TL;DR: The nine palaces is the name for the nine cells of the Luo Shu diagram, a 3x3 square matrix containing the numbers from 1 to 9 such that the three rows, three columns and two diagonals all total 15. In the Eastern divination tradition, the Luo Shu is regarded as a spatial frame of reference by which arts such as Kỳ Môn Độn Giáp (Qimen Dunjia) and Huyền Không Phi Tinh (Flying Star feng shui) place stars and stems in each palace. This is a convention of the discipline, not a table of predictions that has been scientifically verified.
What Is Cửu Cung and Where Does It Come From?
Cửu cung is the nine squares of the Lạc Thư diagram, arranged as a three by three square, each square carrying a number from 1 to 9. The distinctive feature of this arrangement is that the numbers in every horizontal row, every vertical column, and both diagonals all sum to 15. In the Eastern divination tradition, Lạc Thư is treated as the spatial reference map, while Hà Đồ is the reference map of time and the five elements, and these two diagrams are the foundation of many ancient disciplines such as phong thủy and Kỳ Môn.
Legend tells that King Vũ of the Hạ dynasty, while controlling the waters, saw a divine turtle rise from the Lạc River, its shell bearing black and white dots arranged in nine groups, and from this later generations systematized the Lạc Thư as we know it. The name also comes from there: "Lạc" is the name of the river, "Thư" refers to writing, to the patterns on the turtle's shell.
The date and true author of the Lạc Thư remain undetermined. Its nine numbers appear early in the Minh đường chapter of the Đại Đái Lễ ký (大戴禮記), written "二九四七五三六一八", that is the three rows 4 9 2, 3 5 7, 8 1 6 read from right to left, with a commentary saying the nine rooms of the Minh đường hall follow the pattern on the turtle's shell[2]. The story of the divine turtle of the Lạc River should therefore be treated as legend, not as proven historical fact.
Why Is Lạc Thư Called a Magic Square?
The structure of Lạc Thư can be pictured through the familiar mnemonic, found in the commentary to the Số thuật ký di (數術記遺: 二四為肩，六八為足，左三右七，戴九履一，五居中央)[3] and usually recited as: "Nine on the head, one underfoot; left three, right seven; two and four as shoulders; six and eight as feet; five at the center." This memory aid yields the number table below, with the number 5 in the central palace and the other eight numbers surrounding it according to the eight directions.
| Palace | Direction | Number | Element |
|---|---|---|---|
| Tốn | Southeast | 4 | Wood |
| Ly | South | 9 | Fire |
| Khôn | Southwest | 2 | Earth |
| Chấn | East | 3 | Wood |
| Trung | Center | 5 | Earth |
| Đoài | West | 7 | Metal |
| Cấn | Northeast | 8 | Earth |
| Khảm | North | 1 | Water |
| Càn | Northwest | 6 | Metal |
Checking again: the top row 4 + 9 + 2 = 15, the middle row 3 + 5 + 7 = 15, the bottom row 8 + 1 + 6 = 15, and the columns and both diagonals also equal 15. The number 5 at the center carries the Earth element and is regarded as the place where all things converge and are harmonized; the other eight numbers, each corresponding to a direction and an element, form a closed system that mimics the operation of heaven, earth, and all things.
The book Địa lý Nguyên Không Pháp Giám (printed in the 19th year of Đạo Quang, presented as the teaching of Liên Trì tiên sinh) emphasizes the role of the central palace, number 5: "5 is the number of earth. Metal, wood, water, and fire all depend on earth. Without 5, the Hà Lạc numbers cannot be formed." In this understanding, all effects of geography start from the central palace number 5, and if a student does not grasp this point, the eight trigrams and nine stars will be used incorrectly, leading to "a hair's breadth error, a thousand-mile deviation, endless disaster."
Which Divination Arts Use Cửu Cung?
In phong thủy, Huyền Không Học takes as its core the movement of the Cửu Tinh, the nine stars, traveling across the Lạc Thư diagram. This path is called Lường Thiên Xích: a star enters the Trung Cung first, then passes in turn through Càn, Đoài, Cấn, Ly, Khảm, Khôn, Chấn, Tốn, that is in the order of the Lạc Thư numbers 5, 6, 7, 8, 9, 1, 2, 3, 4. Flying forward, the numbers increase palace by palace: if 5 enters the Trung Cung, the next eight palaces receive 6, 7, 8, 9, 1, 2, 3, 4. Flying in reverse, the numbers decrease: 5 enters the Trung Cung and the next eight palaces receive 4, 3, 2, 1, 9, 8, 7, 6.
In Kỳ Môn Độn Giáp, the nine palaces are precisely the spatial frame for arranging the six Nghi and three Kỳ. The six Nghi (Mậu, Kỷ, Canh, Tân, Nhâm, Quý) and three Kỳ (Ất, Bính, Đinh) are set into the nine palaces by the Lạc Thư numbers, starting from the palace that carries the number of the cục. For example, in dương độn cục 9 the six Nghi run forward from palace 9 and the three Kỳ follow in the order Đinh, Bính, Ất: Mậu 9, Kỷ 1, Canh 2, Tân 3, Nhâm 4, Quý 5, Đinh 6, Bính 7, Ất 8.
How Do Cửu Cung and Bát Quái Differ?
An easily confused point is to think that cửu cung and Bát Quái are one and the same. In fact Lạc Thư has nine squares, of which the eight outer squares are linked to the eight trigrams according to Hậu Thiên Bát Quái, while the middle square is the central palace belonging to no trigram. The book Địa lý Nguyên Không Pháp Giám states clearly: "The 9 palaces come from Lạc Thư, the 9 stars emerge from the Bắc Đẩu. Take the 9 stars and arrange them in the 9 palaces, and the principle and energy act as if divine." Thus cửu cung is the nine-square spatial frame, Bát Quái is the eight trigrams attached to the eight outer squares, and Cửu Tinh is the nine stars placed in those nine squares.
Why Does the Same Diagram Get Used Differently by Each Art?
The answer lies in each art selecting a different layer of information from the same nine-square frame. Huyền Không Phi Tinh is concerned with the flight of the Cửu Tinh over time, so its focus is the forward and reverse Lường Thiên Xích and the star plates. Kỳ Môn Độn Giáp is concerned with the positions of the six Nghi, three Kỳ, and nine accompanying stars for each hour, so its focus is the number of the cục, how the Nghi and Kỳ are set into the nine palaces, and how to find Trực Phù and Trực Sử. The same Lạc Thư diagram, yet each art draws its own system of rules, and these systems do not replace one another.
Points to Keep in Mind When Studying Cửu Cung
First, cửu cung is a numerical structure and convention, not a verified energy map. The divination arts use it as a language to describe correlations, and the value of that language lies in the internal consistency of each system, not in the ability to predict specific events.
Second, when reading materials on cửu cung, one must clearly distinguish what is a description of the diagram's structure, what is an interpretation of a school, and what is legend about its origin. These three layers of information are often mixed together in popular books, making it easy for readers to mistake convention for fact.
Gợi ý của Nhật Nguyệt: if you are just starting to learn, begin by memorizing the Lạc Thư number table and the mnemonic "Nine on the head, one underfoot; left three, right seven; two and four as shoulders; six and eight as feet; five at the center." Once you know the table, reading the rules for placing stars, flying stars, or arranging Nghi and Kỳ will be much easier to follow, because every art revolves around those nine squares.
