Farm kids know that chickens in the barnyard have a pecking order wherein one chicken pecks another but is not pecked back, in a descending order from the chicken pecked by none, down to the chicken pecked (or telepecked along a peck-chain -- as "The Three Stooges" slap each other) by all other chickens. This fits a hierarchical model known to humans since Tribal Days. It has been the principal model in The Business World and in The Military. Business types sometimes say, "He's next in the pecking order"". (Elsewhere, I describe the WEB model which is starting to replace the hierarchical model in the business and production world and in the Marines.)PECKING ORDER is a MATHTIVITY I developed in 1962 and taught to kindergarten children at The Campus School of Inter American University, San Germán, Puerto Rico, where I was Head of The Mathematics and Physics Departments.
Children are shown two types of PECKING ORDERS: plain and mixed. In A PLAIN PECKING ORDER, no Peewee pecks another Peewee, but only Yardbird (pecked or telepecked by all in The Order). In A MIXED PECKING ORDER, at least one Peewee pecks another Peewee (who doesn't peck back).
And there's another defining distinction. A PLAIN PECKNG ORDER has only one chick who pecks or telepecks all chicks in THE ORDER, namely, SUPERCHICK. But A MIXED PECKING ORDER has at least one chick, besides SUPERCHICK, which pecks or telepecks all chicks of THE ORDER.
This is gradually explained to the Preschool children, with demonstrations. And they simulate the pecking that takes place in THE PECKING ORDER. This PLANTS IN THEIR MEMORY CONCEPTS TO BE CULTIVATED LATER ON IN SCHOOL.
For, a pecking order is known in MATHEMATICS as a LATTICE, an extension of a PARTIAL ORDERING.
In learning to COUNT, children learn A SIMPLE ORDERING WHEREIN, OF TWO DISTINCT NUMBERS, ONE IS GREATER THAN THE OTHER, that is, IN ORDERING LANGUAGE, DOMINATES THE OTHER. But a PARTIAL ORDERING can CONTAIN TWO DISINCT MEMBERS SUCH THAT NEITHER DOMINATES THE OTHER. When you subject the COUNTING NUMBERS TO THE RELATION OF GREATER THAN OR EQUAL TWO (symbolized: £), YOU OBTAIN A PARTIAL ORDERING, a.k.a. POSET (PARTIALLY ORDERED SET).
TWO OTHER IMPORTANT RELATIONS EXIST IN A POSET: JOIN (symbolized: Ú) and MEET (symbolized: Ù). IN JOIN (Ú), TWO OR MORE MEMBERS (OF THE ORDERING) DOMINATE THE SAME "LOWER" MEMBER. IN MEET (Ù), TWO OR MORE MEMBERS (OF THE ORDERING) ARE DOMINATED BY THE SAME "HIGHER" MEMBER.
A LATTICE IS A PARTIAL ORDERING SUCH THAT EVERY MEMBER HAS A JOIN AND A MEET! (IN PECKNG ORDER TERMS, EVERY CHICK HAS A PECKINGCHICK AS WELL AS A PECKEE).
Preschool children have fun playing with A PECKING ORDER. LATER ON, as shown in the REPERTORY file, BY RELABELING, PECKING ORDER BECOMES FACTORING IN ARITHMETIC, STATEMENT LOGIC, AND MANY MORE STRUCTURES IN MATHEMATICS.
One other notion about LATTICES: DUALITY. Every LATTICE has its DUAL ("mirror-image") in which SUPERCHICK BECOMES YARDBIRD, and vice vera, and A JOIN RELATION BECOMES A MEET RELATION, and vice versa. Children are taught about "The Mirror Pecking Order" of each Pecking Order.
A PROTOYPE OF ALL PLAIN PECKING ORDERS -- AND A MATHTIVITY FOR PRESCHOOL KIDS Below, by hyperlink, you shift to the diagram of a PLAIN PECKING ORDER WITH A YARDBIRD, THREE PEEWEES, THREE MIDDIES (PECKING THE PEEWEES), AND SUPERCHICK. You also see its DUAL ORDER EXTENDING BELOW THE ORDER. Also note that the faces of the CHICKS are colored -- according to a CODE.
The UPPER ORDER MODELS THE ADDITIVE COLOR SYSTEM IN PHYSICS WHEREBY COLORED LIGHTS COMBINE TO CREATE OTHER COLORS. THE THREE ADDITIVE (VISIBLE LIGHT) PRIMARIES ARE RED, GREEN, BLUE -- modeled by PEEWEES. THESE COLORS COMBINE TO CREATE YELLOW (RED, GREEN), MAGENTA (RED, BLUEP, CYAN (GREEN< BLUE) COLORS (VISIBLE LIGHTS) -- modeled by MIDIS. AND THESE LATTER COLORS COMBINE TO CREATE WHITE LIGHT.
The MIRROR ORDERING (DUAL LATTICE) -- extending below the one just descibed -- MODELS THE SUBTRACTIVE COLOR SYSTEM IN PHYSICS WHEREBY COLORED INKS OR PAINTS COMBINE TO CREATE OTHER COLORS. Here, THE PRIMARIES ARE YELLOW, MAGENTA, CYAN -- modeled by ANTI-PEEWEES. THESE COLORS (INKS, PAINTS) COMBINE TO CREATE RED (YELLOW, MAGENTA), BLUE (MAGENTA< CYAN), GREEN (YELLOW, CYAN) COLORS -- modeled by ANTI-MIDDIES. THESE COLORS (INKS, PAINTS) COMBINE TO CREATE BLACK -- modeled by ANTI-SUPERCHICK.
And this has another PHYSICS INTERPRETATION! Modern particle physics speaks of LEPTONS which SEEM TO BE UNANALYZABLE; and PROTONS, NEUTRONS, MESONS WHICH ARE COMPOSED OF QUARKS (pronounced "querks"). It amused a physicist to label the basic MATTER QUARKS AS HAVING A "CHARGE" PROPERTY KNOWN AS "COLOR", and used the ADDITIVE COLOR SYSTEM TO MODEL THIS. In ANTIMATTER, THE SYSTEM IS REVERSED.
So this PECKING ORDER ALSO MODELS QUARKS IN MATTER AND ANTIMATTER PARTICLES OF MODERN PHYSICS!
Here is a SIMPLE PECKING ORDER WITH A YARDBIRD AT THE BOTTOM OF THE (NONMIRROR) ORDERING; THREE PEEWEES; THREE MIDDIES; AND A SUPERCHICK. BELOW THIS IS THE MIRROR ORDERING. Behold.