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of Christian or other Advanced Religion Follower"  by David Scienceman and Dennis Collins,  Emergy Synthesis 10 unpublished manuscript Gainesville, FL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

Tuesday, September 6, 2022

Drama Triangle Cycling of WWII Big Three

On Sept 14, 2019  Dennis Collins presented a paper "Drama Triangle Cycling of Julius Caesar Triumvirate by Newton Dynamics" at the AMS  (American Math Society) Sectional Meeting #1150-81-546 in Madison, WI and also a similar talk at an MAA (Math Assoc of America) Meeting at Wabash College on Oct 26, 2019 and at the Wolfram Tech Conference on Oct 29, 2019.  An astounding fact is that the same chart works to describe the Drama Triangle Cycling of the World War II Big Three with only a re-labeling of columns and change of period from 12 years to 30 years.  The latter 2.5 factor may be partially explained by the increase of life expectancy from around 33 years to 63 years from Roman times to 1945.

Year bce  Year ce    
                                 aggressor/Caesar        victim/Crassus       Rescuer/Pompey
                                 rescuer/Churchill         victim/FDR          aggressor/Stalin
                 1929                                            8.5
                 1931.5                                         8.0
                 1934                                            6.5
55             1936.5          .9                            4.5                        8.0
54             1939           2.4                            2.4                        8.5
53             1941.5        4.5                              .9                        8.0                        
52             1944           6.5                              .4                        6.5
51             1946.5        8.0                              .9                        4.5
50             1949           8.5                            2.4                        2.4
49             1951.5        8.0                            4.5                         .9
48             1954           6.5                            6.5                         .4
47             1956.5        4.5                            8.0                         .9
46             1959           2.4                            8.5                       2.4
45             1961.5         .9                             8.0                       4.5
44             1964           .4                              6.5                       6.5
Here chart values are SIL (Status-in-Life from 0 death or near death to 4.5 equilibrium to 9.0 very powerful, so that FDR dies in 1945, Stalin in 1953, and Churchill in 1965  versus  Crassus in 53, Pompey in 48, and Caesar in 44 bce.  The Caesar ellipse goes counter-clockwise whereas the WWII ellipse goes clockwise.     copyright 2022  Dennis Glenn Collins        

Saturday, September 3, 2022

How far back are we

 How far back are we  by Dennis Glenn Collins

1519 S. State Rd. 119 Apt. 2, Winamac, IN  46996-8550

Aug. 25, 2022  from  July 13, 2020

presentation at Starke Co. Library, Knox. IN  July 13 2020

According to the Conflict in History theory of Dennis Collins, history may more-or-less repeat as conflicts are worked out.  Thus it may be helpful to ask "How far back are we" when studying current events.  The following covers a "presentation"  at the Starke Co. Library July 13, 2020; frequently there were few or no attendees.

In 1998 I wrote something like "The main difference between Mussolini and Netanyahu is that Mussolini only wanted to turn the clock of civilizaqtion back 2000 years to the Roman Empire whereas Netanyahu wants to turn it back 3000 years to the Solomon Empire, or approximately the "invasion of the Sea Peoples" around 1000 bce.  One could also say that the ISIS Caliphate wanted to turn civilization back about 1000 years to around 1000 ce, or that Vladimir Putin wants to turn civilization back to the age of Peter the Great around 1700 ce or 300 years ago.

Recently there is also talk of returning civilization to the age of Abraham or about 4000 years ago or 2000 bce.

However there are drawbacks to turning civilization back.  In 2000 bce there was more or less absolute rule with slavery.  Even after Moses there was slavery persisting into the Roman Empire and beyond.  The idea of equal justice started more with the Romans but was not much prevalent in the age of Solomon of 1000 bce.  Thus there is baggage that comes along with turning civilization back.  Returning to the age of Abraham could also mean re-introducing slavery.  

Nowadays there is danger of turning civilization back to the tower of Babel age of about 5000 years ago or 3000 bce, with the collapse of communication systems; for example cooperation of space exploration seems to be evaporating.