"Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram Sequence"

Richard Cook, STEDT Project Manager, Post-Doctoral Researcher, Dept. of Linguistics

The first and most enigmatic of the Chinese classics is the Book of Changes, and the reasoning behind its binary hexagram sequence remained an unsolved mystery for some 3,000 years (according to the tradition ascribing it to King Wen of Zhou, d. -11th c.). This lecture resolves the classical enigma through a comprehensive analysis of the hexagram sequence, showing that its classification of binary sequences demonstrates knowledge of the convergence of certain linear recurrence sequences (LRS; Pingala -5th c.?, Fibonacci 1202) to division in extreme and mean ratio (DEMR, the “Golden Section” irrational; Pythagoras -6th c.?, Euclid -4th c.). It is shown that the complex hexagram sequence encapsulates a careful and ingenious demonstration of the LRS/DEMR relation, that this knowledge results from general combinatorial analysis, and is reflected in elements emphasized in ancient Chinese and Western mathematical traditions. This lecture will present an introduction of the classical problem, an overview of the solution, while situating the major findings in larger historical context.