1.0. Introduction to Part I.
Among books on the shelf, it is hard to find one more
ancient in origin than the I Ching. This classic, which
survived so many cultural revolutions, actually grew to
its present form through many centuries of gradual accumulation.
It consists of sixty-four hexagrams, appended texts, and numerous
commentaries. The hexagrams and a few lines of the text are more
than three thousand years old, but the rest has undergone changes
and additions through the years, becoming increasingly moral,
philosophical, and cultural in content. Although the relatively
recent additions are full of interest for scholars and philosophers,
it is the esoteric use of the hexagrams, for meditation and divination,
which have fascinated people throughout the ages, and insured the
survival of the book. But the key to the understanding of the
hexagrams was lost long ago, and many have tried to recover it
by studying the hexagrams alone, independent of the literary appendices.
This mystery is the subject of many of the commentaries on the I Ching,
which keep appearing up to the present day.
Among the unsolved problems still engaging scholars are:
- how did the trigrams originate?
- how did the hexagrams originate?
- did the trigrams or hexagrams evolve first?
- why is the character Kua used to refer both to the trigrams and hexagrams?
- how did the yarrow stalk process originate?
- did the yarrow stalk process precede the evolution of the Kua?
- were the Kua used first for divination or some other purpose?
- why were the numbers 6, 7, 8 and 9 used to label the "changes"?
- what is the origin of the names assigned to the hexagrams?
- why have the characters for the trigrams no other meaning in classical Chinese?
- how old is the Shuo Kua commentary?
- how are the Kua related to the oracle bones and tortoise shell oracles of archaic China?
- what is the meaning of the mysterious numbers assigned to the first two hexagrams in the Ta Chuan commentary?
- how was the order of the hexagrams determined?
- why does yang change to yin more frequently than yin to yang?
- how can the I Ching be used for spiritual meditation?
- when was binary arithmetic discovered?
and many others. These questions have intrigued me since
I first came across the I Ching, and reading the existing
literature revealed that scholars of modern times were equally
puzzled. As a mathematician, I undertook to answer these
questions with modern mathematics, using the Kua alone as text
material. The insights which resulted from these studies, together
with meditation on the Kua, suggested the thesis presented in this
part, which answer all of the preceding questions. In addition,
some hints concerning the first emergence of mathematical thought
in the history of man's intellectual development result from this
theory. Apparently this idea of the origin of the I Ching did not
occur to previous modern scholars because of a cultural prejudice
against psi phenomena, especially precognition and divination,
which sterilized their research, and was in opposition to the actual
nature of the I Ching, and the cultural milieu in which it emerged.
But the archeology of wisdom requires a trans-cultural outlook, and
an involvement with ancient values, which transcends scholarship.
Acknowledgements
I am deeply greatful for my informative friends:
Emilia Hazelip, Michael Saso, and Henry Burnham,
for their support for this project.
Revised 18 October 1999 by Ralph H. Abraham
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