He Luo Li Shu (河洛理數)

From Eight Characters to Your Life's Two Hexagrams

Overview

He Luo Li Shu (河洛理數, 'the numerical principles of the He Map and Luo Writing') is the Song-dynasty bridge between China's two greatest symbolic systems: it takes the four pillars of your birth — the same eight characters BaZi reads — and converts them, through the number diagrams said to have emerged from the Yellow River and the Luo River, into your personal hexagrams of the I-Ching. The result is a natal chart written in the Book of Changes itself: a pre-natal hexagram (先天卦) governing the first half of life, a post-natal hexagram (後天卦) governing the second, and within each a single activated line — the 元堂, the seat of the self — fixed by the hour of your birth. From those lines the system unfolds a lifetime of great periods (大限): each yang line rules nine years, each yin line six, walking upward through both hexagrams from birth to old age. Where BaZi reads the eight characters as elemental forces, He Luo Li Shu reads the same characters as a passage of the I-Ching with your name on it — and askTIAN computes it with the same 节气-correct pillar engine its BaZi endpoint uses, locked to the classical text's own worked examples.

Origin & history

The system is attributed to Chen Tuan (陳摶, d. 989), the Taoist master of Mount Hua, and its transmission runs through Shao Yong (邵康節, 1011–1077), the great Song numerologist of the Plum Blossom tradition. Its foundation is the pair of diagrams at the root of Chinese cosmology: the He Tu (河圖), the River Map whose paired numbers generate the five elements, and the Luo Shu (洛書), the nine-palace magic square. Each heavenly stem takes a Luo Shu palace number through the 納甲 correspondences — 壬 and 甲 follow 乾 and take six, 乙 and 癸 follow 坤 and take two, 戊 takes the one of 坎, 己 the nine of 離 — and each earthly branch contributes both numbers of its He Tu element pair: one-and-six for the water branches, three-and-eight for wood, two-and-seven for fire, four-and-nine for metal, five-and-ten for earth. The odd values from all eight characters sum to the heaven number (天數), the even values to the earth number (地數); heaven casts off twenty-fives, earth casts off thirties; and the remainders, mapped through the Luo Shu palaces, become two trigrams. Whether the heaven trigram sits above or below follows the polarity of the birth: for a man born in a yang year or a woman born in a yin year, heaven mounts above earth.

He Luo Li Shu circulated for centuries as a semi-esoteric companion to the mainstream arts — admired for the elegance of deriving a person's I-Ching directly from their birth moment, transmitted through manuscript traditions that did not always agree. The classical text survives with worked examples, and askTIAN's engine is locked to three of them: the chart 甲子·丁卯·庚申·庚辰 for a man casts heaven-number 31 and earth-number 34, reducing to 乾 over 巽 — the hexagram 天風姤 with the 元堂 at the top line; the chart 丁巳·丙午·壬寅·辛丑 for a man casts 29 and 40, reducing to 巽 and 坎 assembled as 水風井; and the text's transformation example carries 澤地萃 with the 元堂 at the fourth line into 地水師 with the 元堂 at the first. The tradition's rough joints are real and askTIAN names them: when a number reduces to five it 'lodges in the centre palace' (五寄中宮) and must be resolved by a table of三元 epochs that the text itself applies inconsistently — the weakest rule in the system; a minority school takes only one number per branch instead of the pair but transmits no exact formula; and a manuscript variant reverses the direction of the hour-count in the pure 乾 and 坤 hexagrams. The annual and monthly layers (流年, 流月) diverge even more heavily between schools, and askTIAN defers them entirely until a second source confirms the rules — the same restraint it applies across its catalogue.

How it works

The endpoint first computes the four pillars with askTIAN's 节气-correct BaZi engine — the same solar-term boundaries, late-Zi-hour handling and sexagenary arithmetic as bazi.chart, so the two systems can never disagree about your eight characters. Each stem then takes its 納甲 Luo Shu number and each branch both numbers of its He Tu pair; odd values sum to the heaven number, even to the earth number, and the response shows every character's contribution so the arithmetic is auditable. Heaven casts off twenty-fives (exactly twenty-five becomes five), earth casts off thirties (exactly thirty becomes three), two-digit remainders keep their ones digit — a trailing zero keeps the tens — and the results map through the Luo Shu: one 坎, two 坤, three 震, four 巽, six 乾, seven 兌, eight 艮, nine 離, with a five lodging in the centre and resolved by the 三元 table by epoch, gender and year-polarity. The 阳男阴女 rule assembles the pre-natal hexagram; the birth hour then seats the 元堂 — the first six hours count the hexagram's yang lines from the bottom, the last six its yin lines, doubling the count when three or fewer match, with a fixed hour-table for pure 乾 and 坤. Flipping the 元堂 line and exchanging the trigrams yields the post-natal hexagram — unless the pre-natal chart is one of the three sovereign hexagrams (坎為水, 水雷屯, 水山蹇) with the 元堂 in the sovereign position, which transform without exchanging (变而不易). Finally the twelve 大限 are walked out: six lines up from the pre-natal 元堂, then six from the post-natal, nine years per yang line and six per yin, in traditional counted age. Every rule the sources dispute is disclosed in the response's method string; nothing is silently chosen.

Good for

Use cases

The Natal I-Ching Report

One call returns both life-hexagrams, their 元堂 lines with classical names (初九 … 上六), and the twelve dated great periods — the complete skeleton of a He Luo Li Shu reading, deterministic and auditable, ready for your own interpretive layer.

Companion Panel to BaZi

Show bazi.chart and heluo.chart side by side from one birth form: the pillars are computed by the same engine, so the eight characters match exactly and the reader sees their chart in both languages — Ten Gods on the left, hexagram lines on the right.

Life-Period Timeline

Render the 大限 array as a timeline: twelve segments from age one, each labelled with its hexagram, line and yang/yin duration. The current segment is the line of the Changes the tradition says you are living through right now.

Hexagram Deep-Dive Chain

Take the 先天卦's King Wen number from this endpoint and pass it to iching.relations for the nuclear, inverse, opposite and exchanged hexagrams — a two-call pipeline from birth data to a full structural study of your natal gua.

Key terms

He Tu / Luo Shu (河圖／洛書)
The two primordial number diagrams — the River Map's element pairs and the Luo Writing's nine-palace square — through which the eight characters become numbers, and numbers become trigrams.
天數 / 地數
The heaven number (sum of all odd stem and branch values) and earth number (sum of the even ones). Heaven casts off twenty-fives, earth casts off thirties; the remainders name the two natal trigrams.
先天卦 (Pre-natal Hexagram)
The hexagram assembled from the heaven and earth trigrams — 阳男阴女 place heaven on top — governing the first half of life.
元堂 (Yuan Tang)
The activated line, the seat of the self, fixed by the birth hour: the first six hours count the hexagram's yang lines from the bottom, the last six its yin lines. The 大限 sequence and the post-natal transformation both start here.
後天卦 (Post-natal Hexagram)
The second-half-of-life hexagram: flip the 元堂 line, exchange the trigrams, and the 元堂 moves three places — except in the three sovereign hexagrams, which transform without exchanging.
三至尊卦 (Three Sovereign Hexagrams)
坎為水, 水雷屯 and 水山蹇 — when the 元堂 sits in their sovereign position (the fifth line in the yin half-year, the sixth in the yang), they 'transform but do not exchange' (变而不易).
大限 (Great Periods)
The life-period sequence: from the pre-natal 元堂 upward through six lines, then through the post-natal hexagram — each yang line ruling nine years, each yin line six, in traditional counted age from one.
五寄中宮 (Five Lodges in the Centre)
When a number reduces to five — the Luo Shu's centre, which is no trigram — it is resolved by the 三元 epoch table by gender and year polarity. The classical text's least certain rule, and askTIAN says so.

API

The askTIAN He Luo Li Shu API computes the four pillars with the same 节气-correct engine as bazi.chart, shows every character's He Tu / Luo Shu contribution, and returns the complete natal derivation: heaven and earth numbers with the classical reduction, both trigrams and who mounts above, the pre-natal and post-natal hexagrams with King Wen numbers, both 元堂 positions with classical line names, the 三至尊卦 flag when the sovereign exception fires, and the twelve dated 大限 periods. Accuracy is the feature: the engine is an independent implementation of the public-domain classical algorithm, cross-verified across four sources and locked to the text's three worked examples as gold tests, with every disputed rule — the 五寄中宮 epoch table, the one-number-per-branch minority, the pure-乾坤 manuscript variant — disclosed in the method string rather than silently chosen. The annual and monthly layers are deferred until a second source confirms them. Pure deterministic compute, no LLM.

Endpoint: POST /trpc/heluo.chart — 15 TIAN Points. See the API documentation and Playground.