Hetu and Luoshu in Yi Numerology — Origin, and Their Full Correspondence with the Trigrams and Five Phases • TIMEACTOR

Hetu and Luoshu in Yi Numerology — The Source of the Number World

Hetu and Luoshu — Two Diagrams Hold Up the Foundation of Yi Numerology

The Hetu and Luoshu are the two most mysterious diagrams in Chinese Yi study. What do they look like? The Hetu sets the numbers one through ten into a cross — one and six below, two and seven above, three and eight at the left, four and nine at the right, five and ten in the center. The Luoshu sets the numbers one through nine into a nine-palace grid — nine on top, one below, three at the left, seven at the right, two and four for the shoulders, six and eight for the feet, five in the center. Both diagrams match the trigrams, the five phases, the directions, and the solar terms; they are the shared source of many branches of Yi study. Where do they come from? The Xici Shang Commentary says: the Yellow River gave forth the diagram; the Luo River gave forth the writing; the sage took them as a model. Legend says that in Fu Xi's time a dragon-horse rose from the Yellow River with the Hetu on its back; in Yu the Great's time a divine turtle rose from the Luo River with the Luoshu on its back. The sage drew the trigrams by following these two diagrams. Whether the legend is true is hard to say, but the place of the Hetu and Luoshu in Yi numerology is real. Understand them and you touch the source of the I Ching's number world.

The Hetu = generating and completing numbers paired with the five phases and five directions; it tells how Heaven and Earth give birth to all things. The Luoshu = nine-palace numbers paired with the Later Heaven trigrams; it tells how the directions turn. The two are not the same thing: the Hetu is ten numbers, the Luoshu nine; the Hetu pairs with the five phases, the Luoshu with the nine palaces. Mix these two up and every later correspondence falls apart.

The Origin of the Hetu and Luoshu — From the Book of Documents to the Xici Commentary

The earliest shadow of the Hetu and Luoshu appears in the 'Guming' chapter of the Book of Documents. That chapter describes the ceremonial display at the death of King Cheng of Zhou; among the jade treasures and vessels it lists the Hetu, set out as a treasure in the eastern corridor. This is the earliest appearance of the words 'Hetu' in literature, but nobody then says what it looked like. The Xici Shang Commentary goes a step further: 'The Yellow River gave forth the diagram; the Luo River gave forth the writing; the sage took them as a model.' The Hetu and Luoshu are said to be the basis on which the sage drew the trigrams. Later, Han-dynasty scholars began to give them concrete numbers and directions, and the diagrams slowly settled. Full pictorialization and systematization had to wait for the Song dynasty. So the concept of the Hetu and Luoshu grew out of literature step by step: first a name, then a legendary origin, and only at the end an exact diagram and set of numbers. As you read, keep the legendary Hetu and Luoshu apart from the diagrams fixed in the Song dynasty.

The Hetu's Number Structure — One of Heaven, Two of Earth, the Generating and Completing Numbers

The Hetu's numbers run from one to ten. It pairs generating numbers with completing numbers: one through five are generating, six through ten are completing; one pairs with six, two with seven, three with eight, four with nine, five with ten. Once paired, they are laid out by direction: one and six in the north, the five phase water; two and seven in the south, fire; three and eight in the east, wood; four and nine in the west, metal; five and ten in the center, earth. This is the source of the saying 'Heaven generates water with one; Earth completes it with six.' The point inside: a generating number is a beginning, a completing number a finish. Water grows from one (the start of generation) to six (completion); fire from two to seven; wood from three to eight; metal from four to nine; earth from five to ten. Every element has a start and a completion. Add the ten numbers and you get fifty-five; the Xici Shang Commentary's line 'the numbers of Heaven and Earth come to fifty-five' points at exactly this. The Hetu's core is how all things move from generation to completion.

The Luoshu's Number Structure — Nine Above, One Below, Fifteen in Every Line

The Luoshu has only nine numbers, set in a three-by-three square. The layout verse runs: nine on top, one below, three on the left, seven on the right, two and four for the shoulders, six and eight for the feet, five in the center. Put into a square: the top row (shoulders) is four, nine, two; the middle row is three on the left, five in the center, seven on the right; the bottom row (feet) is eight, one, six. Once laid out, one thing appears — add across, down, or diagonally, and every line of three numbers comes to fifteen. This is the Luoshu's finest property, which the ancients called 'fifteen across, down, and diagonally.' Concepts like the nine-palace grid and the magic square all trace back to the Luoshu. Its center is five; the four cardinal positions (one, three, seven, nine) take up and down, left and right; the four corners (two, four, six, eight) take the four angles. This scheme of directions was later used to pair with the Later Heaven trigrams, becoming the shared foundation of feng shui, Qimen Dunjia, Zi Wei, and many other arts.

The Hetu and Luoshu's Correspondence with the Trigrams and Five Phases

The division of labor runs like this: the Hetu pairs with the five phases, the Luoshu pairs with the Later Heaven trigrams. The Hetu's five directions match the five phases exactly: north water, south fire, east wood, west metal, center earth. This correspondence is direct and easy to remember; it describes the relation between element and direction and is used to read the distribution and the generating-and-overcoming of the five phases. The Luoshu's nine palaces match the Later Heaven trigrams: Kan one in the north, Kun two in the southwest, Zhen three in the east, Xun four in the southeast, center five, Qian six in the northwest, Dui seven in the west, Gen eight in the northeast, Li nine in the south. See how every Later Heaven trigram takes one number from the Luoshu. The Earlier Heaven trigrams have their own set of numbers (Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight), which is not the same as the Luoshu. Do not confuse them: the Hetu to the five phases, the Luoshu to the Later Heaven trigrams — this is the most basic pairing. Fix it in mind and every later correspondence follows.

Song-Dynasty Diagram Learning — How the Hetu and Luoshu Became Mainstream

The Song dynasty is the key to the Hetu and Luoshu taking their present form. In the early Song, Chen Tuan handed down Yi diagrams of a certain kind; through the work of Liu Mu, Shao Yong, Zhou Dunyi, and others, and by the time Zhu Xi wrote the Original Meaning of the Zhou Yi, nine diagrams were simply hung at the front of the book, with the Hetu and Luoshu placed first. From then on, the Hetu and Luoshu became standard equipment for Yi study. The Song had an interesting argument: which one is the Hetu and which the Luoshu? Liu Mu held that the nine-number diagram was the Hetu and the ten-number diagram the Luoshu; Zhu Xi and Cai Yuanding held the opposite — the ten-number diagram was the Hetu and the nine-number the Luoshu. Zhu Xi's side won; the ten-number Hetu and nine-number Luoshu we use today were fixed by Zhu Xi. The argument itself shows that the names of the Hetu and Luoshu were only formally settled in the Song; earlier accounts were not unified.

How to Use the Hetu and Luoshu — Five Phases, Directions, and Decisions

How to use them? Three downward paths. First, use the Hetu to read five-phase directions. If you are arranging things in a space, first fix the broad directions by the Hetu: north water, south fire, east wood, west metal, center earth. What should go on which side then has a basis. Second, use the Luoshu for nine-cell decisions. Treat the Luoshu's nine palaces as a nine-cell thinking board: the center is five (you, your home ground), and the eight cells match eight directions and eight situations. Facing a choice, lay the options into the nine palaces and see what position each takes. Third, use generating and completing numbers to read rhythm. One through five generate, six through ten complete — any matter has two stages, lighting the fire (generate) and getting it done (complete); do not run the two together. The Hetu and Luoshu hold the most abstract number theory, but put to use they come down to three things: direction, structure, and rhythm.

Have You Really Read the Hetu and Luoshu?

Can you draw the Hetu's five-direction layout from memory — one and six water in the north, two and seven fire in the south, three and eight wood in the east, four and nine metal in the west, five and ten earth in the center — without one error?
In the Luoshu nine palaces, can you say offhand what the three numbers in every row, column, and diagonal add up to? The answer is fifteen — the Luoshu's finest property.
Do you know the basic division that the Hetu pairs with the five phases and the Luoshu with the Later Heaven trigrams? Mixing up the two diagrams' functions is the easiest mistake for a beginner.

Common Breakers

Treating the Hetu and Luoshu as two versions of one diagram. They are two diagrams with different structures: the Hetu is a ten-number cross board, the Luoshu a nine-number nine-palace board, and their functions differ. Lumping them together makes every five-phase and trigram correspondence miss.
Thinking the Hetu and Luoshu are artifacts truly unearthed in the age of Fu Xi. 'The Yellow River gave forth the diagram, the Luo River gave forth the writing' is a textual claim; the dragon-horse and divine turtle are legend. Use them as an ancient number model and be done; do not treat them as archaeological objects, and do not rush to deny their value either.
Remembering only the numbers and not the directions. Both diagrams are numbers plus directions; memorizing numbers alone is memorizing a pile of code. Bind each of water, fire, wood, metal, and earth to its direction and its numbers, and you can both hold them and use them.

Hetu and Luoshu Wisdom: Career, Relationships, Personality, and Health Through Four Lenses

Career & Wealth

The Hetu speaks of generation and completion, mapping straight onto the two stages of a career. Generation is zero to one — the idea, the direction, the start. Completion is one to ten — building it, scaling it, turning it into money. One pairs with six, two with seven, three with eight, four with nine, five with ten; every generating number has a matching completing number: each step of generation you take has a completion waiting behind it. The most common career disease is generating too much and completing too little: ten directions thought up, none finished. The Hetu's reminder: generation and completion pair up; where there is generation there must be completion. Count your generating numbers and force yourself to finish what you have opened; stop starting new heads.

Love & Relationship

In the Luoshu nine palaces, five sits in the center and the eight directions turn around it. In a relationship, you are that five — your center and your bottom line. The eight directions are concrete matters: family, work, social life, habits. The healthy way is to let these turn around your center, not let any one of them push your whole center aside. Many people move the five the moment they fall in love — putting the partner in the center and themselves in a side cell. The Luoshu's structure reminds you: hold the center steady and the surrounding cells stay orderly. Lose the center and the whole nine palaces scatter.

Personality

People drawn to the Hetu and Luoshu like order and correspondence. They cannot stand 'roughly right'; they want to find an exact position for everything. Numbers, directions, pairings put them at ease. Their strength is precision — orderly, methodical work, suited to jobs needing fine alignment. Their weakness is getting lost in the correspondences of detail — layer upon layer piling up, one system not yet learned well before they chase the next. The reminder: a diagram is for use, not for collecting. No matter how well drawn, an unused one is just a nine-palace grid on paper.

Health

The Hetu pairs its five directions with the five organs: north water with the kidney, south fire with the heart, east wood with the liver, west metal with the lung, center earth with the spleen. This correspondence is the base of Chinese medicine and very practical in daily life: late nights harm the kidney (north water), heat rising first vexes the heart (south fire), pent-up feeling injures the liver (east wood), grief and worry drain the lung (west metal), and irregular eating tires the spleen (center earth). You do not need the whole theory; remember the hook between direction and organ, and you know where to adjust when some direction's matching emotion or state keeps troubling you.

Hetu and Luoshu Classic Passages with Plain English Translation

Practical Applications of the Hetu and Luoshu

Use the Hetu's Five Phases to Set Directions in a Space: Take a floor plan of a space where you spend time (a desk, a study — either will do). Fix the five directions by the Hetu: north water, south fire, east wood, west metal, center earth. Then think about which energy your work needs: focused settling (water), face north; lively output (fire), face south; growth and opening (wood), face east; gathering and closing (metal), face west. No need for a big move; match your main activity's direction with the five-phase need and shift one or two pieces of furniture.
Use the Luoshu's Nine Palaces for Nine-Cell Decisions: Facing a wavering choice, draw a three-by-three grid. In the center write yourself and your core demand. The eight cells match eight ways of handling it: act (Zhen), follow the flow (Xun), settle (Kan), see clearly (Li), stop (Gen), open (Dui), hold firm (Qian), carry (Kun). Drop each option into all eight cells in turn and ask: what if I handle it this way? Walk the eight angles and you usually find you had thought of only one or two.
Use Generating and Completing Numbers to Read the Two Stages of Getting Things Done: The Hetu calls one through five generating numbers and six through ten completing numbers; every element has a generation and a completion. Use this frame to sort what is on your plate: which items stopped at generation (opened and never finished)? Which reached completion (delivered)? List all the generations and force yourself to pick just one to finish; hold the rest. The Hetu's core is that generation and completion pair up; if you only open and never close, the ledger runs deeper into loss.

Hetu and Luoshu: Common Questions

Q:Which one pairs with the Earlier Heaven trigrams and which with the Later Heaven trigrams?

The common pairing: the Hetu pairs with the five phases (one may also say it pairs with the Earlier Heaven trigrams' scheme of directions), and the Luoshu pairs with the Later Heaven trigrams — the nine positions of the Luoshu nine palaces match Kan one, Kun two, Zhen three, Xun four, center five, Qian six, Dui seven, Gen eight, Li nine. Keep this basic division in mind — the Hetu for five-phase generating and overcoming, the Luoshu for directional operation — and it is hard to get muddled.

Q:Did the Hetu and Luoshu exist in the age of Fu Xi and Yu the Great?

The textual account says the Yellow River gave forth the diagram and the Luo River the writing, with legends of a dragon-horse bearing the diagram and a divine turtle bearing the writing, and Fu Xi and Yu drawing the trigrams by following them. But this is legend, with no archaeological proof. What is certain is that the Hetu and Luoshu, as exact diagrams, were systematically fixed only in the Song dynasty. Using them as an ancient number model and intellectual tradition is more meaningful than arguing over whether they are real artifacts.

Q:What do the Hetu and Luoshu have to do with today's feng shui and Qimen?

A direct connection. Feng shui's nine-star flying uses the Luoshu's nine palaces as its board, and Qimen Dunjia's chart layout also takes the Luoshu nine palaces as its base, with the Luoshu's nine directions and numbers. These arts split off at different times and use different methods, but the underlying nine-palace scheme of fixing direction traces to the Luoshu. Learn the Luoshu nine palaces well first, then read these arts, and things go much more smoothly.