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Subject: 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)
   
                             [levels.gif]
   
   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.