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# The 'Zhou Yi' Hexagram Sequence: An authentic, intended binary System discloses a rational, bilateral mathematicel Symmetry

### Mondo Secter (Simon Fraser University, Vancouver, B.C. Canada)

The historical texts that discuss or shed light on science in ancient China, do not include the ZhouYi, the oldest portion of the YiJing (Book of Changes).' This paper presents concrete graphic evidence of an intended rational structure to the King Wen ordering of the sixty-four gua (hexagram symbols). These symbols preface the gua ci (judgments), which comprise the first of two textual layers in the ZhouYi.

The paper visually represents a mathematical context embedded in the hexagram sequence and verifies the ZhouYi as system of logic. This graphic evidence illustrates that the King Wen hexagram sequence is both intentional and rational, constructed on an explicit knowledge of binary numbers and a sophisticated understanding of and appreciation for bilateral symmetry. A second object of the paper to disclose something of the author's conceptual frame of mind, mathematical methodology, and style or approach to communicating these ideas.

The question of a rational order and intention to the King Wen hexagram sequence has almost always been answered in the negative, but somehow the subject has never been put completely to rest. The lack of evidence of formal logic or any other mathematical knowledge at the time the ZhouYi was first written (between 950 B.C.-800 B.C.), has led most scholars to conclude that there is not only no mathematical notion or content in the ZhouYi, but that there could not be any. In his book, Researches on the I Ching, Iulian Shchutskii claimed that the reason for denying the possibility of any mathematics in the YiJing is that no meaningful logic existed in China prior to the introduction of Buddhism, which occurred at the end of the first century B.C.

There have been a few efforts to explain the sequence, as distinct from the hexagram system. The McKenna brothers found a hint or order with a horizontal or temporal analysis, by counting the number of different yin and yang lines in adjacent hexagrams. Olsvanger took a vertical or spatial perspective by arranging the Wen sequence in eight rows similar to the FuXi square arrangement, thereby discovering reciprocal number patterns or mirror-image binary symmetry.

Needham dismissed Olsvanger's findings as relatively insignificant. He also dismissed the claim made by Leibniz 300 years ago, that the Chinese had discovered binary numbers 2000 years before he did. Leibniz was not known for making casual comments on such matters. Although he did not leave any material evidence to support his thinking about the Chinese knowledge of binary numbers, this paper will show that he was correct in his assessment. However it will illustrate the binary character and logic of the ZhouYi in a way that Leibniz probably never dreamed of. Perhaps this unconventional methodological approach to deconstructing the hexagram sequence might lend new insight into this historical text, and generate further research into discovering the complete form and content of the Wen sequence.