I. The Philosophical Foundations of the Number of the Great Expansion

"The number of the Great Expansion is fifty; of these, forty-nine are used. Divide them into two to symbolize the Two (Heaven and Earth); set one aside to symbolize the Three; count them off by fours to symbolize the Four Seasons; return the remainder to symbolize the intercalary month. In five years there are two intercalations; therefore, one returns the remainder twice before completing the cycle." — Xici Zhuan (Great Commentary on the Appended Judgments), Yijing

This passage of fewer than a hundred characters constitutes the core canon of ancient Chinese numerological arts.

1. Why "Fifty"$1

Regarding the origin of "the number of the Great Expansion is fifty," Yijing scholars through the ages have offered a multitude of interpretations. The principal views are as follows:

• The sum of the numbers of Heaven and Earth: The Xici Zhuan states, "The number of Heaven is twenty-five; the number of Earth is thirty; together the numbers of Heaven and Earth total fifty-five." The Song dynasty scholar Zhu Xi held that fifty is the number of the Great Expansion, with five (the generative numbers of the Five Phases) removed and left unused, thus yielding fifty.
• The center of the Hetu and Luoshu: In the Hetu (River Chart), the center contains five and ten, whose product is fifty. In the Luoshu (Luo Document), the center is five, and the ten of the five directions likewise accords with fifty.
• The Pythagorean theorem: With a base of three, a height of four, and a hypotenuse of five, the sum of their squares (9 + 16 + 25) is precisely fifty.

Regardless of which explanation one favors, "fifty" invariably symbolizes the "totality" and the "fixed number" of all things in the universe.

2. Why "Of These, Forty-Nine Are Used"$2

In actual divination, one must take a single stalk from the fifty yarrow stalks and reverently return it to the stalk-holder or place it directly before oneself, never to be touched again throughout the entire process. This single stalk holds a position of supreme eminence.

• The dialectic of substance and function (ti-yong): This one stalk represents Taiji (the Supreme Ultimate). Taiji is the origin of the world — utterly still, yet responsive to all stimuli. Precisely because of Taiji's "stillness," the remaining forty-nine stalks are able to "move."
• The mutual arising of the hidden and the manifest: This is a supremely refined philosophical metaphor — truth (the Dao) is often hidden and invisible. All that we can manipulate and calculate is the functioning (yong) that arises after the Dao manifests, not the essence (ti) itself.