Hexagram Relations: Inverse, Reversed, Nuclear

Inverse (cuò 錯): every line flipped

Swap every line of a hexagram, yang for yin and yin for yang, and you get its inverse, the cuò guà 錯卦, also called its “change” or its “lateral link” (pángtōng 旁通).

The simplest case is Qian and Kun: six yang become six yin. After Completion alternates yin and yang in every line; flip them all and it becomes Before Completion, Wèijì 未濟. A more interesting case is Modesty, five yin and one yang. Flip it and you get five yang and one yin: Treading, Lǚ 履, Heaven over Lake. Modesty is “a mountain hidden beneath the earth”; Treading is “treading on the tiger's tail”. One is about holding back, the other about walking correctly through danger. When the Great Commentary lists nine hexagrams for cultivating virtue, the first is “Treading is the foundation of virtue” and the second “Modesty is the handle of virtue”. The two are each other's inverse.

The point of the inverse is to see a situation from the fully opposite angle. When you draw a hexagram, look at its inverse and you see the other face of where you stand. If you are in Modesty now, Treading lies across from you: restraint is right, and after restraint you must still go forward by the rules.

Reversed (zōng 綜): the hexagram turned upside down

Turn the whole hexagram upside down, so that the first line becomes the top and the top the first, and you get its reversal, the zōng guà 綜卦, also called fù 覆. If rotating it in your head makes you dizzy, there is an easy way: leave the figure on the table and walk round to the other side.

Zhun 屯, Water over Thunder, turned over becomes Méng 蒙, Mountain over Water. The hardship of things being born, seen from the other side, is the ignorance of youth that needs teaching. Modesty turned over becomes Delight, Thunder over Earth: Modesty's lone yang in the third place lands in the fourth. One is toil and humility, the other ease and enthusiasm. Cuì 萃, Gathering, turned over becomes Shēng 升, Rising.

The reversal means seeing the same matter from the other party's position. What looks like difficulty to you may look like growth to them; your gathering may be someone else's rise. Many hexagrams are both inverse and reversal of one another. Peace and Obstruction are the classic case: Peace, three yang below and three yin above, becomes Obstruction whether you flip every line or turn it over. After Completion and Before Completion are likewise both. Between finished and unfinished lies a single turn.

Nuclear (hù 互): the hexagram inside the hexagram

Besides the lower and upper trigrams, the four middle lines of a hexagram form two more: lines two, three and four make one, and lines three, four and five make another. These are the nuclear trigrams, hù guà 互卦 (some call the upper one the jiāo guà 交卦). Stack them, lower nucleus below and upper nucleus above, and you get a new hexagram, the nuclear hexagram. So every hexagram actually contains four trigrams, the two outer and the two inner, and all four can inform the reading of a line.

Look at Modesty. Lines two, three and four are yin, yang, yin: Kan. Lines three, four and five are yang, yin, yin: Zhen. Hidden inside Modesty are Kan and Zhen, which stacked give Thunder over Water, Xiè 解, Release. When Modesty's first line spoke of crossing “the great river”, where did the river come from? From this nuclear Kan.

Or look at Yì 益, Increase, Thunder below and Wind above. The Great Commentary says the ancient farmer-sage “cut wood for a ploughshare and bent wood for a plough handle ... taking the idea from Increase”. Xun is wood, Zhen is the foot; the nuclear trigrams are Kun and Gen, earth and hand. Hands holding a wooden tool, feet stepping into the soil: the picture of ploughing.

Most striking is After Completion. Its lines two to four form Kan and lines three to five form Li, so its nuclear hexagram is Before Completion. Inside completion, incompletion is already hidden.

“If not reversed, then inverted”: the paired sequence

Open the sequence of the sixty-four and you find they come in pairs, thirty-two of them: Qian and Kun, Zhun and Meng, Waiting and Conflict, Army and Holding Together, and so on to After and Before Completion. The relation within each pair is summed up in one phrase: fēi fù jí biàn 非覆即變, “if not reversed, then inverted”. Either the second hexagram is the first turned upside down (fù, that is, zōng), or it is the first with every line changed (biàn, that is, cuò).

Most pairs are reversals: Zhun turned over is Meng, Waiting turned over is Conflict, the Army turned over is Holding Together. Only eight hexagrams remain themselves when turned over, because they are symmetrical top to bottom: Qian, Kun, Yí 頤 (Nourishment), Dàguò 大過 (Great Excess), Kan, Li, Zhōngfú 中孚 (Inner Truth) and Xiǎoguò 小過 (Small Excess). These cannot be paired by reversal, so they are paired by inversion: Qian with Kun, Nourishment with Great Excess, Kan with Li, Inner Truth with Small Excess. Fifty-six hexagrams form twenty-eight reversed pairs, eight form four inverted pairs: thirty-two pairs exactly.

One more detail. Count each reversed pair as a single shape, and the thirty hexagrams of the Upper Classic are twelve pairs plus six symmetrical figures (Qian, Kun, Nourishment, Great Excess, Kan, Li): eighteen shapes. The thirty-four of the Lower Classic are sixteen pairs plus two symmetrical ones (Inner Truth, Small Excess): also eighteen. The two halves differ in length but are equal in structure.

With inverse, reversal and nucleus you gain three windows on any hexagram: the inverse shows its opposite, the reversal shows the other party, the nucleus shows what lies within. The Great Commentary speaks of “threes and fives in change, interweaving and reversing the numbers”. The changes of the Yi live in these crossings and turnings.