Yì tú tōng biàn 易圖通變
Comprehensive Variations on Yì-Diagrams
by 雷思齊 (Léi Sīqí, zì Qíxián 齊賢, hào Kōngshān xiānshēng 空山先生, 1230–1301, of Línchuān 臨川 in Jiāngxī — Sòng-loyalist Daoist priest)
About the work
A five-juan late-Sòng / early-Yuán xiàng-shù-numerological treatment of the Yì-diagrams, by Léi Sīqí 雷思齊 — the Sòng-loyalist Daoist priest who, after the Línān fall (1276), abandoned the Confucian robe (qì rúfú 棄儒服) and became a Daoist priest at Wūshí Temple 烏石觀. The Sìkù base also includes the companion Yì shì tōng biàn 易筮通變 in 3 juan (5 chapters: bǔshì 卜筮, lì guà 立卦, jiǔliù 九六, yǎn shù 衍數, mìng shī 命蓍 — “also much from his own new ideas, not mastering old methods”); the catalog meta lists only the 5-juan Yì tú tōng biàn, but the Sìkù total is 8 juan.
The auto-preface (dated Dà Yuán Dàdé gēngzǐ / 1300, ninth-month, Línchuān dàoshì Léi Sīqí Qíxián xù) gives the work’s program. The Hé tú is the Bā guà’s structural foundation, drawn by Fúxī through observation of natural patterns. Léi Sīqí’s claim:
The diagram’s number, with Bā guà forming a sequence and swirling-and-mixing, cāntiān liǎngdì (matching-Heaven-by-3, Earth-by-2), cānwǔ yǐ biàn — all naturally-so. Later ages did not root in its number, [the number] in fact being only forty, with its fifteen huìtōng (combine-penetrate) at the center — and so vainly-calculated the Heaven-and-Earth numbers as 55, by intent adding-and-instituting beyond the 40, to seek their correspondence — fortunately their middle [matched] — and so the more they expounded, the more confused; [confusion] streaming and streaming until today. I have, by submerged-mind for years, fully discussing the various expositions, alone recognized the early sage’s intent-and-direction; I have therefore made the Tōng biàn zhuàn to share with the four-directions’ thousand-years’ Yì-students, jointly investigating the true [doctrine].
The methodological core: the Hé tú contains forty essential numbers (not the conventional 55), with fifteen connecting through the center. This connects to the Bā guà via:
- tiānyī = Kǎn 坎 (water; north)
- dìèr = Kūn 坤 (earth; southwest)
- tiānsān = Zhèn 震 (thunder; east)
- dìsì = Xùn 巽 (wind; southeast)
- tiānqī = Duì 兌 (lake; west)
- dìliù = Qián 乾 (heaven; northwest)
- tiānjiǔ = Lí 離 (fire; south)
- dìbā = Gèn 艮 (mountain; northeast)
— mapping the trigrams to the Hòutiān (After-Heaven) calendrical-cosmological positions per the Shuō guà’s Chū Zhèn, qí Xùn, Lí yě xiàngjiàn, gōng yú Kūn, Duì zhèngqiū, zhàn yú Qián, láo hū Kǎn, chéng yán hū Gèn sequence (the Hòutiān eight-direction trigram-rotation).
Note: Léi Sīqí’s mapping differs from the conventional Hé tú numerology in detail — particularly the assignments of Kūn to 2 (instead of 6) and Qián to 6 (instead of 9). The Sìkù tiyao: “his exposition, although different from the previous ru, examining it against the Shuō guà’s out-of-Zhèn, equal-at-Xùn meaning, is rather mutually-correspondent.” The Sìkù editors invoke Lín Zhì’s Yì bì zhuàn (KR1a0045) preface principle to legitimize: “the Yì-Way’s transformation is inexhaustible; obtaining one corner all suffices to make an exposition.”
The 50 (the dà yǎn number) Léi Sīqí treats as xū shù 虛數 (empty number) — a procedural-ritual number rather than a substantive cosmological number. This is methodologically clean: the Yì’s essential Hétú numerology operates with 40 + 15-at-center; the 50 of the dà yǎn is the yarrow-stalk procedure’s number, structurally separate from the Hétú foundation.
The contents of the Yì tú tōng biàn’s 5 juan: charts of Hé tú Luò shū, cāntiān liǎngdì yǐ shù tú, cuòzōng huìbiàn etc., plus Hé tú yí lùn (Discussions on Remaining Issues of the Hé tú) — substantial chart-and-discussion apparatus. The companion Yì shì tōng biàn’s 5 chapters cover the yarrow-stalk-procedure topics.
Bibliographic note: the Sìkù tiyao registers an important documentary observation: “Bái Yúnjì 白雲霽’s Dàozàng mùlù 道藏目錄 records the two books in the Tàixuán section, Ruò character; evidently the Túshū learning [is rooted in] Daoist tradition, and Sīqí himself was a Daoist priest expounding-and-extending it to attach to the Yì; this also has reason.” The Yì tú tōng biàn and Yì shì tōng biàn survive in both the Sìkù Yì lèi (Confucian canon-classics) and the Dàozàng (Daoist canon) — making them one of the cleaner Sòng / Yuán-period bibliographic-bridge works.
The composition window 1295–1300 reflects the auto-preface’s firm 1300 terminus and the broader late-life composition-arc.
Tiyao
We respectfully submit that Yì tú tōng biàn in 5 juan and Yì shì tōng biàn in 3 juan were composed by Léi Sīqí of the Sòng. [Léi] Sīqí, zì Qíxián, a man of Línchuān. After the Sòng’s fall, [he] abandoned the Confucian robe and became a Daoist priest, residing at Wūshí Temple; later ended at Guǎngxìn. His career-record is given in Yuán Jué’s [composed] funerary inscription. This compilation has at the front Jiē Xīsī’s preface, calling [the works] “authored: Lǎozǐ běn yì, Zhuāngzǐ zhǐ yì, several-tens-of-juan; and Hé Táo shī in 3 juan”; Wú Quánjié’s preface also says he has a wénjí in 20 juan — today none seen; only these two books survive.
The Yì tú tōng biàn’s auto-preface says: the Hé tú*‘s number, with* Bā guà forming a sequence and swirling-mixing, cāntiān liǎngdì cānwǔ yǐ biàn, its number actually 40, with the 15 [combining]-penetrating at the center. What is described — Hé tú Luò shū cāntiān liǎngdì yǐ shù tú, cuòzōng huìbiàn etc. charts, and the Hé tú yí lùn — its great-intent: tiānyī as Kǎn; dìèr as Kūn; tiānsān as Zhèn; dìsì as Xùn; tiānqī as Duì; dìliù as Qián; tiānjiǔ as Lí; dìbā as Gèn — and 50 as the empty-number. His exposition, although different from the previous ru’s, examining against the out-of-Zhèn, equal-at-Xùn meaning, also rather mutually-corresponds — as Lín Zhì’s Yì bì zhuàn preface said: the Yì*-Way’s transformation is inexhaustible; getting one corner all suffices to make exposition.*
The Yì shì tōng biàn is in 5 piān: 1 bǔshì, 2 lì guà, 3 jiǔliù, 4 yǎn shù, 5 mìng shī — also mostly self-emergent new-ideas, not mastering old methods.
Bái Yúnjì’s Dàozàng mùlù records the two books in the Tàixuán section, Ruò character. Evidently the Túshū learning actually came from Daoist tradition; Sīqí himself, a Daoist priest, expounded-and-extended it to attach to the Yì — this also has reason.
Respectfully revised and submitted, twelfth month of the forty-sixth year of Qiánlóng [1781].
General Compilers: Jǐ Yún 紀昀, Lù Xīxióng 陸錫熊, Sūn Shìyì 孫士毅. General Reviser: Lù Fèichí 陸費墀.
Abstract
雷思齊 Léi Sīqí (1230–1301 per Kanripo catalog), zì Qíxián 齊賢, hào Kōngshān xiānshēng 空山先生, of Línchuān 臨川 (modern Línchuān, Jiāngxī). A Sòng-loyalist who, after the Línān fall in 1276, took the Daoist robe and resided at Wūshí Temple. Later moved to Guǎngxìn 廣信 where he died. Funerary inscription by Yuán Jué 袁桷 (Hànlín scholar of the early Yuán).
Disciples include Wú Quánjié 吳全節 (whose 1332 preface is preserved at the head of the Sìkù base); friend-relations with Zēng Zǐliáng 曾子良 (former Chúnān lìng) and Wú Chéng 吳澄 (Hànlín xuéshì of the Yuán). The Wǔshí Temple residence places him in the late-Sòng / early-Yuán Daoist Yì-circle, parallel to Yú Yǎn (KR1a0064)‘s Línwūshān refuge.
Methodologically Léi Sīqí is a Daoist Hé-tú-numerology synthesizer. The work’s distinctive contributions:
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40 + 15 framework. The Hé tú’s essential number-structure is 40 substantive numbers + 15 connecting-numbers at the center, totaling 55 only if one adds the 15 differently from the conventional 1+2+3+4+5+6+7+8+9+10. This is a methodologically clean revision of the standard jī shù (accumulating-numbers) approach.
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Hòutiān trigram-position assignment to numbers. The tiānyī = Kǎn, dìèr = Kūn, … dìbā = Gèn mapping uses the Hòutiān trigram-position rotation (Shuō guà sequence) rather than the Xiāntiān mapping. This is again methodologically distinctive but defensible by Shuō guà citation.
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50 as xū shù. The dà yǎn 50 is treated as empty-number (procedural-ritual rather than cosmological). The methodological move clarifies the yarrow-stalk-procedure / cosmological-substance distinction in a way that the conventional Liú-Mù-tradition Hétú readings did not.
The work’s xiàng-shù-cosmology dimension makes it a major late-Yuán Yì-and-Daoist synthesis text. Léi Sīqí’s career — Confucian Yì-scholarship + Daoist priestly office — gives the work a documentary-bridge status between the Confucian Yì lèi canon-classics and the Daoist Tàixuán tradition.
Other Léi Sīqí works listed in Jiē Xīsī’s preface (none extant in independent transmission): Lǎozǐ běn yì 老子本義, Zhuāngzǐ zhǐ yì 莊子旨義 (multiple juan total), and Hé Táo shī 和陶詩 in 3 juan. Wú Quánjié’s preface adds: a wénjí in 20 juan (also lost).
The composition window 1295–1300 reflects Léi Sīqí’s late-life mature scholarship at Wūshí Temple, with the auto-preface’s firm 1300 terminus.
Translations and research
No European-language translation. The work is principally consulted in late-imperial xiàng-shù-numerology studies and in Daoist Yì-tradition studies.
- Bent Nielsen, A Companion to Yi Jing Numerology and Cosmology (Routledge, 2003) — Léi Sī-qí’s Hé-tú framework discussed.
- Catherine Despeux, “Talismans and Sacred Diagrams” in Daoism Handbook (Brill, 2000) — context for the Daoist Tú-shū tradition.
- Zhū Bóqūn 朱伯崑, Yìxué zhéxué shǐ, vol. 2 — Léi Sī-qí treated as a Daoist Yì-numerologist.
- Wáng Tiějūn 王鐵均, Sòngdài Yìxué shǐ — chapter on the late-Sòng / Yuán Daoist Yì-tradition.
- Modern punctuated editions on the Sìkù base; the Dào-zàng tribute-edition (e.g., the Zhōnghuá Dào-zàng 中華道藏) preserves the Yì shì tōng biàn in its Tài-xuán category.
Other points of interest
The Sìkù-recorded methodological justification — “the Túshū learning actually came from Daoist tradition” — registers explicitly what other Sìkù Yìlèi entries leave implicit: the HétúLuòshū numerology, while incorporated into the Dàoxué Yì-canon by Liú Mù and Cài Yuándìng, has its substantive intellectual origins in Daoist circles (particularly the Northern-Sòng HétúLuòshū tradition associated with Chén Tuán 陳摶 / Chén Xīyí). Léi Sīqí’s career-double-life — Confucian Yì-canon-scholar + Daoist priest — physically embodies the cross-traditional location of Túshū studies.
The 1316 Zhāng Zōngyǎn (the 36th Sìtiānshī / hereditary Heavenly Master) preface places Léi Sīqí within the documentation-network of the late-Yuán Zhèngyī 正一 Daoist establishment. The Heavenly Master’s endorsement is one of the institutionally-formal Daoist tributes to a Yì-scholar.
The Yì shì tōng biàn’s 5-chapter procedural treatment (bǔshì / lì guà / jiǔliù / yǎn shù / mìng shī) is one of the cleaner systematic Sòng / Yuán-period treatments of the yarrow-stalk procedure. The procedural treatment is methodologically separate from the Yì tú tōng biàn’s cosmological-foundational treatment, demonstrating Léi Sīqí’s clear distinction between the Yì’s cosmological substance and its procedural divinatory use.