Discourse on the Luo Writing: Prefatory Note

元吳澄撰。錄自易原第十一。

This piece was written by Wu Cheng of the Yuan dynasty, excerpted from the eleventh chapter, “Origins of the Changes,” of his book Outer Wings of Collected Remarks on the Changes.

洛書者，大禹治水之時，洛有神龜出，而龜甲之坼文有此數也。其數後一前九，左三右七，右前二，左前四，右後六，左後八，中五。四方四隅中央，其位有九。禹平日默計天道人事之大要，其類有九，見洛書之數而有契焉，於是以天道人事分為九類，品其緩急先後之次，以配龜甲一二三四五六七八九之文，是為洪範九疇。所謂大禹因洛書而敘九疇者，此也。以背甲之坼文如書字者之橫畫，故名之曰書。

The so-called “Luo Writing” (Luoshu, 洛書) appeared when the Great Yu was regulating the waters: a numinous tortoise emerged from the Luo River, and the crack-lines on its shell displayed this set of numbers. The numbers are: one at the rear of the tortoise’s body, nine at the front, three on the left, seven on the right; two at the front right, four at the front left, six at the rear right, eight at the rear left, and five at the exact center. The four cardinal directions, the four corners, and the center make nine positions in all. In ordinary days the Great Yu silently pondered the main heads of the Way of Heaven and of human affairs, and they likewise fell into nine categories. When he saw the nine numbers of the Luo Writing, they tallied with what was in his mind; thereupon he divided the Way of Heaven and human affairs into nine classes, weighed the order of their urgency and sequence, and matched them one by one to the crack-lines of one through nine on the tortoise shell. This is the “Nine Divisions” (jiu chou, 九疇) recorded in the Great Plan of the Book of Documents. When the ancients said “the Great Yu arranged the Nine Divisions on the basis of the Luo Writing,” this is what they meant. And because the crack-lines on the tortoise’s back resemble the horizontal strokes used in writing characters, they named it a “writing.”

周書洪範曰：天乃錫禹洪範九疇，初一，次二，次三，次四，次五，次六，次七，次八，次九。此箕子以洛書之數而言也。

The Great Plan in the Zhou Documents of the Book of Documents records: Heaven then bestowed upon the Great Yu the Nine Divisions of the Great Plan, in the order first one, then two, then three, then four, then five, then six, then seven, then eight, then nine. This is how Jizi, when setting forth the great laws of government to King Wu of Zhou, arranged them according to the nine numbers of the Luo Writing.

莊子外篇曰：天有六極五常，帝王順之則治，逆之則凶。九洛之事，治成德備。葢言禹因洛書敘九疇，終於六極，始於五行，五常即五行也。九洛者，謂九疇因洛書之九數也。治成德備者，謂九疇所該，載於國家之治無不完成，人身之德無不具備也。

The Outer Chapters of the Zhuangzi, “The Turning of Heaven,” say: Heaven has the “Six Extremes” and the “Five Constants”; if the emperor and king follow them, the realm is well governed; if they go against them, misfortune is invited. Once the affairs of the Nine Luo are put into practice, the Way of government is accomplished and virtue is complete. Zhuangzi’s words here refer precisely to the Great Yu’s arranging the Nine Divisions according to the Luo Writing: the last division concludes with the “Six Extremes,” the first division begins with the “Five Phases,” and what he calls the “Five Constants” is also the “Five Phases.” “Nine Luo” means that the Nine Divisions take their model from the nine numbers of the Luo Writing; “government accomplished and virtue complete” means that the principles encompassed by the Nine Divisions, when applied to the government of the state, leave nothing wanting, and when applied to the cultivation of personal virtue, leave nothing lacking.

大載禮記明堂篇曰：二九四，七五三，六一八。注云：九室法龜文，故取此數。按：載記明堂篇，秦以前之書也。隋經籍志以為安南太守劉熙注，注之人在鄭玄、王肅、郭象之後。自秦亡漢興以來，河洛圖書不傳於世，人所罕見，而注云法龜文，其言葢有所傳受也。

The Bright Hall chapter of the Elder Dai’s Record of Rites lists the numbers of the nine chambers of the Bright Hall: two, nine, four; seven, five, three; six, one, eight. The old commentary says: the nine chambers of the Bright Hall take their model from the crack-lines of the tortoise shell, and therefore adopt this set of numbers. Wu Cheng’s note: the Bright Hall chapter of the Elder Dai’s Record of Rites is an old text from before the Qin; the Bibliographic Treatise of the Sui History takes the commentary to be by Liu Xi, Grand Administrator of Annan, and Liu Xi’s date is after Zheng Xuan, Wang Su, and Guo Xiang. Since the fall of Qin and the rise of Han, the River Chart and Luo Writing had long been lost, and people of the world rarely saw them; yet Liu Xi in his commentary directly says the nine chambers take their model from the tortoise’s markings. This shows that the saying must have a lineage of transmission, handed down from former generations.

漢許慎說文解字一二三□□□□□□。昔黃帝之史蒼頡制字，文始於數，一二三□皆積其畫之數而為文，至□則變其文，然中央交處、四隅盡處，其數亦五也。六七八九之字乃秦李斯小篆，義莫可通，今不復得見古文之為何如。

Xu Shen of the Han, in Explaining Graphs and Analyzing Characters, collected the ancient-script forms of one, two, three, and the six number-characters that follow (the original book gave the ancient graphs; they are missing in the present recension, and are here replaced by boxes). Formerly Cangjie, the historiographer of the Yellow Emperor, created characters, and the graphs began from numbers: the ancient forms of “one,” “two,” “three,” through “four” were all made by stacking strokes according to the number; only at the ancient form of “five” did the writing change, taking a crossed shape, yet the single point of intersection at the center plus the four ends of the strokes at the four corners still count as five. As for the four characters “six,” “seven,” “eight,” and “nine,” what is seen today is only the small seal script fixed by Li Si of Qin; their meaning can no longer be explained, and the original appearance of the ancient script can no longer be seen.

龜書之文，一為一，二為二，□為三，□為四，□為五，□為六，□為七，□為八，□為九，並如倉頡一二三□之積畫，五六文亦同。

The markings of the Luo Writing on the tortoise shell are likewise thus: one stroke stands for one, two strokes for two, and thereafter boxed shapes stand in turn for three, four, five, six, seven, eight, and nine (the original book here used diagrams, now missing). These are all consistent with the method by which Cangjie accumulated strokes when creating “one,” “two,” “three,” and the boxed form; the writing of the two characters “five” and “six” is also the same.

邵子曰：圓為星也，曆紀之數其肇於此乎？方者土也，畫州井地之法其放於此乎？葢圓者河圖之數，方者洛書之文，故羲文因之而造易，禹箕敘之而作範也。

Shao Yong said: the round symbolizes the stars in Heaven; do not the various numbers of the calendar and its records perhaps take their beginning from this? The square symbolizes the soil of the earth; do not the methods of dividing the provinces and laying out well-fields perhaps take their model from this? In general, what is round is the numbers of the River Chart; what is square is the markings of the Luo Writing. Therefore Fuxi and King Wen followed the River Chart in making the Zhouyi, and the Great Yu and Jizi followed the Luo Writing in making the Great Plan.

員者星也，曆紀之數其肇於此乎，何謂也？曰：天之星有五宮，東宮蒼龍，北宮玄武，西宮白虎，南宮朱鳥，中宮紫薇垣是也。五者有中央四邊而無四角，無四角故員。

“The round symbolizes the stars; the numbers of the calendar and its records take their beginning from this”—how is this to be understood? Answer: the constellations of Heaven are divided into five palaces, namely the Eastern Palace of the Azure Dragon, the Northern Palace of the Dark Warrior, the Western Palace of the White Tiger, the Southern Palace of the Vermilion Bird, and the Central Palace of the Purple Tenuity Enclosure (the original text’s “ziwei yuan” with the hibiscus graph is the Purple Tenuity Enclosure). These five palaces have only a center and four sides, and have no four corners; precisely because they have no four corners, their shape is round.

曆紀之數皆以五起，五者五行之一周也。五日為一候，二其五者十干之一周也，十日為一旬；三其五為一氣，六其五為一月，九其五為一節，十二其五者干支相乘之一周也，十八其五為一時，七十二其五為一歲。每歲木火土金水各王七十二日，是為五辰。凡此曆紀之數，皆起於天星五宮之五，故曰其肇於此乎。

All the various numbers of the calendar and its records are counted from “five”: five is one circuit of the Five Phases. Five days make one hou (候); two fives are ten days, one circuit of the ten Heavenly Stems, called a xun (旬); three fives make one qi (氣, a solar-term unit); six fives make one month; nine fives make one jie (節); twelve fives make sixty days, one circuit of the pairing of the Heavenly Stems and Earthly Branches; eighteen fives make one shi (時), that is, one season; seventy-two fives make three hundred sixty days, one year. Each year Wood, Fire, Earth, Metal, and Water each preside in prosperity for seventy-two days, together called the “Five Chen.” All these numbers of the calendar take their rise, without exception, from the “five” of Heaven’s five palaces; therefore Shao Yong said, “Do not the numbers of the calendar and its records take their beginning from this?”

方者土也，畫州井地之法其放於此乎，何謂也？曰：地之土有九曲，正東、正南、正西、正北、西北、東北、東南、西南及中區是也。九者有中央四邊而又有四角，有四角故方。

“The square symbolizes soil; the methods of drawing provinces and well-fields take their model from this”—how is this to be understood? Answer: the soil of the earth is divided into nine regions, namely due east, due south, due west, due north, northwest, northeast, southeast, southwest, plus the central region. These nine have both a center and four sides, and moreover have four extra corners; precisely because they have four corners, their shape is square.

畫州井地之法皆分為九：以中國方三千里分為九州島，此畫州之九也；以農田九百畝之地溝之作井字分為九夫，此井地之九也。凡此所畫所井之法，皆放效地域九區之九，故曰其放於此乎。

The methods of drawing provinces and well-fields are both divided into nine parts: the territory of the Central States, three thousand li square, is divided into the Nine Provinces (the original text’s “Nine Provinces islands” is an error for “Nine Provinces”), and this is the “nine” of drawing provinces; nine hundred mu of farmland are ditched in the shape of the character “well” and allotted to nine men to till, and this is the “nine” of well-fields. All these methods of drawing provinces and well-fields, without exception, imitate the “nine” of the earth’s nine regions; therefore Shao Yong said, “Do not the methods of drawing provinces and well-fields take their model from this?”

圓者河圖之數，方者洛書之文，何謂也？曰：河圖洛書者，天地所呈自然之端。河圖之數亦是五位，合於天星五宮之圖：一六居北者，玄武之星也；二七居南者，朱鳥之星也；三八居東者，蒼龍之星也；田九居西者，白虎之星也；五十居中者，紫薇垣之星也。

“What is round is the numbers of the River Chart; what is square is the markings of the Luo Writing”—how is this to be understood? Answer: the River Chart and the Luo Writing are the natural hints presented by Heaven and Earth. The numbers of the River Chart happen to be arranged in five positions, matching the distribution of Heaven’s five palaces: one and six occupy the north, corresponding to the stars of the Dark Warrior; two and seven occupy the south, corresponding to the stars of the Vermilion Bird; three and eight occupy the east, corresponding to the stars of the Azure Dragon; four and nine occupy the west, corresponding to the stars of the White Tiger (the original text has “field nine”; “field” is a corruption of “four”); five and ten occupy the center, corresponding to the stars of the Purple Tenuity Enclosure.

洛書之文亦是九位，合於地土九區之方：前載九者，正南之土也；後履一者，正北之土也；左身三者，正東之土也；右身七者，正西之土也；右肩二者，西南之土也；左肩四者，東南之土也；右足六者，西北之土也；左足八者，東北之土也；中脊五者，中區之土也。

The markings of the Luo Writing also happen to be arranged in nine positions, matching the square distribution of the earth’s nine regions: the nine worn at the front of the tortoise’s body is the soil of due south; the one trodden at the rear of the tortoise’s body is the soil of due north; the three at the left flank is the soil of due east; the seven at the right flank is the soil of due west; the two at the right shoulder is the soil of the southwest; the four at the left shoulder is the soil of the southeast; the six at the right foot is the soil of the northwest; the eight at the left foot is the soil of the northeast; the five at the middle of the spine is the soil of the central region. This is precisely the image of the tortoise’s back of which the ancients said, “Wearing nine and treading one, three on the left and seven on the right, two and four as the shoulders, six and eight as the feet, five occupying the center.”

羲文因之而造易，禹積敘之而作範，何謂也？曰：河圖之位五，每位各有一奇一耦，數雖十而位止五，故羲皇則其奇偶之數，畫奇偶之畫：一其奇耦而為初畫，倍而二之則為二畫，又倍而四之則為三畫，又倍而八之則為四畫，又倍而十六之則為五畫，又倍而三十二之則為六畫，而卦成矣。此則其一奇一偶之數者然也。

“Fuxi and King Wen made the Zhouyi on the basis of the River Chart; the Great Yu and Jizi made the Great Plan on the basis of the Luo Writing” (the original text’s “Yu Ji” as “Yu accumulated” should be “Yu and Ji”)—how is this to be understood? Answer: the River Chart has only five positions, and each position contains one odd number and one even number; though the numbers are ten, the positions are only five. Therefore Fuxi took as his model its numbers of one odd and one even, and drew the two kinds of line, odd and even: taking one of each, odd and even, he made the first drawing, which is the Two Modes; doubling them to two makes the second drawing, which is the Four Images; doubling again to four makes the third drawing, which is the Eight Trigrams; doubling again to eight makes the fourth drawing; doubling again to sixteen makes the fifth drawing; doubling again to thirty-two makes the sixth drawing; when the six drawings are complete, the sixty-four hexagrams are accomplished. This is the result obtained by taking as model the River Chart’s numbers of one odd and one even.

初三四上象東南西北，二五象中央，此則其中央四旁之位者然也。東西南北各一而中有二者，旁位之奇偶合，中位之奇偶分，象北極見、南極不見而皆為中宮之星也。

Among the six lines of a hexagram, the first, third, fourth, and top lines symbolize east, south, west, and north respectively; the second and fifth lines symbolize the center. This is the result obtained by taking as model the River Chart’s five positions of center and four sides. East, west, south, and north each occupy only one line, while the center occupies the two lines of the second and the fifth, because at the side positions the odd and even are joined in one place, while at the center the odd and even occupy two places separately; just as the north celestial pole is always visible and the south celestial pole cannot be seen, yet both belong to the stars of the Central Palace.

洛書之位九，每位或一奇或一偶，數有九而位亦九，故大禹則其一二三四五六七八九之位數，而定五行、五事、八政、五紀、皇極、三德、稽疑、庶徵、五福六極之次第也。造易者羲而並言文，作範者禹而並言箕，文之易即羲之易，箕之範即禹之範也。

The Luo Writing has nine positions; each position has either one odd number or one even number; the numbers are nine and the positions are also nine. Therefore the Great Yu took as his model its positional numbers from one to nine, and thereby arranged the sequence of the Nine Divisions: one, the Five Phases; two, the Five Affairs; three, the Eight Policies; four, the Five Regulations of Time; five, the Royal Ultimate; six, the Three Virtues; seven, Examining Doubts; eight, the Various Verifications; nine, the Five Blessings and the Six Extremes. As for the fact that it was Fuxi who made the Changes yet King Wen is mentioned along with him, and it was the Great Yu who made the Great Plan yet Jizi is mentioned along with him: that is because the Changes that King Wen elaborated are the Changes of Fuxi, and the Plan that Jizi set forth is the Plan of the Great Yu; they succeed one another, and are originally one affair.