Yì xué qǐméng xiǎo zhuàn 易學啟蒙小傳
Minor Tradition on the Yì-Studies Beginner’s Primer
by 稅與權 Shuì Yúquán (撰) — zì Xùnfǔ 巽甫, fl. 1248, of Línqióng 臨卭 in Bājùn 巴郡 / Sìchuān; disciple of 魏了翁 Wèi Liǎowēng.
About the work
A one-juan supplementary-treatise to 朱熹 Zhū Xī’s Yì xué qǐméng 易學啟蒙 (Beginner’s Primer in Yì-Studies, 3 juan, the joint ZhūCài work), by Shuì Yúquán 稅與權 — one of the second-generation disciples of the Zhū-Wèi-school transmission line, who learned 邵雍 Shào-Yōng-school xiàngshù from 魏了翁 Wèi Liǎowēng (Hèshān 鶴山). The Sìkù base also includes an appendix, the Yì xué qǐméng gǔ jīng zhuàn 易學啟蒙古經傳 in 1 juan, with the Zhōuyì gǔjīng fā tí 周易古經發題 (“Topic-Setting on the Ancient Canon of the Zhōuyì”) as front-matter.
The methodological problem the work addresses is one Zhū Xī himself had explicitly left unfinished. Zhū Xī’s Qǐméng substantially expounded Shào Yōng’s Xiāntiān 先天 (“Before-Heaven”) diagrams. But for the Hòutiān 後天 (“After-Heaven”) Yì — the sequence-arrangement of King Wén’s hexagrams in the upper-and-lower jīng — Zhū Xī, in correspondence with 袁樞 Yuán Shū (zì Jīzhòng 機仲), had said: “I have used the hexagram-strokes vertically-and-horizontally, back-and-forth, and ultimately could not find the intent by which King Wén arranged [the hexagrams]; therefore I am cautious-and-fearful and do not dare invent any explanation.” The Hòutiān arrangement was, on Zhū Xī’s express verdict, beyond systematic recovery.
Shuì Yúquán’s claim is that, through Wèi Liǎowēng’s exposition of Shào Yōng’s writings, he found in Shào’s Guānwù piān 觀物篇 a systematic Hòutiān Yì shàngxià jīng xùguà tú 後天易上下經序卦圖 (“Sequence-of-Hexagrams Chart for the Upper-and-Lower Jīng of the After-Heaven Yì”) that solves the ZhūXī problem. Cross-checking with three additional witnesses — the Zá guà zhuàn 雜卦傳 (the wing-treatise on hexagram-transformations); 揚雄 Yáng Xióng’s claim that “King Wén doubled the Yì*; the six lines mutually-use both hexagrams, the twelve lines*”; and 孔穎達 Kǒng Yǐngdá’s “the 64 hexagrams two-by-two paired, [if] not reverse, then transform” — Shuì Yúquán arrives at his structural reading:
The 64 hexagrams divide into two structural categories:
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Bù yì zhī bā guà 不易之八卦 (“the eight non-varying hexagrams”): those eight hexagrams whose 180-degree rotation produces the same hexagram (palindromic hexagrams). These are Qián 乾, Kūn 坤, Kǎn 坎, Lí 離, Yí 頤, Zhōngfú 中孚, Dàguò 大過, Xiǎoguò 小過. These constitute the trunk (gàn 幹) of the upper-and-lower piān.
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Hù yì zhī wǔshíliù guà 互易之五十六卦 (“the fifty-six mutually-varying hexagrams”): the remaining 56 hexagrams form 28 paired couples (each pair being a hexagram and its 180-rotation). These constitute the use (yòng 用) of the upper-and-lower piān.
Reading the chart this way: the upper jīng (30 hexagrams) and lower jīng (34 hexagrams), each counted as paired-couples, both reduce to 18 distinct shapes — “beginning-and-end not exiting the number nine (since 18 = 2 × 9), clarifying that FúXī’s and King Wén’s Yì are seemingly different but the same.”
The mathematical-structural framing extends further (per the auto-preface):
- The Yì uses 18 transformations to produce a hexagram (the standard shī fǎ 蓍法 / yarrow-stalk procedure).
- The Tàixuán uses 18 cè 策 to produce a day.
- The 64 hexagrams “do not exceed Qián-Kūn’s nine-strokes-of-odd-and-even”; Qián and Kūn together have 2 × 9 = 18 strokes, which when squared (chóng 重) equals the 64-hexagram total seen as paired-couples.
- Gé 革 (hexagram 49) sits at “18 × 2 = 9 in Xiāntiān; in Hòutiān at the 49 yarrow-stalks’ extreme” — Gé is the hexagram of change-and-removal; Dǐng 鼎 follows at 50, the hexagram of new-establishment. The succession Gé → Dǐng mirrors the cosmological succession change-old-to-establish-new.
- Hé tú and Luò shū are mutually-used: Xiāntiān expresses the Hé tú’s 9 (split left-and-right, doubled to twice-9, circulating through 64); Hòutiān expresses the Luò shū’s 9 (combining upper-and-lower, summing to twice-9 = 36 across the whole).
The Sìkù tiyao’s assessment is methodologically articulate: “[Shuì Yúquán’s argument] expounds Shàozǐ’s exposition to supplement the Qǐméng’s incompleteness — what is called ‘holding-with-grounds, executing-with-principle.‘” Quoting 史子翬 Shǐ Zǐhuī’s back-colophon, the tiyao notes that Shǐ derived from Shuì Yúquán’s chart his own further insight into the QiánKūn nàjiǎ 乾坤納甲 doctrine: Qián runs from jiǎ to rén (gan-counting 1 to 9), Kūn from yǐ to guǐ (gan-counting 2 to 10) — both summing to 9. Shǐ then questioned: Qián’s 9 contains Kūn’s 6, but Kūn’s yīn should not contain Qián’s yáng. He resolved: 6 contains 1, 3, 5 within it — so the number 9 is concealed within 6. This is one of the cleaner Sòng-period exchanges on the nàjiǎ numerology.
The Sìkù editors’ closing balance: “The world’s numbers do not exit odd-and-even; whichever one-meaning is taken up, all have explanations through which they make sense; the more they make sense, each has its own principle. This kind is so. To say it is not the Yì*‘s root is permissible; to say it is not one meaning of the* Yì is also impermissible.” The verdict is methodologically nuanced: the xiàngshù numerology is one valid reading-channel among many, neither the canonical core nor irrelevant.
The composition window is fixed at 1248 by the auto-preface (Chúnyòu wùshēn mid-yuan day = 15th of 7th month, 1248), signed Bājùn Shuì Yúquán. The Shǐ Zǐhuī back-colophon is dated Chúnyòu 8th year (1248) eighth-month-second-day — i.e., shortly after the preface.
Tiyao
We respectfully submit that Yì xué qǐméng xiǎo zhuàn in one juan was composed by Shuì Yúquán of the Sòng. [Shuì] Yúquán’s [biographical] beginning-and-end is not fully clear. Per his auto-preface we know he was a disciple of Wèi Liǎowēng. Per the back-colophon by Shǐ Zǐhuī we know his zì is Xùnfǔ. Per Chén Zhènsūn’s Shūlù jiětí (recording his Zhōulǐ zhézhōng 周禮折衷 [a separate work]) we know he is a man of Línqióng.
Originally Master Zhū composed Yì xué qǐméng, much-developing the meaning of Master Shào’s Xiāntiān charts. As to his correspondence with Yuán Shū on Hòutiān Yì, [he] said: “I have once used hexagram-strokes vertically-and-horizontally and back-and-forth seeking — finally cannot find the intent by which King Wén arranged [the hexagrams]; therefore I am cautious-and-fearful and dare not lightly produce an exposition.”
[Shuì] Yúquán, following Wèi Liǎowēng’s exposition of Shàoshì’s various books, in the Guānwù piān obtained the Hòutiān Yì shàngxià jīng xùguà tú, verifying with the Zá guà zhuàn, with Yáng Xióng’s saying that “King Wén doubled the Yì; the six lines mutually-used both hexagrams, twelve lines,” and with Kǒng Yǐngdá’s saying “the 64 hexagrams two-by-two paired — if not reverse, then transform” — and so understood: Qián, Kūn, Kǎn, Lí, Yí, Zhōngfú, Dàguò, Xiǎoguò — the eight non-varying hexagrams — as the trunk of the upper-and-lower two piān; the 56 mutually-varying hexagrams as the use of the upper-and-lower two piān. Following the chart back-and-forth, the upper-and-lower jīng both become eighteen hexagrams; beginning-and-end not exiting the number nine — clarifying that the Xī-and-Wén Yì seem different but are the same. Evidently, expounding Shàozǐ’s exposition to supplement the Qǐméng’s incompleteness — what is called holding-with-grounds, executing-with-principle.
Shǐ Zǐhuī’s back-colophon claims that, following this book, he understood the meaning of QiánKūn nàjiǎ: Qián from jiǎ through rén, Kūn from yǐ through guǐ — the numbers both 9. He suspected: Qián’s 9 can contain Kūn’s 6; Kūn’s yīn cannot contain Qián’s yáng — but the Qián-yáng exposition holds that within 6 there are 1, 3, 5, so the number 9 is fundamentally concealed within 6. He wished to discuss further with [Shuì] Yúquán.
The world’s numbers do not exit odd-and-even; whichever one-meaning is taken up, all have explanations that make sense; and the more they make sense, the more each has its own principle. This kind is so. To say it is not the Yì’s root is permissible; to say it is not one meaning within the Yì is also impermissible.
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
Shuì Yúquán (稅與權, fl. 1248), zì Xùnfǔ 巽甫, of Línqióng 臨卭 in Bājùn 巴郡 (modern Pújiāng county, Sìchuān, in the Chéngdū metropolitan region — the same district as his teacher 魏了翁). CBDB records him without lifedates; principal CBDB note: “authored Jiàozhèng Zhōuyì gǔjīng 12 juan; Yì xué qǐméng xiǎo zhuàn 1 juan.”
His Jiàozhèng Zhōuyì gǔjīng 校正周易古經 (12 juan) is a separate work — a critical-edition recension on Lǚ Dàfáng 呂大防 / Lǚ Zǔqiān 呂祖謙’s gǔyì tradition. It survives separately and is cited by Zhū Yízūn’s Jīngyì kǎo (and is the source for the Sìkù editors’ defense of Lǚ Zǔqiān’s independent gǔyì recension in their tiyao on KR1a0043). The Yì xué qǐméng xiǎo zhuàn is the methodological-exposition companion to this critical-edition project.
Methodologically Shuì Yúquán is a second-generation Wèi-Liǎowēng-Shào-school disciple. The WèiLiǎowēng line preserves and transmits the Shào Yōng xiàngshù materials within the Zhū-school orthodox framework — Wèi Liǎowēng’s Yào yì / Jí yì compilation pair (KR1a0054) gave the canonical-and-Lián-Luò materials; Shuì Yúquán’s Xiǎo zhuàn applies Shào Yōng’s xiàngshù to fill an explicit gap left by Zhū Xī. The methodological self-positioning — xiǎo zhuàn (minor tradition) supplementing the Qǐméng — is a clean Zhū-school-discipleship gesture.
The bù yì zhī bā guà / hù yì zhī wǔshíliù guà (eight non-varying / 56 mutually-varying) categorization is one of the cleaner Sòng-period structural readings of the upper-and-lower jīng hexagram-sequence. The structure is mathematically sound: the eight palindromic hexagrams (those whose 180-rotation produces themselves) really do form a structurally distinct subgroup, and the 56-hexagram couplings really do produce 28 distinct paired-couple shapes. Modern Yì scholarship (especially the work on the Mǎwángduī and Shànghǎi Bówùguǎn manuscripts) has confirmed this structural insight as historically present in the canonical text-organization.
The 1248 composition date places the work in the late-Lǐzōng period, contemporary with Zhào Yǐfū’s Yì tōng (KR1a0051, 1246) and several years before Zhū Jiàn’s Wéngōng Yì shuō (KR1a0056, assumed 1230s–1250s).
Translations and research
No European-language translation. The work is principally consulted for the Hòutiān hexagram-sequence reading.
- Joseph A. Adler, Reconstructing the Confucian Dao: Zhu Xi’s Appropriation of Zhou Dunyi (SUNY, 2014) — context for the Zhū-Xī Hòutiān problem and Shào-Yōng-school responses.
- Zhū Bóqūn 朱伯崑, Yìxué zhéxué shǐ, vol. 2 — Shuì Yúquán treated as a Wèi-school xiàngshù exponent.
- Wáng Tiějūn 王鐵均, Sòngdài Yìxué shǐ — chapter on the late-Sòng Zhū-Wèi school Yì-tradition.
- Liào Mínghuó 廖名活, articles in Zhōuyì yánjiū on the bù yì / hù yì hexagram-categorization.
- Modern punctuated editions on the Sìkù base.
Other points of interest
The eight palindromic hexagrams Shuì Yúquán identifies are not an arbitrary subgroup: they are precisely the hexagrams that are unchanged under 180-degree rotation. This is a real symmetry-group structural feature of the 64-hexagram set. The Yì’s own arrangement of the upper-and-lower jīng — placing Qián-Kūn-Kǎn-Lí at the structural turning-points (1-2 / 29-30) and Yí / Dàguò / Zhōngfú / Xiǎoguò in symmetrically-distributed positions — appears to implicitly recognize the palindromic structure even without explicit theoretical articulation. Shuì Yúquán’s contribution is to explicitly recognize and theorize what the canonical sequence already encodes.
The Shǐ Zǐhuī back-colophon’s nàjiǎ exchange — “9 contains 6 because 1+3+5 = 9 sits within 6” — is methodologically interesting as an instance of Yì-numerology being treated as a topic of substantive philosophical exchange between disciples-of-disciples in the late Southern Sòng. The nàjiǎ doctrine itself derives from the Hàn xiàngshù tradition (Zhèng Xuán, Yú Fān 虞翻); its survival into late-Sòng intellectual exchange testifies to the comprehensiveness of the Wèi-school documentary preservation.