Lo Shu

In Chinese: 洛書洛书 luòshū

The magic square of three, 4 9 2, 3 5 7, 8 1 6, every line making fifteen: the map of the nine palaces on which Feng Shui’s numbers and stars move.

Meaning

The Lo Shu, the “Writing from the Luo river”, is a square of nine cells holding the numbers 1 to 9 so that every row, every column and both diagonals add up to fifteen: 4 9 2 across the top, 3 5 7 through the middle, 8 1 6 along the bottom. The 5 stands in the centre; the odd numbers, yang, hold the four cardinal points, the even ones, yin, the four corners; and any two numbers facing each other across the centre make ten.

Legend tells that Yu the Great, while taming the floods, saw a turtle rise from the Luo river with this pattern of dots on its shell, and took it as a model for setting the world in order. Its companion, the River Chart (He Tu), came out of the Yellow River on the back of a dragon-horse. Chinese diagrams put south at the top, so the square is also a compass: 9 in the south, 1 in the north, 3 in the east, 7 in the west, and the four even numbers in the corners between them.

That compass is the map of the nine palaces, the eight directions and the centre, and Feng Shui reads almost everything through it. Each number has its home palace and its trigram in the Later Heaven arrangement, 1 Kan in the north, 9 Li in the south, and so round, while the 5, at the centre, has none.

In practice

The Kua number: a person’s Kua is one of the Lo Shu’s numbers, and its trigram and direction come from the number’s palace; a Kua of 5, with no trigram, becomes 2 or 8, as most schools do.
The Flying Stars: the nine stars are the Lo Shu’s nine numbers, and they fly along the square’s own path, from the centre to the north-west, west, north-east, south, north, south-west, east and south-east, the order in which 5, 6, 7, 8, 9, 1, 2, 3 and 4 sit in it.
Periods, years and months: the periods of twenty years are numbered by it, the ninth from 2024 to 2043; the year’s star in the centre is the 1 in 2026 and one less each year after, and each month has its own.
In numerology the birth grid can be laid out on the same square, so that a birth date’s digits fall in the Lo Shu’s cells.

Across traditions

In Renaissance Europe Heinrich Cornelius Agrippa gave the same square to Saturn, the first of seven planetary squares in his De occulta philosophia of 1533; Western magic and later numerology inherited it from him.
In the Islamic world the square was known by the letters of its even corners, budūḥ, and written on charms and in books of letters and numbers for centuries.
In India Narayana Pandita’s Ganita Kaumudi of 1356 set out methods for building magic squares of every size, of which the square of three is the smallest.

Origin and history

The name is older than the square. The Great Commentary of the Book of Changes says that “the River gave forth the Chart, the Luo gave forth the Writing”, and the sages took them as models, without saying what either looked like. The arrangement itself appears in the Mingtang chapter of the Da Dai Liji, in the 1st century, as the order of the nine halls of the Hall of Light: two, nine, four; seven, five, three; six, one, eight. A diviner’s board found at Shuanggudui, in a tomb closed in 165 BC, already sets out the nine palaces in the same order.

The square and the name met in the Song dynasty. In the 11th century Liu Mu called the nine-number square the River Chart; in the 12th, Zhu Xi and Cai Yuanding, in their Yixue Qimeng, called it the Lo Shu, and their naming stayed. Feng Shui’s compass schools built their nine palaces, their periods and their flying stars on it, and Schuyler Cammann’s study of 1961 traced its long life in Chinese thought and ritual.

How Ulune calculates it

Ulune keeps the Lo Shu as the map of its Feng Shui. The Kua is reduced to one of its numbers, whose palace gives its trigram and from which its Eight Mansions follow; the period chart, the mountain and water stars, and the stars of the year and the month all fly along the square’s path, a number forward or backward at each step. The period counts twenty years at a time from Period 1 in 1864, and the year’s star from the 1 in 2026, one less each year at Lichun.

Correspondences

Number	Palace	Trigram	Phase	Star
1	North	Kan ☵	Water	1 White
2	South-west	Kun ☷	Earth	2 Black
3	East	Zhen ☳	Wood	3 Jade
4	South-east	Xun ☴	Wood	4 Green
5	Centre	None	Earth	5 Yellow
6	North-west	Qian ☰	Metal	6 White
7	West	Dui ☱	Metal	7 Red
8	North-east	Gen ☶	Earth	8 White
9	South	Li ☲	Fire	9 Purple

TrigramsThe eight figures of three lines, whole or broken, from which the Book of Changes builds its hexagrams and Feng Shui its eight directions.
Flying StarsThe school of Feng Shui that reads a home through time: nine stars, the numbers of the Lo Shu, flying through nine palaces from its period and facing.
Kua numberA person’s number in Feng Shui, one of the eight trigrams, from the solar year of birth and the yin or yang count: the key to their eight directions.
Nine periodsThe Flying Stars’ clock: nine periods of twenty years in a cycle of 180, each ruled by a star; the present is Period 9, from Lichun 2024 to Lichun 2044.
Annual starsThe year’s own flying stars: one number in the centre for each solar year, one less each year, laid over every home’s chart and every person’s directions.
Birth gridThe digits of the birth date in a 3 × 3 square, zeros aside, read for full and empty lines in Phillips’s layout or in the Lo Shu square.

Sources

Book of Changes (Yijing), “Great Commentary” (Xici), Warring States period
Da Dai Liji (Record of Rites by the Elder Dai), Mingtang chapter, 1st century
Zhu Xi and Cai Yuanding, Yixue Qimeng, 12th century
Heinrich Cornelius Agrippa, De occulta philosophia, 1533
Schuyler Cammann, The Magic Square of Three in Old Chinese Philosophy and Religion, 1961