A hexagram is a symbol made-up of six stacked lines. It can also be considered as a symbol made-up of two three-line symbols, called trigrams, one on top of the other.
In the I Ching, a line has one of two possible forms, a fixed line linked to the expansive concept of yang, and a 'broken' line linked to the contractive concept of yin. These concepts, yin and yang, form the aspects of a whole, or more specifically, any aspects of the whole that form a pair, or are considered to form a pair; this includes the pairing of whole/aspects. (See sample list of yin/yang pairings)
In the traditional I Ching, a hexagram is built by the creation of a line from a 'random' process whilst thinking
of a question. Too many, this is a 'synchronistic' process, where synchronicity can be considered as the linking
of apparent random events that generates 'meaning'; this linking process happens to be a property of metaphor.
A modern-day form would be some of De Bono's 'lateral thinking' concepts.
Each line created has four possible states:
The most common way of creating a hexagram is through the tossing of three coins, the head/tail outcome of which determines the character of a line. Since there are six lines, this is done six times, building the hexagram from the bottom upwards, whilst 'holding' a question in one's mind. The resulting 'meaning' of the hexagram is then considered within the context of the question.
When tossing coins (the commonest method) the head/tail results create the lines thus:
3 tails means a changing yang line, symbolized as ----O----
3 heads means a changing yin line, symbolized as --- X ---
2 heads and a tail is a stable yang line, symbolized as ---------
2 tails and a head is a stable yin lin, symbolized as --- ---
Usually one would think that yin is even, yang is odd. Yang is the head, yin is the tail. Since yin/yang manifest
2/3 (1 = t'ai chi) so a yang is either 9 (changing) or 7(fixed) and a yin is either 6 (changing) or 8 (fixed).
These numeric associations comes from the yarrow stick method of determining a line.
BUT then if so, using heads=3, tails=2 an unchanging yang line should = 8 (3+3+2) which is an EVEN number. You
need to link tails = 3 and heads = 2 to map the coins to the yarrow stick.
3 heads = 6 (changing yin)
3 tails = 9 (changing yang)
2 heads + a tail = 7 (all yang)
2 tails + a head = 8 (all yin)
thus the odd numbers go with yang and the even numbers go with yin. Note however that the intuitive association
of heads = yang AND odd, tails = yin AND even is 'screwed' :-).
There is no problem with doing the reverse, it just means that the odd/even numbers get mixed up rather than the
head/tails getting mixed up.
If you keep to numeric terms then a 9 is a changing yang line (Greater Yang). A 7 is a non changing yang line (Lesser
Yang) a 6 is a changing yin line (Greater Yin) and an 8 is an unchanging yin line (Lesser Yin). you need to manipulate
whatever system you use to ensure these numeric associations.
The resulting symbol can look like this:
--- X --- --------- ----O---- --- --- --- --- is changing into --- --- --------- --------- --------- --------- --- --- --- ---
The left-hand symbol is the hexagram which is changing into the right-hand symbol. Each of these hexagrams is given a number and linked to some text that describes what the hexagram represents. For the questioner, the above implies a changing process.
In this site a slightly different method is used, in that you are asked questions rather than to toss coins or get the computer to generate a random number; we thus combine a causal approach with a synchronous approach. We believe that by doing this one get's a far better understanding of the processes involved, especially the structure of metaphor and how we humans deal with wholes and their aspects. This approach does extend the consultation process, but it leads one into a deeper analysis of a situation and gives better results with which to work. (there is scope to feed-in coin toss data if you wish.)
The origin of the traditional numbering of the hexagrams is unknown and seems to bare no 'logical' ordering
(although there may be a semantic influence - see Comments on the Traditional Sequence.
We can however derive a number from the line structure of a hexagram. This is done by considering each line
position representing a power of 2. A line in a position determines if the number for that position is used
or not. The rule is, for each position filled by a yang (or changing yang) line, we add it's number to any others
of the same type (yang lines in the position). Thus the hexagram with all yin lines has a value of 0, whilst the
hexagram with all yang lines has a value of 63.
The line position numbers are:
top - 1
5th - 2
4th - 4
3rd - 8
2nd - 16
bottom - 32
In the hexagram table, these numbers are paired with the 'traditional' numbers. This pairing of numbers is intentional, since most references use the order of the hexagrams according to the traditional method - unfortunate, since the structure of the hexagrams can help lead to a number without having to lookup a trigram table - a common tool in I Ching books.
You will find that in this site, I use the traditional numbers to maintain a degree of 'continuity' with the past, but I also use the binary number to get around. At all times assume the traditional number is being used unless told otherwise (like here).
(for the binary 'purists' note that the order is top down and thus limited, rather than a more 'logical' bottom-up sequence which would be open-ended).
The traditional I Ching gives each trigram a character, and each hexagram can be considered as a description of one character (the top trigram) within the context set by the other (bottom trigram).
Through the centuries, the 'meanings' of these relationships have been considered and written-down. Their 'success' is due to the manner of analysis (dichotomy) being common across all systems with dichotomous roots; the I Ching is a metaphor for wholes and aspects categorization within the process of dichotomous analysis; it thus 'resonates' with any other system based on dichotomous categorization - we 'see' the I Ching in mathematics just as we see mathematics in the I Ching. In fact what we detect is the resonance of the metaphor template; common to both systems, and thus allowing for the ease in making analogies.