1. Heaven is one, earth is two; heaven is three, earth four; heaven is five, earth six; heaven is seven, earth eight; heaven is nine, earth ten.
In the traditional form of the text, this section comes just before chapter x. It was transposed to its present position by Ch'êng Tzŭ in the sung period and joined with the section that follows, which originally came after section 3. The two sections undoubtedly belong together, but they are only very loosely connected with what follows. They contain speculations about numbers similar to those in the section entitled Hung Fan in the Book of History [Shu Ching]. Probably they represent the beginning of the connection between the number speculations of the Book of History and the yin-yang doctrine of the Book of Changes, which played an important role in Chinese thought especially under the Han dynasty. To understand this connection, which can be mentioned here only in passing, we must go back to the diagram known as Hu T'u, the Yellow River Map, said to have originated with Fu Hsi [fig. 4] This map shows the development out of even and odd numbers of the "five stages of change" (wu hsing, usually incorrectly called "elements").
Water in the north has sprung from the one of heaven, which is complemented by the six of earth. Fire in the south has sprung from the two of earth, which is complemented by the seven of heaven. Wood in the east has sprung from the three of heaven, which is complemented by the eight of earth. Metal in the west has sprung from the four of earth, which is complemented by the nine of heaven.
Water in the north has sprung from the one of heaven, which is complemented by the six of earth. Fire in the south has sprung from the two of earth, which is complemented by the seven of heaven. Wood in the east has sprung from the three of heaven which is complemented by the eight of earth. Metal in the west has sprung from the four of earth, which is complemented by the nine of heaven. Earth in the middle (t'u, the soil, the earth substance as distinguished from ti, the earth as a heavenly body) has sprung from the five of heaven, which is complemented by the ten of earth.
The second arrangement, according to which the numbers separate again and combine with the eight trigrams, is that of the Lo Shu, the Writing from the River Lo [fig. 5].
2. There are five heavenly numbers. There are also five earthly numbers. When they are distributed among the five places, each finds its complement. The sum of the heavenly numbers is twenty-five, that of the earthly numbers is thirty. The sum total of the heavenly and earthly numbers is fifty-five. It is this which completes the changes and transformations and sets demons and gods in movement.
No further comment is needed in explanation of this. Like section 1, it undoubtedly belongs to a later period.
3. The number of the total is fifty. Of these, forty-nine are used. They are divided into two portions, to represent the two primal forces. Hereupon one is set apart, to represent the three powers. They are counted through by fours, to represent the four seasons. The remainder is put aside, to represent the intercalary month. There are two intercalary months in five years, therefore the putting aside is repeated, and this gives us the whole.
Here the process of consulting the oracle is brought into relation with cosmic processes. The procedure in consulting the oracles is as follows:
One takes fifty yarrow stalks, of which only forty-nine are used. These forty-nine are first divided into two heaps [at random], then a stalk from the right-hand heap is inserted between the ring finger and the little finger of the left hand. The left heap is counted through by fours, and the remainder (four or less) is inserted between the ring finger and the middle finger. The same thing is done with the right heap, and the remainder inserted between the forefinger and the middle finger. This constitutes one change. Now one is holding in one's hand either five or nine stalks in all. The two remaining heaps are put together, and the same process is repeated twice. These second and third times, one obtains either four or eight stalks. The five stalks of the first counting and the four of each of the succeeding countings are regarded as a unit having the numerical value three; the nine stalks of the first counting and the eight of the succeeding countings have the numerical value of two. When three successive changes produce the sum 3+3+3=9, this makes the old yang, i.e., a firm line that moves. Seven is the young yang, and eight the young yin; they are not taken into account as individual lines (cf. the section on consulting the oracle in Appendix I, pp. 721 ff.).
4. The numbers that yield THE CREATIVE total 216; those which yield THE RECEPTIVE total 144, making in all 360. They correspond with the days of the year.
When THE CREATIVE is made up of six old yang lines, that is, on nines only, the following numbers result when the oracle is consulted.
| Total number of stalks | 49 |
| Subtracted the first time | 5+4+4=13 |
| |
36 |
When this is repeated six times (for the six lines), the total of the six remainders (36x6) is 216 stalks.
When THE RECEPTIVE consists of sixes only--that is, of old yin lines--the following numbers result.
| Total number of stalks | 49 |
| Subtracted for a six (old yin) | 9+8+8=25 |
| 24 |
When this has been done six times (for the six lines of a hexagram), the total of the remainders (24x6) is 144 stalks. If now one adds together the numbers obtained for THE CREATIVE and the numbers obtained for THE RECEPTIVE, the result is 216+144=360, which corresponds with the average number of days in the Chinese year.
5. The numbers of the stalks in the two parts amount to 11,520, which corresponds with the number of the ten thousand things.
In the whole of the Book of Changes there are 192 lines of each kind--in all, 384 lines (64x6), of which half are yang and half yin. As has been shown in the section above, after a moving yang line is obtained there remain thirty-six stalks, so that we have altogether 192x36=6912. Each of the moving yin lines yields a remainder of twenty-four stalks: 192x24=4608. together 96+4608=11,520
6. Therefore four operations are required to produce a change; eighteen mutations yield a hexagram.
The words "change" and "mutation" are used here in the same sense. Each line, as shown above, is composed of three mutations or changes. The four operations are: (1) dividing the stalks into two heaps; (2) taking up one stalk and inserting this between the ring finger and the little finger; (3) counting off the left-hand heap by fours and inserting the remainder between the ring finger and the middle finger; (4) counting off the right-hand heap by fours and inserting between the forefinger and the middle finger. These four operations yield one change or mutation--that is to say, the numerical value two or three (see above). When this change is carried out three times, one obtains the value of the line, either a six or a seven, and eight or a nine. Six lines (3 changes x6=18 changes) produce the structure of the hexagram.
7. The eight signs constitute each a small completion.
The hexagram is made up of two trigrams. The "eight signs" are the eight primary trigrams. In a hexagram the lower trigram is also called the inner, and the upper trigram is also called the outer.
8. When we continue and go further and add to the situations all their transitions, all possible situations on earth are encompassed.
Each of the sixty-four hexagrams can change into another through the appropriate movement of one or more lines. Thus we arrive at a total (64x64) of 4096 transitional stages, and these represent every possible situation.
9. It reveals tao and renders nature and action divine. Therefore with its help we can meet everything in the right way, and with its help can even assist the gods themselves.
This section refers again to the Book of Changes in general. Its theme is that the book reveals the meaning of events in the universe and thereby imparts a divine mystery to the nature and action of the man who puts his trust in it, so that he is enabled to meet every event in the right way and even to aid the gods in governing the world.
10. The Master said: Whoever knows the tao of the changes and transformations, knows the action of the gods.