The Relationship Between I Ching and Chinese Numerals

A diviner sits with a bundle of fifty dried yarrow stalks. She divides them into two piles, removes one stalk, and counts the remainder by fours. The result is a number: 6, 7, 8, or 9. That number determines whether a line is changing or stable, yin or yang. She repeats this six times, and the hexagram that emerges is not a random image but a precise numerical structure. The I Ching, or Yijing, is a book of numbers before it is a book of words. The relationship between the I Ching and Chinese numerals is foundational: the 64 hexagrams are generated by binary combinations of yin (broken line, associated with 6 and 8) and yang (solid line, associated with 7 and 9), and the divination process uses numerical remainders to select each line. Beyond the mechanics, Chinese numerology — the symbolic meanings of numbers from 1 to 10 — shapes the philosophical framework of the I Ching, as seen in the River Map (Hetu) and the Great Treatise’s numerical cosmology.

Explore how the I Ching uses Chinese numerals — from yarrow stalk divination to the binary logic of yin and yang, to encode cosmic change.

How the Yarrow Stalk Method Turns Numbers into Hexagrams

The oldest surviving divination method for the I Ching uses fifty yarrow stalks. The practitioner sets one stalk aside as a symbol of the Supreme Ultimate (Taiji), leaving forty-nine. She divides the pile into two bundles (representing heaven and earth), removes one stalk from the right bundle (representing humanity), and then counts the left bundle by fours (representing the four seasons). The remainder, 1, 2, 3, or 4, determines a numerical value. After three such manipulations, the sum yields one of four numbers: 6, 7, 8, or 9.

These four numbers are the core numerical vocabulary of the I Ching. Six is old yin (a changing yin line). Seven is young yang (a stable yang line). Eight is young yin (a stable yin line). Nine is old yang (a changing yang line). The distinction between young and old matters: old lines change into their opposites, producing a second hexagram that represents the future outcome. The numbers are not arbitrary. They encode the cycle of yin and yang, with even numbers (6, 8) belonging to yin and odd numbers (7, 9) belonging to yang.

This method is described in the “Great Treatise” (Xici zhuan), one of the Ten Wings traditionally attributed to Confucius but compiled by Han dynasty scholars around 200 BCE. The text states: “The stalks are used for the numbers; the numbers are used for the changes.” The numerical process is the engine of the oracle.

Where the Numbers Come From: The River Map and Luo Writing

That history explains why the numbers 1 through 10 appear in the I Ching’s cosmological diagrams. Two legendary charts, the River Map (Hetu) and the Luo Writing (Luoshu), are said to have revealed the numerical patterns underlying the universe. According to tradition, the mythical emperor Fu Xi (traditionally 2800 BCE) received the River Map from a dragon-horse emerging from the Yellow River. The map displayed a pattern of dots: white dots for odd (yang) numbers and black dots for even (yin) numbers, arranged in a cross formation. The Luo Writing appeared to Yu the Great (c. 2200 BCE) on the shell of a turtle from the Luo River, showing a magic square where every row, column, and diagonal sums to 15.

These diagrams were formally linked to the I Ching during the Han dynasty (206 BCE–220 CE). The scholar Liu Xin (c. 50 BCE–23 CE) and others argued that the River Map corresponded to the eight trigrams and the Luo Writing to the nine palaces (the basis of the Later Heaven trigram arrangement). The numbers in the River Map (1–10) align with the five phases and the directions: 1 and 6 for water (north), 2 and 7 for fire (south), 3 and 8 for wood (east), 4 and 9 for metal (west), and 5 and 10 for earth (center). The Luo Writing’s magic square provides the numerical skeleton for the “flying star” system of feng shui, where numbers 1 through 9 move through time and space.

The human consequence: a diviner or feng shui practitioner does not simply read numbers; she reads the cosmic forces they represent. The number 1 is not just a digit but the beginning of all things. The number 5 is the pivot of the five phases. The number 9 is the completion of a cycle.

The Binary Logic of Yin and Yang

The most famous numerical aspect of the I Ching is its binary structure. Each hexagram consists of six lines, each line either yin (broken, represented by 0) or yang (solid, represented by 1). The 64 hexagrams are all possible combinations of six binary choices, from 000000 (hexagram 2, Kun) to 111111 (hexagram 1, Qian). This binary system was recognized explicitly by the Song dynasty philosopher Shao Yong (1011–1077 CE). Shao Yong arranged the 64 hexagrams in a sequence that corresponds exactly to binary counting from 0 to 63, with yin as 0 and yang as 1. He published this arrangement in his work “Huangji Jingshi” (Supreme Principles Governing the World), completed around 1060 CE.

Shao Yong’s binary order later caught the attention of the German mathematician Gottfried Wilhelm Leibniz in 1701. Leibniz, who had developed binary arithmetic independently, saw the I Ching hexagrams as evidence that the Chinese had discovered binary logic millennia earlier. He corresponded with the Jesuit missionary Joachim Bouvet, who sent him a copy of Shao Yong’s arrangement. Leibniz wrote in his “Explication de l’Arithmétique Binaire” (1703): “The ancient Chinese philosopher Fu Xi had knowledge of binary arithmetic, and this is the foundation of the 64 hexagrams.”

But Shao Yong’s order is not the only one. The traditional “King Wen” order, which dates to the Zhou dynasty (c. 1000 BCE), does not follow binary progression. The King Wen sequence pairs hexagrams by inversion or opposition, not by numerical value. The hexagram numbers 1 through 64 in that order are not binary positions; they are mnemonic and symbolic. For example, hexagram 1 (Qian, pure yang) is followed by hexagram 2 (Kun, pure yin), but hexagram 3 (Zhun, difficulty) is not the binary 000011. The two orders coexist, and practitioners use both depending on context.

What Each Number Means in the I Ching System

The numbers 1 through 10 carry specific symbolic weight in the I Ching’s cosmology. The “Great Treatise” lays out a generative chain: “In the Changes there is the Supreme Ultimate (Taiji), which generates the Two Modes (liangyi, yin and yang), which generate the Four Images (sixiang, major and minor yin and yang), which generate the Eight Trigrams (bagua).” This is a numerical progression: 1, 2, 4, 8. The number 3 appears as the Three Powers (heaven, earth, humanity) that each hexagram contains in its pairs of lines. The number 5 corresponds to the Five Phases, which are embedded in the River Map. The number 6 is the number of lines in a hexagram. The number 7 is the number of stars in the Big Dipper, a celestial marker used in I Ching-based calendrics. The number 8 is the trigrams themselves. The number 9 is the nine palaces of the Luo Writing. The number 10 is the ten heavenly stems, which combine with the twelve earthly branches to form the sexagenary cycle used in I Ching date calculations.

In yarrow stalk divination, the numbers 6, 7, 8, and 9 are the only ones that appear. Six and eight are yin; seven and nine are yang. The old numbers (6 and 9) change; the young numbers (7 and 8) remain stable. This mirrors the natural cycle: yin reaches its extreme at 6 and turns to yang, yang reaches its extreme at 9 and turns to yin. The numbers are not static labels; they are processes.

How the I Ching Numbers Are Used Beyond Divination

The numerical framework of the I Ching extends into Chinese medicine, feng shui, and personal numerology. In the “Yellow Emperor’s Inner Canon” (Huangdi Neijing, compiled c. 200 BCE), the twelve main meridians are correlated with the twelve hexagrams of the “Biography of the Yellow Emperor” (a later text). Each hexagram represents a month and a phase of qi flow. The number 12 comes from the twelve earthly branches, which themselves are paired with the ten heavenly stems to create the sixty-year cycle, a number that echoes the 64 hexagrams (close but not identical).

In feng shui, the “Eight Mansions” system assigns each person a personal trigram based on their birth year. The calculation uses the last two digits of the birth year, reduced modulo 9, and then mapped to a trigram number. For example, a person born in 1985: 85 mod 9 = 4, which corresponds to the trigram Xun (wind). The numbers 1 through 9 from the Luo Writing are used to determine auspicious directions. The “flying star” system (Xuan Kong Fei Xing) uses a grid of nine squares, each with a number that changes annually, monthly, and daily. The numbers are not arbitrary; they follow the sequence of the Luo Writing magic square.

Personal numerology based on the I Ching also exists. Some practitioners calculate a “life hexagram” by reducing the birth date to a number between 1 and 64, then consulting the corresponding hexagram. This practice is modern (20th century) but draws on the ancient principle that numbers reveal pattern.

Common Misconceptions About I Ching and Numbers

The first is that the I Ching is purely a fortune-telling tool. It is a philosophical text that uses numbers to describe the dynamics of change. The divination method is a practical application, not the whole system.

The second is that the numbers 6, 7, 8, 9 are arbitrary. They are derived from a specific mathematical process (division by four, three times) and carry symbolic weight from Chinese numerology. The number 6 is associated with water and the north; 7 with fire and the south; 8 with wood and the east; 9 with metal and the west. These correspondences come from the River Map.

The third is that the binary system was invented by Leibniz. Shao Yong’s arrangement predates Leibniz by six centuries. Leibniz recognized the pattern, but he did not create it.

The fourth is that the hexagram number (1–64 in the King Wen order) determines the hexagram’s meaning. The meaning comes from the lines, the trigrams, and the image, not from the ordinal number. Hexagram 1 is not “the first” in a hierarchy; it is pure yang. The number is a label, not a cause.

The fifth is that the yarrow stalk method is the only legitimate method. The coin method (using three coins, each head = 3, tail = 2, sum gives 6,7,8,9) is a later simplification from the Tang dynasty (618–907 CE). It produces the same four numbers but loses the numerical ritual of the stalks. Both are valid, but the stalk method preserves the full numerical symbolism.

FAQ

What do the numbers 6, 7, 8, and 9 mean in I Ching divination?
They represent the four types of lines: 6 is old yin (changing), 7 is young yang (stable), 8 is young yin (stable), 9 is old yang (changing). The old lines change into their opposites, producing a second hexagram.

How does the yarrow stalk method produce numbers?
The diviner divides 49 stalks, counts by fours, and records the remainder. After three such manipulations, the sum of the remainders yields one of the four numbers. The process is repeated six times to build a hexagram.

Are the I Ching hexagrams related to binary code?
Yes. Each line is either yin (0) or yang (1), and the 64 hexagrams are all possible six-digit binary combinations. Shao Yong (1011–1077 CE) arranged them in binary order, which Leibniz later recognized as binary arithmetic.

The Numbers Are the Bones

The I Ching is often approached as a book of wisdom, but its skeleton is numerical. Every hexagram, every line, every divination result is a number before it is a word. The yarrow stalks, the River Map, the binary logic of yin and yang, these are not decorations. They are the structure that makes the oracle work. To understand the I Ching is to understand how its numbers generate meaning.

For a deeper look at how numbers function in other divinatory systems, see our numerology hub. The glossary entry on I Ching trigrams explains the eight basic symbols that combine into hexagrams. And our guide to I Ching divination methods covers both yarrow stalk and coin techniques in detail.