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 Discussion: All Topics Topic: Pecking Order: Lattice Theory for Preschoolers

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 Subject: Pecking Order: Lattice Theory for Preschoolers Author: Sonny Date: Jun 16 2004
In a barn yard, a chicken may peck one or more chickens without being pecked
back. This hierarchy is homologous to the partial ordering of dominance in
lattice theory (and hioerarchies in business and miltary services). By
constructing pecking orders, children implicitly learn lattice theory and
prepare for factor theory in arithmetic. The lattice on
factors of 30 (a complemented lattice) finds representation in (is homologous
to) a Simple Pecking Order, consisting of YARDBIRD (pecked or telepecked by all
in the Order); three PEEWEES, who peck YARDBIRD; three MIDDIES, who peck the
PEEWEES, thereby telepecking Yardbird; and SUPERCHICK, who pecks or telepecks
all chicks in the Order, but is pecked by none. This is shown as homologous to
the ADDTIVE THEORY OF COLOR AND OF QUARKS IN PHYSICS. Its ANTI-PECKING-ORDER
(an anti-lattice) is homologous to the SUBTRACTIVE THEORY OF COLOR AND OF
ANTI-QUARKS IN PHYSICS. A MIXED PECKING ORDER (with a second-order PEEWEE)
models factors of 12 (a distributive, only
partly complemented, lattice). I've taught this mathtivity to many children.
(ONLINE at
http://members.fortunecity.com/jonhays/preschool.htm .)