Archive of Yijing scans from Chinese and other sources

Gradually I am building an archive of scanned material from rare and hard-to-find books and journals. So far practically all the important Yijing diagrams can be found here, as well as Arthur Waley's 1933 essay 'The Book of Changes', which was very difficult to track down even in research libraries before it was made available here.

Yijing diagrams from the Zhouyi Tushi Dadian

These scans were taken from the 'Zhouyi Tushi Dadian' ('Encyclopedia of Zhouyi Diagrams.' Beijing: Zhongguo gongren chubanshe, 1994, 2 vols). The scans range in size from 120 Kb to 200 Kb and are numbered according to their page number in the original work. I have appended notes to a few of the diagrams, and in due course I may write notes on others, although they are mostly self-explanatory to those studying the subject.

Circular Xiantian diagrams

I have gathered below scans of circular diagrams relating to Shao Yong's Xiantian ('Before Heaven') diagram. See my article on Yijing hexagram sequences.

† In ztd367 the circle is shown split into two halves (actually quadrants if you look closely). The semicircle of hexagrams on the right is 'flipped' from top to bottom from the natural order arising around the circumference of a circle from the Xiantian progression. Hexagrams 1 and 2 are together at the top in diagrams such as ztd758, but in diagrams like ztd367 hexagram 1 is at the top and hexagram 2 is at the bottom, because the right semicircle is inverted. This semicircle is also inverted in ztd1022 and ztd1261, but in those diagrams the circle is shown whole, which is the usual representation. In circles like this where the right half is flipped top to bottom hexagrams 1 and 44 are next to each other at the top rather than hexagrams 1 and 2, and all hexagrams are diametrically opposite their complementary hexagrams (yin lines in one are yang lines in the other, and vice versa). The 32 hexagrams in the left semicircle are known the 'yang hexagrams', because they contain 112 yang lines and 80 yin lines in total, whereas the 32 hexagrams in the right semicircle are the 'yin hexagrams', having 112 yin lines and 80 yang lines. The term used for the 'Before Heaven' square arrangement of the 64 hexagrams placed inside the circular arrangement is Xiantian fangyuan tu ('Before Heaven square and circle diagram').

‡ See my notes on a 'compass rose' star pattern in ztd758, of which ztd55 and ztd911 are other examples.

12 sovereign hexagrams (bigua)

Below are scans relating to the 12-hexagram bigua sequence, which correlates 12 hexagrams showing the fall and rise of yin and yang with the 12 months and the 12 'Earthly Branches'.

Rectangular Xiantian diagram

The following diagrams show or relate to the rectangular Xiantian diagram. The diagram, when it has built up to three levels, forms the eight trigrams in the Fuxi order, and then when it has built up to six levels it forms the 64 hexagrams. This type of diagram is explained in detail in Yijing hexagram sequences. The wide 64-hexagram diagram, shown in the bottom two scans, is known as the dahengtu, or 'great horizontal diagram', while the eight-trigram diagram, the upper diagram in the first scan, is called the xiaohengtu, or 'small horizontal diagram'.

The first two scans break up the dahengtu into eight blocks, in order from qian to kun (right to left). Each block consists of a group of eight hexagrams all having the same lower trigram, black being yin and white yang. The upper half of each block is the xiaohengtu. Chinese texts sometimes mention hexagrams having 'one lower trigram and eight upper trigrams', referring to such groups. Another way to see it is that each upper xiaohengtu rests on one eighth of the lower xiaohengtu. Equally, you can regard the dahengtu as consisting of a single xiaohengtu in the bottom three levels, with eight xiaohengtu forming the top three levels.

Unequal division

The two scans below relate to the unequal two-part division of hexagrams in the received order. See Note 2 for an explanation.

Yin-yang hexagram arrangement

These next four scans show the 1–6–15–20–15–6–1 arrangement of the 64 hexagrams according to the distribution of yin and yang lines. 20 hexagrams have three yin lines and three yang. 15 hexagrams have two yin and four yang, and a further 15 have four yin and two yang. Six hexagrams have one yin and five yang, another six have five yin and one yang. One hexagram has six yin and one has six yang. (See my review of József Drasny's site, relating to this arrangement. Note also that the sixth row of Pascal's Triangle, starting with n = 0, is 1–6–15–20–15–6–1.)

There is a mistake in ztd661. In the row of six hexagrams with five yin and one yang, hexagram 3 appears instead of hexagram 24. In this diagram hexagrams 29 and 30 aren't drawn, just the circled Chinese character given.

Before Heaven nuclear hexagrams

There are two nuclear trigrams embedded in a hexagram in lines 2-3-4 and lines 3-4-5. They overlap, sharing the two middle lines of the hexagram. These two nuclear trigrams can be separated and combined to form a new hexagram, which is the 'nuclear hexagram' at the heart of the first hexagram. The lower and upper nuclear trigrams remain in lower and upper positions in the new hexagram.

When you take out the nuclear hexagrams from each of the 64 you find that you can extract only 16 different hexagrams: 1, 2, 23, 24, 27, 28, 37, 38, 39, 40, 43, 44, 53, 54, 63, and 64. When you take the nuclear hexagrams out of those 16, they reduce down to just four, namely hexagrams 1, 2, 63, and 64. If you try to take the process further, hexagrams 1 and 2 can only become themselves, and 63 and 64 alternate between each other. So the process is like a sorting machine for yin and yang.

Notice that the 16 nuclear hexagrams from the 64 are in pairs. 1/2 and 27/28 are complementary; 23/24, 37/38, 39/40, and 43/44 are the inverse of each other; 53/54 and 63/64 are both complementary and inverse. It's also worth noting that in the 32 pairs of the King Wen sequence the inverse pairs have an inverse pair of nuclear hexagrams, the complementary pairs have a complementary pair of nuclear hexagrams, and the pairs that are both complementary and inverse have pairs of nuclear hexagrams that are likewise.

The 'Before Heaven' sequence of hexagrams, by contrast, is in pairs that have the same nuclear hexagram. This is a consequence of the fact that this sequence is in pairs where only the top line differs, which of course is outside of the lines forming the nuclear trigrams.

ztd1144

This diagram shows in the outer circle the 64 hexagrams in the 'Before Heaven' or Xiantian arrangement (hexagram 1 and 44 are at the top of the circle, or, they would be had the circle been placed on the page straight). Both hexagrams of pairs in the outer ring have the same nuclear hexagram, which forms the middle ring of 32 hexagrams, consisting of 16 different hexagrams each appearing twice. The 32 hexagrams are again in pairs that have the same nuclear hexagram, producing an inner ring of 16 hexagrams, containing four each of hexagrams 1, 2, 63, and 64.

Geomantic figures and nuclear hexagrams

Bob McGee pointed out to me a correlation between the 16 geomantic figures and the 16 nuclear hexagrams that I don't believe has been noticed before. If you take the geomantic figures as tetragrams and then take the top three lines of the tetragram as an upper trigram and the bottom three lines as a lower trigram, expanding to a hexagram, it just so happens that the 16 hexagrams resulting are precisely the nuclear hexagrams. Well they would be, naturally, since nuclear hexagrams are formed from the four lines at the centre of a hexagram, of which there are 16 possible combinations of yin and yang line, but now it turns out that the geomantic figures are equivalent to the nuclear hexagrams.

A consequence of the way nuclear hexagrams are formed is that you can remove the central two lines (a digram) of any nuclear hexagram to arrive back at the associated tetragram. There are four each of the four types of digram, also known as the sixiang or 'four images', at the centre of these hexagrams. In the case of the two digrams formed from one yin line and one yang line (lesser yang and lesser yin) the digram at the centre of a hexagram is the inverse of the digram at the centre of its respective tetragram. They are actually also inverted in the case of the all-yin and all-yang digrams (greater yin and greater yang) but of course they look the same. The digrams are inverted because, when expanding the overlapping trigrams, the bottom line of the digram at the centre of the tetragram becomes the top line of the digram at the centre of the nuclear hexagram, and the top line becomes the bottom line. This gives you a method of forming the hexagrams from the tetragrams in addition to expanding the interlocked trigrams, as you can take the central digram of a tetragram and insert it inverted between the upper digram and the lower digram. This is effectively what you're doing when forming a nuclear hexagram described without trigrams.

Or you could simply expand the three overlapping nuclear digrams in the central four lines of the 64 hexagrams in the same way as nuclear trigrams without inverting the central one, in which case half of the resulting 16 nuclear hexagrams would be different, namely those where the central digram of the originating hexagram is composed of one yin line and one yang line, the ones with all yin or all yang would remain the same. Here are the nuclear hexagrams with the new ones in bold and what they were with nuclear trigrams in brackets: 1, 2, 11 (54), 12 (53), 17 (63), 18 (64), 23, 24, 25 (37), 26 (38), 27, 28, 43, 44, 45 (39), 46 (40). Then, curiously, if you extract the nuclear hexagrams out of those in the same manner you end up with hexagrams 1, 2, 11, and 12, instead of 1, 2, 63, and 64 in the equivalent procedure using nuclear trigrams. Clearly that's a significant pattern, indicating the procedure is just as valid. And expanding the nuclear digrams in 1, 2, 11, and 12 yields exactly the same hexagrams, whereas expanding the nuclear trigrams in 1, 2, 63, and 64 the former two remain the same while the latter two alternate. The nuclear hexagrams recognised today are currently trigram-centric; when you form a nuclear hexagram from nuclear digrams instead you have another pattern to consider that is just as interesting, if not more so.

The tetragrams above are also the solely yin-yang subset of the 81 tetragrams of the Taixuanjing, the whole set of which is formed from the combination of yin and yang lines and a third type of line broken twice, representing the 'three powers' or sancai, namely Heaven (yang), Earth (yin), and Human (broken twice). See also the rectangular diagram showing the 16 yin-yang tetragrams in Before Heaven order in the row immediately above the eight trigrams.

Trigram arrangements

The first two scans below both show the Before Heaven (xiantian) or Fuxi arrangement on the left page and the After Heaven (houtian) or King Wen arrangement on the right. The bottom line of each trigram is the inner line. The third scan shows the two arrangements concentrically, with Before Heaven on the inside, and the fourth shows concentric rings with Before Heaven on the outside and both circles turned 90° clockwise on the page:

ztd1046_1047 also shows the Luoshu diagram, the 'Luo (river) writing', in the centre of both circles. Alternative translations for 'Before Heaven' are 'Earlier Heaven' and 'Preceding Heaven', while 'After' can appear as 'Later' and 'Succeeding'. The Before Heaven diagram is most easily recognised from qian, usually at the top, being opposite kun. Then notice that all the trigrams opposite each other are similarly complementary or 'laterally linked' (pantonggua), meaning one has a yang line where the other has a yin line and vice versa. This means, in the 'family relationships' notion of the trigrams, that father is opposite mother, eldest son opposite eldest daughter, middle son opposite middle daughter, and youngest son opposite youngest daughter.

(One should beware of casually identifying the After Heaven diagram from li, usually at the top, being opposite kan, because they are also opposite each other in the Before Heaven diagram. In the After Heaven diagram kun and qian are at 90° to each other in the right semicircle.)

FAMILY RELATIONSHIP TRIGRAMS BY GENDER:

The sons have a single yang line, the daughters a single yin line. These correspond to their position in the family hierarchy, the eldest or first son or daughter being yang or yin at the bottom, and so on for middle or second, youngest or third.

Arthur Waley’s 1933 essay ‘The Book of Changes’

This 22-page essay on the Yijing, which introduced to the west the new approach of 'context criticism' that was gaining ground among Chinese intellectuals, contains some astoundingly beautiful ideas. It was first published in 'The Bulletin of the Museum of Far Eastern Antiquities', No. 5, Stockholm 1933. It was republished as an off-print in 1937, from which these scans are taken. So far as I know the work never appeared again. Waley's essay is a genuinely exciting read, and it is a pity he never returned to write further on the Book of Changes in his long career (he was born in 1889 and died 1966). I discuss some of the ideas contained in this essay in The Mandate of Heaven. The scans are on average 220 Kb.

I have also 'bound together' the scans into a PDF: waley.pdf (4.85 Mb, right-click and choose 'Save Link As…' if you wish to download). In this form the essay is a lot easier to print out. Make sure that 'Shrink oversized pages to paper size' is checked in the print dialog box. (The Warring States Project compiled a hexagram index to Waley's essay.)

Note 1: An interesting 12-pointed star

The 'Zhouyi Tushi Dadian' has a surprising number of diagrams relating to the 12-hexagram bigua sequence, which correlates 12 hexagrams showing the fall and rise of yin and yang with the 12 months and the 12 'Earthly Branches'. One diagram has at the centre of the circle a unicursal 12-pointed star. By following the line round in either direction the hexagrams connected form a fascinating sequence. Note that in this diagram the bottom line of each hexagram is outermost; in many circular diagrams the bottom line is innermost.

Take, for example, the sequence formed by starting at hexagram 1 and following the star around in an anti-clockwise direction (sequence below from top left to bottom right):

The pattern is easy to see but hard to describe. Let's look at the pattern starting from hexagram 1 and following around the unicursal 12-pointed star clockwise:

If you can't quite see it try following it through every second hexagram. You have a criss-cross interweaving, as it were, of the bigua sequence. Here is the first diagram with the interweaving shown:

Following hexagram 1 (all yang) going backwards or forwards in the normal bigua sequence you would have a hexagram consisting of five yang and one yin (43 or 44), with the solitary yin line at top or bottom (exiting or entering), as shown on this isolated section of the sequence:

but in the sequence formed by following the unicursal star (i.e., across the row in the block diagrams above) you have the complementary hexagram, five yin with one yang at top or bottom (23 or 24):

And this pattern of 'crossing over' complementary hexagrams is followed throughout. To put it another way, the hexagram above or below every second hexagram in the blocks of 12 is the hexagram that would normally follow in the actual bigua sequence, but they are swapped over because the unicursal 12-pointed star effectively skips a hexagram by crossing over to its complement, which, you will notice by looking again at the original Chinese diagram (ztd1165), is diametrically opposite in the circle of 12. This can be illustrated schematically on a block diagram:

The hexagram below every second hexagram in the top row it is the hexagram that would normally follow in the bigua sequence.

There is another diagram in the 'Zhouyi Tushi Dadian' showing a 12-pointed star, in this the hexagrams aren't shown but the 12 Earthly Branches are, which are also labelled in the first diagram.

Note 2: An old Yijing mystery solved

A paper by Edward Hacker and Steve Moore – 'A brief note on the two-part division of the received order of the hexagrams in the Zhouyi' – looks to have solved an old Yijing mystery. The paper was published in the June 2003 issue of the 'Journal of Chinese Philosophy' (30:2, pp 219–221). I believe Ed Hacker arrived at the solution by his own thinking. He shared it with Steve Moore, who looked through various Chinese works and discovered a diagram showing the idea was known in the Yuan (Mongol) dynasty.

In short, people have long wondered why the 64 hexagrams in the received order have been divided into two unequal parts, the first part containing 30 hexagrams and the second 34. A number of theories have been put forward, but I believe the Hacker & Moore solution is the correct one, which is backed up by a diagram in the 'Zhouyi Tushi Dadian' they have cited from page 601 (the original comes from the 'Zhouyi Qimeng Yizhuan' by Hu Yigui, born 13th century). I have found a further diagram on page 762 showing the same idea.

Essentially, the principle rests on this: some hexagrams are the same upside down whereas other hexagrams are a different hexagram when inverted. If you look at the scan of ztd601 you will see two rows of 18 hexagrams, and notice that the hexagrams that are different when inverted have the hexagram name written upside down above them (the table reads from right to left, with hexagram 1, Qian, upper right). This is the secret of it, a single hexagram is made to represent two hexagrams when its inverse differs. There are eight hexagrams the same both ways up, occurring in the following pairs: 1/2, 27/28, 29/30, and 61/62. If you look now at the diagram you can see that six of these hexagrams occur in the top row of 18 hexagrams while only two appear in the bottom row of 18. This means that the top row represents 30 individual hexagrams while the bottom row accounts for 34 hexagrams. This very clever and yet simple arrangement appears to be the reasoning behind the unequal division, which is actually an equal division when 'dual hexagrams' are used in this way. The same principle is also shown in ztd762.

Addendum, May 2009 – I've now uploaded the original paper in PDF, as it's always interesting to see how findings were first presented. I might also note that this idea must have already been thought obvious by Bent Nielsen, since he mentions it in passing on page 83 of his 2003 book 'A Companion to Yi Jing Numerology and Cosmology' without any great fanfare, presumably writing before the Hacker/Moore paper was published.

Addendum, August 2010 – It turns out that the 'Journal of Chinese Philosophy' had published the solution thirteen years earlier in their September 1990 issue: Larry J Schulz, 'Structural motifs in the arrangement of the 64 gua in the Zhouyi' (17.3, pp 345–358). In this article [PDF] it is shown that Lai Zhide (1525–1604) offered the same explanation for the unequal division.

YIJING DAO