I AM THE CHOICES I CAN MAKE! I AM THE ROLES I CAN PLAY!

Another file uses TRAFGRAFS to LEARN CHOICE-MAKING. This file uses TRAFGRAFS to LEARN ROLE-PLAYING.

Mathematicians call such graphs, "Matching Graphs": A ROW OF NODES REPRESENTING ROLE-PLAYERS IS TO MATCH 1-1 WITH A ROW OF ROLES.

But "I am the Roles I play", imply a SINGLE NODE FOR ROLE-PLAYER. So, the typical CLOSED MATCHIHG GRAPH BECOMES AN OPEN TREE, which I'll illustrate for moi:

                                    JOHN   HAYS
                                   / | | | | | \
                                  /  | | | | |  \
                                 /   | | | | |   \
                                V    | | | | |    V
                          FATHER     | | | | |     HUSBAND
                                    /  | | |  \
                                   /   | | |   \
                                  V    | | |    V
                           TEACHER     V | V     MATHEMATICIAN
                                      /  |  \
                                     /   V   \
                                    /    |    \
                             CITIZEN     |     PROPERTY-OWNER
                                         |
                                       WRITER

I now show how GRAF may become INDUCTIVELY USEFUL, by INVOKING THE FIGURE-GROUND STRATEGY. Let this ROLE-TREE BECOME THE FIGURE, and my EXPERIENCE become the GROUND. Does MATCHING IN THE ROLE-TREE describe my experience? or do other NODES of this FIGURE CONNECT?

• Yes, clearly, HUSBAND ÞFATHER: being a HUSBAND can INDUCE THE ROLE OF FATHER.
• And (at least to moi) being a father affects how I play my ROLES as TEACHER and MATHEMATICIAN: TEACHERÜFATHERÞMATHEMATICIAN.
• And being a WRITER can help my ROLE-PLAYING as TEACHER and MATHEMATICIAN: TEACHERÜWRITERÞMATHEMATICIAN.
• Etc. Just as writing a BUDGET helps you think out your ROLE as CONSUMER; writing a SCHEDULE helps your ROLE as a MANAGER -- so GRAPHING YOUR ROLE-PLAYING can HELP YOU REALIZE how ONE ROLE COULD OR SHOULD CONNECT WITH ANOTHER. This WIN-WIN STRATEGY CAUSES YOU TO ASK QUESTIONS YOU WOULD OTHERWISE NEVER CONSIDER.

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                (Tune: "Old MacDonald")
		Is there Order in your life?
		"Tramsitivity Knows!"
		Or is Disorder oft and rife?
		"Transitivity Shows!"
		Proffer deference
		To intransitive Preference.
		Intransitive Competition
		Can mush your Mission!
		Dig you Information?
		Dog you Control?
		"Transitivity Knows! Knows! Knows!"

ONE CONDITION is needed for ORDER-STRUCTURES: TRANSITIVITY. We easily graph TRANSITIVITY via different COLORED ARROWS for THREE PATHWAYS: Given ÞÞ   and given also   ÞÞ   then TRANSITIVITY means   ÞÞÞ

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ROLEROLL ALGORITHM

TRANSITIVITY is at issue in TOURNAMENTS. But lack of TRANSITIVITY in many Sports Tornaments yields unfair RANKINGS. Why? Because EVERY PARTICIPANT DOES NOT PLAY EVERY OTHER PARTICIPANT.

This is avoided by ROUND-ROBIN TOURNAMENTS. To the mathematician, "tournament" means "round-robin tournament".

The graph of a TOURNAMENT is known as a COMPLETE GRAPH: EVERY NODE IS CONNECTED TO EVERY OTHER NODE. This provides ROLL-CALLING your CHOICES OR ROLES. It is made CANONICAL by using REGULAR n-GONS: POLYGONS OF n EQUAL SIDES. So, I put together pieces in the Literature for a ROLLROLE ALGORITHM:

1. given a SET of n MEMBERS (CHOICES, DECISIONS);
2. form a REGULAR n-gon;
3. provide each NODE with a MATCHING-TREE (similar to mine, above, matching every other NODE) -- yielding a graph known to mathematicians by the label "K_n";
4. starting with any NODE, traverse all other NODES and their MATCHING-TREES, WITHOUT RETURNING TO STARTING NODE to yield all possible "RANKINGS".
5. the resulting ACYCLIC "TOURNAMENT" is TRANSITIVE, with legitimate and UNIQUE RANKING;
6. this provides n distinct CHOICES for "calling the roll" and a unque RANKING according to a given VALUATION..

Examples: These can be constructed by Tinkertoy rods and spools, except for some of the cross-connections, which can be improvised.

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THE "DIRTY LITTLE SECRET" ABOUT SPORTS AND ECONOMICS ("GET REAL!")

COMPETITION is the default motive in SPORTS, where it is assumed to be TRANSITIVE. But COMPETITION is only QUASI-TRANSITIVE. Think about it. Given teams or individual contestants, if A beats B, and B beats C, DOES IT NECESSARILY FOLLOW THAT A beats C? No! And COMPETITION is often the motive in Work and in other human activities.

Also, the underlying assumption of ECONOMICS is that PREFERENCE is TRANSITIVE. But it is only QUASI-TRANSITIVE. (A person may prefer apples to oranges, and oranges to bananas, but also prefer bananas to apples. Don't say that's "illogical", for there is noting in Logic to ensure it.)

The INTRANSITIVIIES in COMPETITION and PREFERENCE create COMPLEXITIES in our daily lives. We can't control or correct or always predict those intransitivities. But we possess a STRATEGY OF FIGURE-AND-GROUND.

1. SURROUND YOURSELF WITH TRANSITIVE PROCESSES; ACT TRANSITIVELY WHENEVER YOU CAN.
2. You thereby CREATE A "GIANT" FIGURE AGAINST WHICH THE INTRANSITIVIES OF THE WORLD-GROUND WILL SHOW UP .
3. Act protectively.