The Liang Yi System

The two primary forms (Liang Yi):

Old form



Modern form



Among the ancient traditions of China there is a unique system of symbols called the yih ( 02500), i.e., “permutations” or “changes,” which consists of all possible combinations of two elements, called liang yi ( 02600), i.e., the two elementary forms, which are the negative principle, yin ( 02601), and the positive principle, yang ( 02602). The four possible configurations of yang and yin in groups of two are called ssu shiang ( 02603), i.e., “the four [secondary] figures”; all further combinations of the elementary forms into groups of three or more are called kwa ( 02604). In English, groups of three elementary forms are commonly called trigrams, and groups of six, hexagrams.

The four figures (Ssu Shiang)








Mentality (or leadership)

Unity (or origin)

The nature of things (essence)


Great Monarch



Fixed Stars


Corporality (bodily organism)


Compound things 1







Materiality (inertia; bodily substance)


Multiplicity 2







Sensuality; passion


Attributes of things



The book in which the permutations of yang and yin are recorded, was raised in ancient times to the dignity of a canonical writing, a class of literature briefly called king in Chinese. Hence the book is known under the title of Yih King.

The Yih King is one of the most ancient, most curious, and most mysterious documents in the world. It is more mysterious than the pyramids of Egypt, more ancient than the Vedas of India, more curious than the cuneiform inscriptions of Babylon.

The eight Kwa figures and the binary system







02801 ch‘ien to come out; to rise, sunrise; vigorous; (present meaning) dry. 02809 111 7
02802 tui to weigh; to barter; permeable. 02810 110 6
02803 li to separate 02811 101 5
02804 chan to quake; to thunder 02812 100 4
02805 sun peaceful; a stand or pedestal 02813 011 3
02806 k‘an a pit; to dig a pit. 02814 010 2
02807 kan a limit; to stop; perverse. 02815 001 1
02808 kw‘un earth; to nourish; yielding. 02816 000  0

In the earliest writings, the yang is generally represented as a white disk and the yin as a black one; but later on the former is replaced by one long dash denoting strength, the latter by two short dashes considered as a broken line to represent weakness. Disks are still used for diagrams, as in the Map of Ho and the Table of Loh, but the later method was usually employed, even before Confucius, for picturing kwa combinations.

The trigrams are endowed with symbolical meaning according to the way in which yin and yang lines are combined. They apply to all possible relations of life and so their significance varies.

Since olden times, the yih system has been considered a philosophical and religious panacea; it is believed to solve all problems, to answer all questions, to heal all ills. He who understands the yih is supposed to possess the key to the riddle of the universe.

The yih is capable of representing all combinations of existence. The elements of the yih, yang the positive principle and yin the negative principle, stand for the elements of being. Yang means “bright,” and yin, “dark.” Yang is the principle of heaven; yin, the principle of the earth. Yang is the sun, yin is the moon. Yang is masculine and active; yin is feminine and passive. The former is motion; the latter is rest. Yang is strong, rigid, lordlike; yin is mild, pliable, submissive, wifelike. The struggle between, and the different mixture of, these two elementary contrasts, condition all the differences that prevail, the state of the elements, the nature of things, and also the character of the various personalities as well as the destinies of human beings.

The Yih King ( 02800) is very old, for we find it mentioned as early as the year 1122 B.C., in the official records of the Chou dynasty, where we read that three different recensions of the work were extant, the Lien Shan, the Kwei Ts‘ang and the Yih of Chouof which, however, the last one alone has been preserved.

This Yih of Chou, our present Yih King, exhibits two arrangements of the kwa figures, of which one is attributed to their originator, the legendary Fuh-Hi, the other to Wen Wang. Fuh-Hi is also called Feng, “wind,” and Tai Ho, “the great celestial,” and he lived, according to Chinese records, from 2852 to 2738 B.C. It speaks well for the mathematical genius of the ancient founders of Chinese civilisation that the original order of the yih, attributed to Fuh-Hi, corresponds closely to Leibnitz’ Binary System of arithmetic. If we let the yin represent 0 and the yang, 1, it appears that the eight trigrams signify the first eight figures from 0–7, arranged in their proper arithmetical order, and read from below upward. Leibnitz knew the yih and speaks of it in terms of high appreciation. Indeed it is not impossible that it suggested to him his idea of a binary system.

While Fuh-Hi’s system exhibits a mathematical order, Wen Wang’s is based upon considerations of occultism. It stands to reason that Fuh-Hi (by which name we understand that school, or founder of a school, that invented the yih) may not have grasped the full significance of his symbols in the line of abstract thought and especially in mathematics, but we must grant that he was a mathematical genius, if not in fact, certainly potentially. As to further details our information is limited to legends.

The case is different with Wen Wang, for his life is inscribed on the pages of Chinese history and his character is well known.

The personal name of Wen Wang (i.e., the “scholar-king”) is Hsi-Peh, which means “Western Chief.” He was the Duke of Chou, one of the great vassals of the empire, and lived from 1231 to 1135 B.C. In his time the emperor was Chou-Sin, a degenerate debauché and a tyrant, the last of the Yin dynasty, who oppressed the people by reckless imposition and provoked a just rebellion. Wen Wang offended him and was long kept in prison, but his son Fa, surnamed Wu Wang, being forced into a conflict with Chou-Sin, overthrew the imperial forces. The tyrant died in the flames of his palace which had been ignited by his own hands. Wu Wang assumed the government and became the founder of the Chou dynasty which reigned from 1122 until 225 B.C.

Wen Wang was a man of earnest moral intentions, but with a hankering after occultism. During his imprisonment he occupied himself in his enforced leisure with the symbols of the yih, and found much comfort in the divinations which he believed to discover in them. When he saw better days he considered that the prophecies were fulfilled, and his faith in their occult meaning became more and more firmly established.

Trigrams as family relations



Eldest Son

Second Son

Youngest Son

Eldest Daughter

Second Daughter

Youngest Daughter

The eight permutations of the trigrams apparently form the oldest part of the Yih King. They have been an object of contemplation since time immemorial and their significance is set forth in various ways. The trigrams consisting of three yang lines are called the unalloyed yang, and of three yin lines, the unalloyed yin. In the mixed groups the place of honor is at the bottom, and if they are conceived as family relations, the unalloyed yang represents the father and the unalloyed yin, the mother. The three sons are represented by the trigrams containing only one yang; the eldest son having yang in the lowest place, the second in the middle, and the third on top. The corresponding trigrams with only one yin line represent in the same way the three daughters.


The trigrams are also arranged both by Fuh-Hi and Wen Wang in the form of a mariner’s compass. In the system of Fuh-Hi the unalloyed yin stands at the north, the unalloyed yang at the south. The others are so arranged that those which correspond to 1, 2, 3, of Leibnitz’ Binary System proceed from north through west to south in regular order, while 4, 5, 6, start from south taking the corresponding places in the east. In this mathematical arrangement we always have the opposed configurations in opposite quarters, so as to have for each place in every opposite kwa a yang line correspond with a yin line and vice versa; while if they are expressed in numbers of the binary system, their sums are always equal to seven.


Wen Wang rearranged the trigrams and abandoned entirely the mathematical order attributed to Fuh-Hi. The following quotation from the Yih King evinces the occultism which influenced his thoughts:

“All things endowed with life have their origin in chan, as chan corresponds to the east. They are in harmonious existence in siuen because siuen corresponds to the southeast. Li is brightness and renders all things visible to one another, being the kwa which represents the south. Kw‘un is the earth from which all things endowed with life receive food. Tui corresponds to mid-autumn. Ch‘ien is the kwa of the northwest. Kan is water, the kwa of the exact north representing distress, and unto it everything endowed with life reverts. Kan is the kwa of the northeast where living things both rise and terminate.”

Since this new arrangement is absolutely dependent on occult considerations, the grouping must appear quite arbitrary from the standpoint of pure mathematics. It is natural that with the growth of mysticism this arbitrariness increases and the original system is lost sight of.

The yin and yang elements are supposed to be the product of a differentiation from the t‘ai chih, “the grand limit,” i.e., the absolute or ultimate reality of all existence, which, containing both yang and yin in potential efficiency, existed in the beginning. The grand limit evolved the pure yang as ether or air, which precipitated the Milky Way, shaping the visible heaven or firmament; while the yin coagulated and sank down to form the earth. But the earth contained enough of the yang to produce heat and life. Some unalloyed yang particles rose to form the sun, while correspondingly other unalloyed yin particles produced the moon, the two great luminaries, which in their turn begot the fixed stars.

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