The Traditional 'Sequence' of the I Ching : its Source and Meaning

(a code cracked)

(Copyright © 2001 C.J.Lofting)

Introduction

The traditional sequence of hexagrams found in the I Ching has for some time been considered 'unusual'. Coming from a software background my own preference has been for the Fu Hsi ordering that is derived through recursion where each level generates a set of symbols from basic yin/yang (level 1) to 64 hexagrams (level 6).(See diagram below, see later text for comments on additional material in the diagram)

The Fu Hsi pattern, derived vertically, develops into a left-right sequence of hexagrams at level 6 with an ORDINALITY bias in that each hexagram is the quantitative successor of the previous when 'read' left-right. Thus the numbering does not in any way 'map' to the traditional hexagram numbering. For example, starting with the traditional hexagram 1, the first sequence of eight hexagrams in binary order are those with the traditional numbers of 1,43,14,34,9,5,26,11. The binary numbering is 63,62,61,60,59,58,57,56...

In reflecting on the traditional sequence, and currently smitten by the cardinality/topology 'bug' (and so thinking topology and more vertical than horizontal), I realised that the 'unusual' pattern in the traditional sequence, where hexagram PAIRS are formed, actually reflects the same derivation process as used in the FU HSI patterns!

The clue was the pairing in that they reflect the end-pairs of a binary tree (as reflected in the cell pairs at level 6 in the above diagram; thus a level 5 cell has two cells below it in level 6 and these cells are occupied by a hexagram pair). The pairing in the traditional sequence is simple:

01,02 03,04 05,06 07,08 etc

There IS a weak structural aspect, but working from a cardinality emphasis I ignored the lines, the often favoured ordinality emphasis within hexagrams, and went for an 'unknown' qualitative emphasis driving the derivation of the sequence from a vertical perspective, IOW the left-right SEQUENCE at level 6 (see diagram) was NOT intentional, it is an artifact, the sequence developed from the vertical, top-down derivation of the hexagrams and these hexagrams were THEN numbered 1-64. left to right.

From this process I have been able to determine that the traditional sequence reflects ALCHEMY with a distinct semantic emphasis on PURE -- MIXED.

Method

The traditional I Ching has 64 hexagrams numbered 1 to 64. The numbering does not seem to relate in any refined way to any semantic element. There is a structural pattern in the sequence but this is only limited to PAIRS of hexagrams and as such there is a 'gap' between the pairs that is not easy to 'fill' with precise meanings; there is a weak degree of semantic link in the sequence due to the method of derivation itself in that the method contains a 'begin-end' emphasis that is subtly 'encoded' in any process based on that method.

Focusing on the first eight hexagrams, we see the following pairings:

01,02 03,04 05,06, 07,08

Structurally, the 3,4 5,6 7,8 pairings reflect 180 degree rotations; the 1,2 reflect this at a more semantic level.

Working from a cardinality aspect, where meaning is not strongly related to line structure, I applied the principle that the traditional sequence of 64 reflects a binary tree level equated with 2^6 (2 raised to the 6th power). This level, labeled level 6 in the above diagram, is the 'last' level in creating 64 symbols out of yin/yang combinations, or any other qualitative categorisation based on the same principles, where we have moved from level 1 (top) to level 6.

If you work backwards and so 'up' the tree, so level 5 contains 32 cells, level 4 contains 16, level 3 contains 8 etc.

The cells at level 5, from a SEMANTIC perspective, capture the general essence of the cells, and so pairs of hexagrams that are derived from level 5 into level 6. In the traditional sequence of the I Ching, the first two hexagrams, numbered 1 and 2, emphasise the concept of PURITY where hexagram 1 emphasises pure 'yang' and hexagram 2 emphasises pure 'yin'. Thus folding these two hexagrams back into the cell above them in level 5 generalises the meaning to an undifferentiated concept of 'purity'.

Applying this folding to the first eight hexagrams of the I Ching gives us a set of four general meanings at level 5, filling the first four cells, left to right; fold these cells back to level 4 and you have two even more general meanings; fold these back to level 3 and you have ONE general meaning. What is noteworthy is that in the Fu Hsi system, level 3 reflects the level of the trigrams and these are fundamental sources of 'meaning' that get converted into composite forms as hexagrams. Thus we are working from a trigram perspective, or a qualitative category that is mapped in the same way.

If we apply the same folding 'rule' to the whole sequence of hexagrams, at level 3 we end up with 8 'meanings', as yet undefined other than two general meanings that reflect 'purity' in level 3 cell 1 and 'mixed' in level 3 cell 8. The only way we can determine the meanings more precisely, since we are working backwards, is to mark at each level the embedded hexagram numbers from level 6 and try to identify a common GENERAL theme throughout..

Specific Themes Detection

For the first cell at level 5, the cell into which hexagrams 01 and 02 have been folded back into, where we identified this level 5 cell as manifesting the general concept of 'purity', we can place the bracketed hexagram numbers thus: ((1)(2)). This symbolism manifests a POTENTIAL, the cell contains the bud that branches into the next level as the fully expressed hexagrams 1 and 2.

Thus level 5 for the first four cells, eight hexagrams, two hexagrams per cell, looks like this:

((1)(2)), ((3)(4)), ((5)(6)), ((7)(8))

To fold them back to level 4 we just group the four into two where these two fill the first two cells of level 4:

(((1)(2)), ((3)(4))) , (((5)(6)), ((7)(8)))

To fold them back into level 3 we group the two into a single octet:

((((1)(2)), ((3)(4))), (((5)(6)), ((7)(8))))

What this 'means' is that at level 3 lies the root context in which these 8 proto-hexagrams exist, the meaning which unites these hexagrams in some way.

So far all we have done is apply a more syntactic bias, we need to validate the conjecture through analysis of any meaning encoded in the octets.

Validation

Since we are applying the Fu Hsi method of derivation, we apply one of the principles of Fu Hsi, namely that of opposition/complementarity. Applying this principle to the octets, there should be semantic level meaning when we oppose the the hexagrams within the octets by using reflection thus:

1,2,3,4 vs 5,6,7,8

or working from level 5, the more GENERAL level, we have ((1)(2)) ((3)(4)) vs ((5)(6)) ((7)(8)) where, for example ((1)(2)) reflects the GENERAL concept of 'purity'.

What this mapping 'says' is that 1,2 should oppose/complement 7,8 just as 3,4 should do the same for 5,6.

Note that the level 5 emphasis for the 1,2 blend was given as 'purity'. When we review the meanings of 7,8 we find that their joint meaning is 'unity' IOW MIXING.

If we now zoom-out to consider the full sequence from 1-64, we should find at that level the same general pattern, and we do:

01,02 purity (octet 1)-- 63,64 mixing (octet 8) This mapping format reflects the 'fractal' nature where the same meanings are applied at each level at finer details.

As in the Fu Hsi derivation of binary order so the SAME principle has been applied to some as yet not fully determined qualitative root meaning that obviously deals with alchemy and the emphasis on purity -- mixing. I have been able to identify the semantic influence on the octets that is derived from level 3, the level we usually associate with the trigrams. This was possible since we can apply patterns discovered in the Fu Hsi sequence to the King Wen due to the common background. The eight octets will within themselves reflect the SAME mixing correspondences (blend, bond, bound, bind). Here are the octets together with their overall emphasis:

01,02 03,04 05,06 07,08 - purity issues (01-08 oppose)

09,10 11,12 13,14 15,16 - gain issues (09-16 oppose)

17,18 19,20 21,22 23,24 - belief issues (17-24 oppose)

25,26 27,28 29,30 31,32 - involvement issues (25-32 oppose)

33,34 35,36 37,38 39,40 - tension release issues (33-40 oppose)

41,42 43,44 45,46 47,48 - foundation issues (41-48 oppose)

49,50 51,52 53,54 55,56 - loyalty issues (49-56 oppose)

57,58 59,60 61,62 63,64 - mixing issues (57-64 oppose)

The pairings in the octets all reflect the same basic semantics as in the 1,2 vs 7,8 and 3,4 vs 5,6 shown in the first row. Each octet has a subtle qualitative variation as we move through the sequence, octet at a time, from 'pure' emphasis to 'mixed' emphasis. Thus in octet 8, the most 'mixed' emphasising octet, 57 and 58 symbolise the 'pure' aspect of that octet compared to 63,64 emphasising the most mixed aspect of that octet, and when the whole sequence of octets are generalised so 63,64 serve as the 'most mixed' elements compared to the two hexagrams at the other end of the sequence -- 01 and 02, symbols of purity.

I have here listed out the pairs in each octet for clarity followed in brackets with the more specific 1:1 relationships:

Octet 1 - Purity issues:

01,02 (purity; singular) -- 07,08 (purity - group(also interpretable as mixing)) (1 to 8, 2 to 7)

03,04 -- 05,06 (3 to 6, 4 to 5)

Octet 2 - Gain issues:

09,10 -- 15,16 (9 to 16, 10 to 15)

11,12 -- 13, 14 (11 to 14, 12 to 13)

Octet 3 - Belief issues:

17,18 -- 23,24 (17 to 24, 18 to 23)

19,20 -- 21,22 (19 to 21, 20 to 22)

Octet 4 - Involvement issues:

25,26 -- 31,32 (17 to 24, 18 to 23)

27,28 -- 29,30 (25 to 32, 26 to 31)

Octet 5 -Tension release issues:

33,34 -- 39,40 (33 to 40, 34 to 39)

35,36 -- 37,38 (35 to 38, 36 to 37)

Octet 6 - Foundation issues:

41,42 -- 47,48 (41 to 48, 42 to 47)

43,44 -- 45, 46 (43 to 46, 44 to 45)

Octet 7 - Loyalty issues:

49,50 -- 55,56 (49 to 56, 50 to 55)

51,52 -- 53,54 (51 to 54, 52 to 53)

Octet 8 - Mixing issues:

57,58 -- 63,64 (57 to 64, 58 to 63)

59,60 -- 61,62 (59 to 62, 60 to 61)

As you will find, there are *strong* semantic relationships established when using this method of analysis, working with the concept that the so-called 'sequence' of the I Ching was not there to start with, it is an artifact of applying top-down generation of a semantic tree based on the distinction of PURE vs MIXED but from a qualitative emphasis rather than a rigidly structural emphasis -- structural patterns DO emerge (e.g. PURE is 1, 2 - all yin and all yang and MIXED is 63, 64, oscillating yin/yang lines showing MIXING) but the emphasis in deriving the 'traditional' sequence was on using Fu Hsi's method overlayed with more qualitative, topological, concepts than the rigid ordinality of the binary sequence.(I cannot, for example derive the six line symbol for heaven or earth out of the same general 'space' that I can by using the meanings without explicit symbolisms; the symbols in this case act to 'cloud' what is going on. where hex 1 and 2 come out of a general cell marked 'purity' at level 5 but cell 5 does NOT contain 5 protolines as it does in the binary sequence.)

The qualitative bias in these octets are reflected in the comparison of the NAMES, the ideograms, of the hexagrams, thus the purity in 01 is complemented/opposed by the emphasis on unity, combining with others in 8. This same pattern is reflected in the 02 to 07 mapping but note that 7 reflects the 'disciple' aspect of 2, to follow not lead (as in an Army obeys orders).

The 03 to 06 mapping reflects initial difficulties complemented by making compromises where making compromises requires MIXING with others whereas 03 has a more 'purest' emphasis.

The 04 to 05 emphasises the difference between the youth who does not wait, does not plan, compared to 05s emphasis on serving ones' dues, waiting for the 'right' moment -- 05 demands socialisation, mixing, 04 fights it to some degree.

More Reflections

A level 6 the pairs reflect 'yang/yin' patterns where interpretation is based on the first two hexagrams of the sequence (01,02) the first 'pure' pair - proactive/reactive, male/female, pure/mixed etc. (note that the I Ching would map 01 to pure and 02 to not so pure, it follows 01).

At level 6 we are mapping the expression of each element in a PAIR. At level 5 each element is not so clear, we see a general emphasis on 'pure' etc but we map in FOURS. Move up to the OCTET level and the same patterns but now over 8 .. move to the top and the same pattern but now over the whole 64. I would even say that there is a reverse pattern where you can see all pairs reflecting the purest of MIXED states i.e. (63,64).

I have always used the binary ordering a la Fu Hsi since I found so much in it but I never applied it to the traditional sequence since Fu Hsi has an explicit strong ordinal emphasis that I could not 'see' in the traditional sequence. My recent exposure to topology concepts and the work of Cantor and transfinite numbers and so cardinality acted to 'open-up' my mindset such that I could recognise pure 'semantic' processes that could not be expressed in an ordinal format (as in clear step-by-step derivation IN THE SYMBOLS). You have to suspend the ordinal bias to let out the cardinal and so understand how a set of symbols can be expressed with no EXPLICIT ordinal process involved. Thus the Fu Hsi derivation process works at an intuitive level that is hard to symbolise and can even be blocked by symbolisation; the ordinality in the form of lines in the hexagrams etc acted to hide full expression. The ordinal emphasis can act to hide, prohibit, spontanious expression which HAS an order but it is IMPLICIT. This is the difference between the male (ordinal bias - step-by-step, clear development path) and the female (cardinal bias - steps are there but implicit leading to a 'sudden' change, no clear detection of development) :-)

There is a concept of metonymy where the emphasis on making distinctions is based on part-for-whole processing. This reflects how our brain works with a multi task process of local distinctions (objects - parts/wholes) and general distinctions (relationships - all is linked together. This is implicit wholeness since only the local can express things explicitly) In the 'backwards' process we move from map (64 hexagrams) back to pairs, we move from metaphor to sub metaphor down to part-for-whole. Usually we move forewards (! - hard to not use ordinal terms!)

The process of making these distinctions causes us to use induction, to group local discrete experiences and from that create maps. With good maps you will often treat the map as if it was the territory. The map is a metaphor and in our case is in the form of the I Ching.

In all of this distinction making is a hidden level, that of our neurology in the form of our brain. It can only process data as 'object' or 'relationship', just like a computer hardware only 'sees' positive or negative voltage. This is too general for us to communicate and so we use language to help particularise.

This method we use has structure in that all meaning is contained in the method - thus when working with the I Ching we treat the I Ching as representing 'all there is'.

The beauty of the I Ching is that is closely maps the method our brain uses in that our brain processes data using dichotomies (pairs) and applies each dichotomy to itself to get refined meaning; out of the neurochemistry comes complex patterns of meaning.

In the 'old days' of direct experience, prior to the maps, the SAME method of determining meaning was used such that the experience of seasons in non-equitorial cultures would lead to the distinction of four seasons - in the equator it is two -- wet and dry. BUT there is a border area of APPROACHING wet or APPROACHING dry or RETREATING wet or RETREATING dry (hexagrams 19,20); thus even in 2s we find 4s - the difference is in 2s the other 2 are on the borders of wet/dry. Go further North or South and these borders expand into their own seasons and we find 4 (we can extend them into 8, as does the I Ching extend into 8 through the use of compasses etc)

Regardless of whether it is 2 or 4 or 8 we are talking binary mappings, powers of 2. The seasonal mappings introduce ordinality where X follows from Y; in cardinality we can have X seemingly out of nowhere.

The mapping of these experiences would lead to the binary distinctions being encoded into the maps as some sort of feeling and being binary the feelings at first would be X or Y. Culture then works on the border between the feelings, making 'finer' distinctions and so out of the 'middle' of these basic feelings come more 'seasonal' expressions.

These expressions however will always contain the 'root' binary elements such that these root elements influence our categorisations implicitly and when we work backwards we uncover the 'root' elements.

When using a binary tree to build our maps so novel expressions are associated with the explicit concepts but underneath is a constant. That constant enables us to detect the PAIRS in the traditional sequence -- we notice the proactive/reactive distinctions. That constant in the I Ching is the Fu Hsi METHOD of derivation; the binary 'sequence' acts as a guide - a template - for the more King Wen sequence where we move on from syntax and 'yin/yang' to sets of feelings such that we can derive the traditional sequence from thinking only of a feeling (pure/mixed) and from that derive a sequence where the hexagrams appear 'out of nowhere' in that we cannot detect clear ordinality at work until the last moment; as we find in complexity/chaos theories.

Since the moon is also seasonal (as in four to eight phases are used to identify the cycle) so its cycle will map into the I Ching (note that the 384 lines = number of days in a lunar year (13 months))

The I Ching in turn maps onto my template in that that template reflects the source of meaning for the SPECIES. Thus the object/relationship pattern is fundamental. In the binary 'sequence' we find the SAME PAIRING principle in that for all hexagrams with the trigram of the creative as base we have 1,43,14,34,05,09,26,11.

These actually group into 1+43, 14+34, 5+9, 26+11 and this pattern of grouping reflects the METHOD of derivation; this grouping pattern is the clue that derivation was not primary left-to-right/right-to-left but more top-down that LED us to the sequence.

There are many references to the King Wen distinctions as being overlayed onto the Fu Hsi distinctions and as we can see in my article on the traditional sequence this is so in that the Fu Hsi METHOD formed the backdrop for creating the sequence, what has not been made clear (or is 'hidden' in the texts) is to make the distinction of ordinal from cardinal such that you can detect the perspectives. Thus the western translations have always emphasises this ordinal pattern as dominant rather than it stemming from a cardinal process where we EXAGERATE the basic yin/yang distinctions by stacking the distinctions into trigrams etc etc

As you go through these octets and discover the patterns encoded by the originator of the sequence so you will be working with something that has perplexed I Ching enthusiasts for centuries. We have found the key and unlocked the door, we have thus discovered the source of the 'traditional' I Ching sequence and its numbering and from that discovery comes more work as we re-analyse the I Ching and the new connections, new associations, that the 'traditional' sequence has been shown to reflect.

Good Luck in your studies :-)

Chris Lofting.