T3 sufficiently harms the T1 before their defense is implemented through segregation.  

4. Conclusion

Conflict resolution can be seen as an attempt at self-healing a group by aligning its individuals to NL for the health of the larger organism.  In the case of individuals committing extreme criminal behavior, the individual (or diseased cell) should be removed from the society (or organism) by imprisonment or death.  Some hopelessly dysfunctional cells (e.g. the noncriminal homeless) may just be bypassed.   

There is only one group of different individuals that can be unnaturally joined.  That is the organism united by salvation (John 3:16) and having the goal of compliance with all NLF called the church.  Only the Creator of the first cause of all effects--God--can voluntarily bind differing individuals and groups.  Their self-healing works much like a body of cells to repair breaks in its skin or surface for the good health of the whole human system.  Knowing this makes the use of the tessellation tools of a moral abacus and cellular automata obviously important for understanding the elasticity of conflict resolution planes in negotiations between inter- and intra-theological individuals and groups. 


List of forgiveness examples:
-Esau and Jacob (Gen 33:4-15)
-Joseph (Gen. 45:8-15)
-Moses (Num. 12:1-13)
-David (II Sam. 19:18-23)
-Solomon (I Kings 1:53)
-Jesus (Luke 23:34)
-Stephen (Acts 7:60)
-Paul (II Tim. 4:16)

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