Resources / Taoist cosmology
He Tu and Luo Shu
Two figures of the numbers, the River Diagram of one to ten and the Luo Writing of one to nine. Choose a number to see where it stands in each, and trace the lines of the Luo Shu that all sum to fifteen.
Both are drawn as the Song diagrams draw them, south at the top, odd numbers as white dots and even as black, with the names Zhu Xi fixed. The phases and trigrams laid over them are later correlations, shown when asked for.
The number chosen · odd, yang, a white dot
Five
He Tu: the centre, Earth · Luo Shu: the central palace
5五
South at the top, east on the left · odd numbers white, even numbers black
Side by side
What changes between the two
- Numbers
- He TuOne to ten
- Luo ShuOne to nine
- Total
- He Tu55: odd 25, even 30
- Luo Shu45
- Centre
- He Tu5, with 10 in two rows above and below it
- Luo Shu5 alone
- Arrangement
- He TuFour pairs round a centre, each number inside the one five greater
- Luo ShuA square of three by three, every line summing to 15
- Odd (white) numbers
- He Tu1 and 3 inside, 5 at the centre, 7 and 9 outside
- Luo ShuOn the four sides and at the centre
- Even (black) numbers
- He Tu2 and 4 inside, 6 and 8 outside, 10 at the centre
- Luo ShuAt the four corners
- South
- He Tu2 and 7, Fire
- Luo Shu9, Fire
- West
- He Tu4 and 9, Metal
- Luo Shu7, Metal
- Trigrams laid over it
- He TuNone in the figure itself
- Luo ShuThe Later Heaven eight, one to a palace
The tradition
The River Diagram (He Tu) and the Luo Writing (Luo Shu) begin as names without pictures. The Xici says that the River brought forth a diagram and the Luo a writing, and the sages took them as their models; in the Analects Confucius laments that the River gives forth no diagram. A three-by-three square of the numbers one to nine, every line summing to fifteen, appears in the Han in the Bright Hall (Mingtang) chapter of the Da Dai Liji, and its nine palaces run through Han cosmology and divination.
The dotted diagrams known today are Song. Liu Mu, in the eleventh century, published both, but called the nine-number square the River Diagram and the ten-number figure the Luo Writing. Zhu Xi and Cai Yuanding reversed the names in the Yixue qimeng (1186) and printed the diagrams at the head of Zhu Xi's Zhouyi benyi; their naming is followed almost everywhere since, and here.
Reading the instrument
- Odd numbers are yang and even numbers yin, as the Song diagrams draw them, white dots and black. On this dark ground the white dots are ivory discs and the black ones gold rings.
- South is at the top by default, so east lies on the left. The He Tu pairs each generating number, one to five, with its completing number, six to ten: one and six in the north, two and seven in the south, three and eight in the east, four and nine in the west, five and ten at the centre.
- The Luo Shu wears nine on its head and treads on one, three on the left and seven on the right, two and four for shoulders and six and eight for feet, as the old formula has it, with five at the centre. Every row, column and diagonal sums to fifteen; choose a line to see it summed.
- Choose a number in either diagram to see where it stands in both: its pair, phase and direction in the He Tu, its palace, trigram and lines in the Luo Shu. A number often stands differently in the two, which is what comparing them shows.
- The odd (heavenly) numbers of the He Tu sum to 25 and the even (earthly) to 30, together 55, the number of Heaven and Earth in the Xici. The Luo Shu's nine sum to 45.
Where it descends from
- Xici zhuan (Great Commentary)
- The River's diagram and the Luo's writing (part A, chapter 11); the numbers of Heaven and Earth, twenty-five and thirty, fifty-five in all (part A, chapter 9).
- Analects
- Confucius on the phoenix that does not come and the River that gives forth no diagram (book 9).
- Da Dai Liji, Mingtang (the Bright Hall)
- A Han ritual compilation whose Bright Hall chapter numbers its nine rooms as the square.
- Liu Mu, Yishu gouyin tu
- The eleventh-century diagrams that first drew both figures in dots, with the names the other way round.
- Zhu Xi and Cai Yuanding, Yixue qimeng (1186)
- Fixed the names in use today and set out the numerology of both diagrams.
What this does not claim
The diagrams are received figures, and their origin stories, a dragon-horse rising from the Yellow River and a turtle from the Luo, are legend: the dotted drawings are not known before the Song. The phase and trigram overlays are the correlations later tradition laid over the numbers; the trigrams on the Luo Shu follow the Later Heaven arrangement, and the centre has none. The sums are arithmetic and are shown, not asserted.
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