Info

jia

yi

bing

ding

wu

ji

geng

xin

ren

gui

Be in womb

you

sben

zi

hai

zi

bai

mao

yin

wu

si

Be nourished

xu

wei

chou

xu

chou

xu

chen

chou

wei

chen

Be born

hai

wu

yin

you

yin

you

si

zi

shen

mao

Be bathed

zi

si

mao

sben

mao

shen

wu

hai

you

yin

Be of age

chou

eben

eben

wei

eben

wei

wei

xu

xu

chou

Be in office

yin

mao

si

wu

si

wu

shen

you

hai

zi

To flourish

mao

yin

wu

si

wu

si

you

shen

zi

hai

To decline

eben

chou

wei

eben

wei

chen

xu

wei

chou

xu

To be ill

si

zi

sben

mao

shen

mao

hai

wu

yin

you

To die

wu

bai

you

yin

you

yin

zi

si

mao

shen

To be.buried

wei

xu

xu

chou

xu

chou

chou

chen

chen

wei

Be in extinction

sben

you

bai

zi

bai

zi

yin

mao

si

wu

Table 2.4 shows the phase of any particular stem in any particular month (represented by the branches) of the year.8 Here the lunar months are denoted by the branches, beginning with yin for the first lunar month, mao for the second, chert for the third, and so forth. The 'birth' or 'long life' phase, the 'becoming official' phase and the 'flourishing' phase are significant in the three cosmic boards and important in the art of fate-calculations, particularly for the Yang stems. 'To become ill', 'to die', 'to be buried' and 'extinction' are significant phases where different interpretations are adopted between the three cosmic board systems and the art of fate-calculations. Also, in the art of fate-calculation, the phase 'to be buried' (mu) has special significance only where the Yin stems are concerned. The phases indicate the strength or weakness of the stems and whether they gain or lose support. While fate-calculations employed the cycle of 12 phases, which are reminiscent of the Buddhist Twelve Nadanas (shier yinyuan "t"^.®^), the 12 chains in the link of existence, the three cosmic boards use instead only five phases, namely xiu ft (Rest), wang (EE (Prosperity) or EE (King), xiang ffi (Accordance), qiu 0 (Imprisonment) and si Wj (Death). The Wuxing dayi provides a list of the stems and branches under each phase in the seasons of the year.9 From this list the following definitions can be derived:

Table 2.5

Prosperity When the xing of the season is the same as that of the ordinal concerned.

Accordance When the xing of the season produces the xing of the ordinal concerned.

Rest When the xing of the season is produced by the xing of the ordinal concerned.

Imprisonment When the xing of the season is subjugated by the xing of the ordinal concerned.

Death When the xing of the season subjugates the xing of the ordinal concerned.

Without using the seasons, the branch of the month is taken into consideration in other cases. From the Wubeizhi KMiS (Treatise on Armaments) the following slightly different definitions can be derived instead:10

Table 2.6

Prosperity When the xing of the month produces the xing of the ordinal concerned.

Accordance When the xing of the month is similar to that of the ordinal concerned.

Rest When the xing of the month subjugates the xing of the ordinal concerned.

Imprisonment When the xing of the month is subjugated by the xing of the ordinal concerned.

Death When the xing of the ordinal concerned produces the xing of the month.

The divergence between the definitions one obtains by taking the season as the basis and those one obtains by taking the month as the basis, as shown in Tables 2.5 and 2.6, is noteworthy. Here is an example to illustrate the lack of consistency among the methods and different schools of thought in this area of study. Multiplicity and divergence provided flexibility in interpretations in the repertoire of a skilful diviner.

States of strength or weakness are also indicated by the way stems and branches are combined. For example, a branch cannot be very strong with only the support of a weak stem. Here the principles of mutual production and mutual conquest come into play. The xing to which the stems and branches belong are shown in Table 2.1. Combinations of two stems, combinations of a stem and a branch, while distinguishing between ordinals of the year, month, day and double-hour, and combinations of two and even three branches play a major role in many forms of sbushu. A typical example of a system employing a vast number of ordinal combinations, each with its own special term, is that of zeri flP 0 (day selection), a system that gives us a host of astrological terms in the Chinese almanac.11 One ancient method assigned two Yangs or two Yins to a stem and one Yang or one Yin each to a branch. Stem-branch combinations in Table 2.2 resulting in three Yangs were regarded as auspicious and three Yins being otherwise. Astrological terms arising from combinations between stems and branches of the year, the month, the day and the time were given names of auspicious spirits (sben ) or ominous spirits (sha M or ft). Some of these terms are common to the Liuren system as well as the two systems of fate-calculation, namely the Ziping method and the Ziwei doushu system of astrology referred to in Appendix II and Chapter 3 respectively.

Jiugong Jl'M magic square

The earliest known textual references on the magic square appeared in China in two different sources, one of which is a Confucian text and the other a mathematical writing. Recent archaeological excavations have recovered a divinatory board bearing the same magic square at Fuyang that dated back to Early Han, a couple of centuries earlier.12 In the Mingtang (Hall of Brightness) Chapter of Dai De's Mil Da Dai l.iji :*:tS?it£ (Record of Rites by the Elder Dai), a work dated approximately to the year ad 80, is an arrangement of the numbers 1 to 9 in sets of three as follows:13

The purpose of these numbers is not explained in the book, and has not been clearly understood. It is to be noted that these numbers were left out later by Dai Sheng JKlK in his abridgement of the l.iji (Record of Rites), perhaps because the ritual based on these numbers was no longer performed by then, or the numbers had already lost their significance and were no longer understood by the Later Han period. It is only known that the Mingtang consisted of nine halls at which the Zhou emperors performed their ceremonial rites.

These nine numbers, in sets of threes, also appeared in a commentary of a mathematical text, the Shushu jiyi SiilJfE.yt, said to be written in the year 190 bc by Xu Yue 14 Here the set of numbers is referred to as the 'jiugong AST (nine-palaces). Henceforth, until the twelfth century ad, the Chinese magic square of order 3 was known only as the nine-palaces (jiugong) or the nine-palaces diagram (jiugongtu A.HHI). The Sbushu jiyi also mentions an arrangement of numbers for calculation known as the 'nine-palaces calculation' (jiugongsuan fi'S'M-), but gives no details apart from indicating numbers that circulate round (within the nine-Palaces). This might also be a system of divination that used the jiugong magic fundamental principles square, remembering that the traditional Chinese concept of mathematics made no distinction between divination and what is now known to us as mathematics. Unfortunately, as suggested by the title of this book, the method of 'nine-palaces calculation' was apparently already forgotten by the time of Xu Yue.

Two important figures or diagrams had dominated Chinese thought since ancient times. These were the Hetu MB Diagram and the Luoshu Chart. There are different theories about their origins; the most popular ones say that the legendary emperor Fuxi obtained the Hetu Diagram from a dragon-horse at the Yellow River. The legend continues to relate that, during the eleventh century bc, Wenwang jtEE, father of the first Zhou emperor, received inspiration from this diagram and produced the eight Trigrams that he used in his method of divination.15 Then Yu H, who later became the first king of the Xia dynasty - a dynasty which modern archaeologists are still trying to confirm - observed at the Luoshui River a tortoise carrying the Luoshu Chart on its back. The Lunyu Uto (Confucian Analects) and the Yijing both mention the Hetu and the Luoshu. However, we have no evidence of the existence of any actual figures of the Hetu and Luoshu which would enable us to be certain that such a diagram or chart did exist at the time of Confucius. Considerable discussions took place in succeeding generations concerning the numbers in the Hetu and the Luoshu as well as their applications to astrology and divination. Then, in the tenth century, the famous Daoist Chen Tuan Sfll first pronounced that the jiugongtu was the Hetu Diagram. But his argument did not prevail for more than two centuries. During the twelfth century, Cai Yuanding HtuJS (1145-1198), a disciple of Zhu Xi fcM (1130-1220), identified the Hall of Brightness and the nine-palace arrangement as the Luoshu Chart. Cai Yuanding had already established himself as a great geomancer of his time and, with the support of his teacher's (i.e. Zhu Xi) fame as a neo-Confucian scholar, his theory was raised beyond challenge. Henceforth, scholars have talked about the Luoshu magic square as synonymous with the jiugong diagram. Regardless of the name it is known by, modern scholars consider it as the earliest magic square known to the ancient world.

The Luoshu Chart and the Hetu Diagram, as they were known since the twelfth century, are shown in Figures 2.2 and 2.3. Figure 2.2 is essentially the same as the series of numbers in the Mingtang, but Figure 2.3 does not qualify as a modern magic square, and has been put aside by modern scholars studying Chinese magic squares.16 This is rightly so if one takes the modern definition of magic squares. However, to the traditional Chinese mathematician, the two figures are of equal importance, both mystically and philosophically. Nevertheless, at this point we shall also leave the Hetu Diagram aside, since the three cosmic boards were mainly concerned with the jiugong or Luoshu magic square. In Figure 2.2 we can see that numbers are represented by little black and white circles, black circles for the odd or so-called heavenly or Yang numbers and white for the even or earthly

Figure 2.2 The Luosbu Chart, from Tushu bian, ch. 1; p.20a [Qinding siku qiiansbu edition],

Yin numbers. The numbers also represent the wuxing. These are shown in Table 2.7.

Table 2.7

Wuxing Heavenly numbers (Yangj Earthly numbers fYinj

Water 1 6

Fire 2 7

Wood 3 8

Metal 4 9

Neo-Confucian philosophers saw great significance in the position placement of the number '5' at the centre of the Luoshu Chart. To them, '5' is the most important 'heavenly number', manifesting itself in the wuxing, in

Figure 2.3 The Hetu Diagram, from Tushu bian, ch. 1, p.14a [Qinding siku quanshu edition].

the five virtues in ethics, in the five colours and the five tastes in human perceptions, in the five cereals that sustain human life, in the five human relationships that govern human behaviour, and so on. Beginning with the two numbers 1 and 6, which represent Water, and moving anticlockwise, we come across the two numbers 7 and 2, which represent Fire and are conquered by Water. Moving again anticlockwise, we find that Fire, represented by 7 and 2, conquers Metal, represented by the numbers 4 and 9. Then 4 and 9 conquer 3 and 8 which represent Wood. Wood then conquers Earth at the centre represented by the number 5. The number 5, representing Earth, then conquers tj^e numbers 1 and 6, representing Water again. Here, the Chinese found a powerful symbolism both to represent and to 'prove' the Principle of Mutual Conquest as applied to their wuxing theory.

One cannot fail to notice the role played by numerology in ancient China. Indeed, one can see that numerology had a more profound as well as a more lasting effect on Chinese thought than it had on the Pythagorean school in ancient Greece and in Western thought in general. The occurrence of certain numbers, e.^. 5, 9, 25, 49, 50 and 64, in Chinese magic squares is a case in point. In the jiugong magic square we have already come across the numbef 5. The number 9 is the supreme heavenly number, while the number 5 is the supreme earthly number.l/ In fact, the numbers 9 and 5 referred to the emperor, the one who occupied the most exalted position. The number 25 is the sum of all the heavenly and earthly numbers, from 1 to 9. Forty-nine stalks of milfoil used for divination in the Yijing system gave importance to the number 49. Also of significance are the numbers 50 of dayan ^ctff (Great Extension) and 64, which comes from the number of hexagrams in the Yijing. Numerology is intertwined with the principles of Yin and Yang and the wuxing to form a universal set of explanations which the Chinese, particularly the Song neo-Confucian philosophers, applied to natural phenomena, ethics, human relationships and, indeed, almost everything under the sun.

Magic in the magic square

As mentioned earlier in the previous chapter, J. G. Frazer, the Cambridge anthropologist of Golden Bough fame, had stated two general laws on magic.18 For the ancient magician there was a law of similarity, of like producing like, and there was one of contiguity or contagion, according to which things which have been in contact, but which are no longer, continue to act upon one another. The first law is eminently applicable to the jiugong magic square. Let us take the interesting example of a sequence of steps in Daoist liturgy known as the Yubu ^^ or bugang ¿^H, already in use by the shamans during the time of the Warring States, although the steps made then are not exactly known.19 There are several studies of the Daoist Bugang practices.20

The most important constellation in the heavens to the Daoist is the Plough (or Dipper). The stars in this constellation, known to the Chinese as Beidou have all along been worshipped with great reverence by the Daoist. In Chinese astronomy the Beidou consists of only seven stars, but to the Daoist there are nine stars, two of which are said to be invisible. According to an old Star Manual, Xingjing MM, Beidou originally consisted of nine stars but two of them had already gone out of sight. If the 'handle' of the Plough is extended downwards it would meet or get quite near to some stars in the constellation Bootes. Among them is y Bootis, which was the star Zhaoyao iSjiS to the ancient Chinese. This star played an important role in the ceremonies of the ancient Chinese. If one speculates that this was one of the nine stars seen in ancient China to belong to the Plough, then it had already left the circle of perpetual visibility around the year 1500 bc due to the precession of the equinoxes. This would also prove the antiquity of Chinese astronomy beyond the year 1500 bc. Perhaps we can find another explanation of the nine stars by taking a parallel in Greek

Figure 2.4a Yubu steps following the Plough [Zhengtong Daozang edition].

Figure 2.4a Yubu steps following the Plough [Zhengtong Daozang edition].

numerology. The Pythagorean Philolaus invented a 'counter earth' to make up ten heavenly bodies to match the perfect number 10. Could it be that the ancient Chinese also created two invisible stars of the Plough to make up their supreme heavenly number 9? Of course, neither of these two speculations can be taken as conclusive evidence.

In Daoist ceremonies the priest moves his feet following the pattern of the 'nine stars' of the Plough, as shown in Figure 2.4a. This is called Yubu or bugang. By tracing the pattern of the Plough, the performer of the rites tries to invoke the celestial power of the nine stars. This exemplifies like producing like, Frazer's first law in action. Now the Spirits of the nine stars of Beidou are also thought to reside within the jiugong nine-palaces. This gave rise to another, and perhaps more powerful, Yubu or bugang variation by using the jiugong, in which the practitioner steps from 1 to 2, then to 3, and so forth until he reaches the number 9, or conversely starting from 9, and moves successively to 8, 7, 6, 5, 4, 3, 2 and 1. An illustration from a Daoist text is given in Figure 2.4b. By imitating the pattern of the Beidou stars in the jiugong diagram, the Daoist thought that he could invoke not only spiritual power from the Plough, but also the force of nature embodied in the principles of Yin and Yang and the wuxing, represented in the Luosbu Chart.

The jiugong magic square has played an important role in Chinese astrology and divination. It was used in two of the three cosmic board systems, namely the system of Taiyi and that of Dunjia. The jiugong magic square

Figure 2.4b Yubu steps following the jiugong magic square [Zhengtong Daozang edition].

was also employed in the Astronomical Bureau for astrological purposes in the art of zeri (day selection). In all these techniques it is essential to understand the basic principle of movement within the nine palaces, known to the practitioners of the art as feigong fHH, literally 'flying across the palaces'. This could be either in a clockwise direction (sbunfei JUKI) or in an anticlockwise direction (nifei In the former, the number 1 is added to each of the nine cells, remembering that 9 becomes 1 when 1 is added to it. Repeating the process, the original jiugong diagram produces eight other diagrams, making a total of nine as shown in Figure 2.5. The same diagrams can also be produced in a different sequence by subtracting 1 from each of the nine cells in the jiugong magic square, remembering that subtracting 1 from cell One makes cell Nine. The movement is in an anticlockwise direction. Colours are assigned to the nine numbers in the cells, namely: 1 = white, 2 = black, 3 = blue-green, 4 = green, 5 = yellow, 6 = white, 7 = red, 8 = white, 9 = purple.21 The jiugong diagram with its colours, aptly referred to in Smith (1991) as a colour-coded diagram, is shown in Figure 2.6.

The nine diagrams in Figure 2.5 are named according to the number and colour of their central cells. Thus the jiugong magic square is simply called '5 yellow' and the other eight diagrams in a clockwise direction are called '6 white', '7 red', '8 white', '9 purple', '1 white', '2 black', '3 blue-green', and '4 green' respectively. This is the Chinese astrologer's system of zibet,I

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