Saturday, April 15, 2023

Coalition, Puzzle Solving, and Drama Triangle Cycling

 This poster covers a presentation at the Indiana Sectional Meeting of the MAA (Math Association of America) at Indiana University Kokomo, IN on April 1, 2023 by Dennis Glenn Collins, retired math prof. from UPR-Mayaguez.  1519 S. State Rd. 119, Apt. 2, Winamac, IN 46996-8550.

In a 1981 talk "RT" Robert Thomas Jones (May 28, 1910-Aug 11, 1999) cites Gerald O'Neill as telling how a scientist brought to life from 200  years ago would be completely bewildered by what he saw, whereas a politician would recognize perfectly well the kind of thing that was going on in politics and the general conduct of human affairs . . . He ends with the conclusion that

    the idea of progress, in the form responsible for the revolution in science, must somehow find its way into political science.   p. 255   2005  vol 86 Memoirs of the National Academy of Sciences.


p. 174  2019  Chapter 33  "Toward Transformity of Christian or other Advanced Religion Follower"  by David Scienceman and Dennis Collins,  Emergy Synthesis 10 unpublished manuscript Gainesville, FL

The goal of a "moral code weather equation" would be to have an equation, similar to equations which predict the weather, say velocity field or wind velocity . . . . A typical weather equation is the following for the rate of change of velocity U with respect to time t:   dU/dt   =  . . . . 

The simplest case would be dU/dt = 0 (which implies by integration U = constant wind or velocity, say a "front" coming through).  This case seems to happen in Drama Triangle Cycling.  

CORRECTION  The blog post "Drama Triangle Cycling--4 Cases" by Dennis Glenn Collins has a circle diagram at upper left, which is supposed to have row vectors from the chart below.  However some "6's" were incorrectly replaced by "4's."  The original poster from MAA Oct 2022 Rose-Hulman did not have this mistake.  Thus (4.5,.4,4.5) should be (6.5,.4,6.5).

The question is how could constant velocity occur.


We have the 3 members of the Triumvirate circling around the equilibrium  SIL (Status In Life) value 4.5.  Each has a balance, where w = angular velocity

centrifugal force out = government spring force in

m w^2 R = k R

where R is distance from 4.5.  If  R is not 0 or the system is not at equilibrium, then we can cancel R to get    m w^2 = k   or  w^2 = k/m  or   w= sq root(k/m)  or period T = 2 Pi/w = 2 Pi sq root(m/k).  Thus T is a constant independent of R.

Here centrifugal force out must be interpreted relative to SIL.  For example if the member is near SIL 0 out would be even smaller, whereas if the member is near maximum, then SIL out would be even larger.

This result means Drama Triangle Cycling occurs at a constant radians per year, say 30 degrees (= 360/12)  in the case of Julius Caesar.  

 The cycling is basically a three-part round in music.  A common question is what about 4 members versus 3.  The Rose-Hulman poster had a 4-member cycling in 12 years which exactly matches the 4-part "Frere Jacques" round, although with 3 steps for  8 beats.  There is a question if this pattern occurs in politics.

copyright 2023  Dennis Glenn Collins