The trigrams and the 64
The Book of Changes is written with an alphabet of two letters: a whole line and a broken line, yang and yin. The Great Treatise puts them in a single sentence: yin and yang taking turns, it says, are the Dao — not one or the other, but their alternation. Everything the book can say, it says by combining these two lines.
Three lines, one above another, make eight figures: the trigrams. They bear the names of things of the world — Heaven, Earth, Thunder, Water, the Mountain, Wind, Fire, the Lake — and the book thinks of them in pairs: heaven and earth fix the places, mountain and lake exchange their breaths, thunder and wind kindle each other, water and fire make no war on each other. They are the eight natures you find again in the map of this Library.
Each has a character, and the book says it in a word: Heaven is strength, Earth yields, Thunder is motion, Wind penetrates, Water is the danger of the abyss, Fire clings and gives light, the Mountain stands still, the Lake is joy. And they have a family: Heaven and Earth are the father and the mother; Thunder, Water and the Mountain the three sons, from the eldest to the youngest; Wind, Fire and the Lake the three daughters.
Two trigrams, one above the other, make a hexagram: six lines, and sixty-four possible figures, eight by eight. The one below is called lower, and it is the first to form, because the lines settle from the bottom; the one above, upper. The Treatise on the Trigrams says it in one line: doubled, the trigram gives the six lines. In the map of this Library the columns are the upper trigram and the rows the lower: each cell is a hexagram, and the map is the whole combinatorics of the book, with nothing left over.
Much of a figure’s meaning lies already in the meeting of its two natures, and the Image — the commentary of the Wings that accompanies each hexagram — almost always begins there. Heaven below and Earth above: «heaven and earth unite», and it is Peace, the eleventh. Earth below and Heaven above: «heaven and earth do not unite», and it is Standstill, the twelfth. The same two natures, with their places exchanged: two worlds.
On the page of each hexagram you find, in order, its glyph and the two trigrams, above and below; then the Judgement, the Image and the Lines. The Judgement is the oldest text, the sentence that weighs the whole figure; the Lines are the six texts that tradition attributes to the Duke of Zhou, one for each place.
The lines are counted from the bottom: the first is the lowest, the sixth the highest. And they are called by a number that tells their nature: nine the whole line, six the broken line. So «Nine at the beginning» is a whole line in the first place, «Six in the third place» a broken line in the third, «Nine at the top» a whole line at the very top.
The numbers come from the count. With the coins, three faces added together give six, seven, eight or nine. Seven and eight are young lines, still: stable yang, stable yin. Nine and six are old lines, which have run their course and turn over into their opposite: changing yang, changing yin. When a line changes, the figure changes, and from the hexagram that came out of the coins a second one is born: this is the transformation. The first and the second hexagram have a seventh text, for the rare case in which all six lines change together: three hundred and eighty-four lines in all, plus those two.
The sixty-four stand in the order that tradition attributes to King Wen and that the book has carried for as long as we have known it: in pairs. Each figure is followed by its inverse, the same read upside down; and the eight that stay the same when inverted — the Creative and the Receptive, and then 27 and 28, 29 and 30, 61 and 62 — pair with their opposite, where every line changes sign. Twenty-eight pairs one way, four the other. Why the pairs stand in this order and not in another, no one has ever been able to say with certainty; one of the Wings, the Sequence, tries to tell it as a chain of consequences — it begins from heaven and earth, from which all things were born — and closes on Before Completion, because the succession of things, it says, can have no end.
Other orders have existed: the Mawangdui manuscript groups the hexagrams by upper trigram, eight by eight; Shao Yong set them out in his square. This Library keeps two: the map follows the trigrams, the list and the page-turning follow the number. Whatever figure comes out of your six lines, it sits in a cell of the map and has a number in the list; it has a name, a Judgement, an Image, six Lines — and, if a line moves, a door towards the figure next to it. Sixty-four ways in which the world transforms: not one more, not one less.