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chrislofting
(deceased)
- Joined
- Nov 19, 1971
- Messages
- 394
- Reaction score
- 3
Hi all,
[What is presented here is a property of recursion that is reflected in interpretations of hexagrams pairs etc in the I Ching].
A tool useful in computer programming is that of 'masking'. Basically one uses a pattern of 'bits' (0s and 1s) to draw-out a pattern in a particular sequence of bits. We can detect this process at work in the I Ching through our use of recursion where we have:
[0]
[1] yin (0)/ yang (1)
[2] 00, 01 / 10, 11 [digrams]
[3] 000, 001, 010, 011 / 100, 101, 110, 111 [trigrams]
...
...
[6] 000000 ..... / ..... 111111 [hexagrams]
Thus each level gives us a finer set of distinctions that are the PARTS of the WHOLE at [0]. (also see graphic - http://pages.prodigy.net/lofting/btree.png )
The process of recursion ensures the whole is in all parts (each level is in fact the whole just re-presented with finer details) and that includes the prime distinction at [1] above such that at level [3] we find PAIRS of trigrams that reflect interpretations of the trigrams from the perspective of level [1], the basic yin/yang pair.
Thus at level [3] we have pairings of (000,001), (101,011), (100,101), (110,111) interpreted in the context of the general qualities of [1]. This means that in the pair 000,001 the 000 element reflects qualities of 'yin-ness' compared to the qualities of 001 that reflect qualities of 'yang-ness' where these differences fall within the bounds of the sameness of both elements, namely their initial bits of 00 - the top line is thus the 'difference'.
This interpretation is applied across all of the above pairs allowing for detailed analysis of the differences in the elements of these pairs created by the process of recursion.
Given this 'pair perspective' we can also apply level [2] as a mask in that it draws out the qualities from sets of fours, quartets, as does the application of level [3] that draws out qualities of sets of eights - octets.
When we move to level [6], the level of the 64 hexagrams, so we have five previous levels usable as filters for interpreting differences (and samenesses) in hexagram relationships. Thus, for a basic analysis of 64-hexagram sequences we have at least(a) the qualities of the individual hexagrams (and so each hexagram can be interpreted as a whole, as T'ai chi, - level [0]) and (b) the shared qualities of pairs of hexagrams as determined by the nature of the pair at [1]. IOW the pair at level [1] act as a mask to bring out relationships in the hexagram pairs at level [6].
In the binary sequence of the I Ching the pair at level [1] reflects the 'pure' differences of, the competitive nature of, yin vs yang as well as the cooperative nature of yin and yang. The differences are LOCAL at level [6] focusing on pairing adjacent hexagrams as in hex 02 - 000000 compared to hex 23, 000001 where the difference is in the top line and reflects subtle differences in concepts of integration (yin top line) vs differentiation (yang top line). As we move 'outwards' from these pairs so the differences become increasingly global until we reach the level of pairing hex 02 ( 000000 at one end of the sequence) with hexagram 01 (111111 at the other end of the sequence) where the difference is globally 'opposite' (light vs dark) but also globally 'cooperative' (male + female).
What we notice here is that the poles of the 64-hexagram sequence, level [6], reflect the properties of the generic pairing at level [1] - thus at [1] I have '0/1' whereas at [6] I have '000000/111111' - IOW the generic quality remains constant.
Thus, for the eight hexagrams of the binary sequence of hexagrams starting at the hexagram 02 end (000000) we have:
02, 23, 08, 20, 16, 35, 45, 12......
Applying the level [1] filter, so in the pair of 02/23, 02 is to 23 as 02 is to 01, 23 is to 02 as 01 is to 02. Or 08 is to 20 as 02 is to 01 etc etc to the other end of the sequence where we have 43 is to 01 as 02 is to 01 (but limited to a top line difference). With the association of 'integrating' to yin and 'differentiating' to yang so hexagrams 02 and 23 are BOTH reflective of devotion to others/another (determined by the base trigram) but differ at the top line where the yin line of 02 reflects a focus on devotion expressed through integration whereas the yang line of 23 reflects a focus on devotion expressed through differentiation through the act of 'pruning', of cutting back the chaff to reveal the wheat ('stripping the bed' where the bed symbolises what one 'rests' upon - one's belief system)
This particular order of hexagrams, derived from recursion of yin/yang gives us fundamental relationships of yin/yang described at level [1] as 'yin/yang' and at level [6] as whole hexagrams but also as pairs reflecting the fundamental yin/yang relationship. As such we can order the sequence of hexagrams into relational pairs that move from a tight association to a distant opposite/complementary association e.g.
02, 23
02, 08
02, 20
02, 16
...
...
02, 01
What is of interest with the 'naturally' derived sequence of 64 hexagrams, where we have applied recursion to yin/yang, is that if I rotate all of the hexagrams in the sequence I will derive a new sequence which is in fact the sequence of changing line combinations possible through the hexagrams of 01 or 02 (depending on which direction you read the sequence - see the example for hexagram 01 - http://pages.prodigy.net/lofting/lofting/h01lnx.html).
Thus, for the eight hexagrams of the binary sequence of hexagrams starting at the hexagram 02 end we have:
02, 23, 08, 20, 16, 35, 45, 12......
Rotate these and we have:
02, 24, 07, 19, 15, 36, 46, 11 where this sequence reflects the initial eight hexagrams derived through applying recursion to hexagram 02, where the order of change is:
02 - no change
24 - change line 1 of 02
07 - change line 2 of 02
19 - change lines 1 and 2
15 - change line 3
36 - change lines 1 and 3
46 - change lines 2 and 3
11 - change lines 1, 2, and 3
..
..
..
..
01 - change all lines of 02
(these two types of sequences are shown for all hexagrams in http://pages.prodigy.net/lofting/icmatrix.html)
What is of interest here is that, from the derivation of the binary sequence of hexagrams I can use level [1] of that derivation to interpret hexagram pairs at level [6]. Rotate that level [6] sequence and I get a sequence for changing line patterns through hexagrams 01/02, a sequence also explicitly derivable from applying recursion to either hexagram 01 or hexagram 02. Implicit here is that by applying recursion to *any* hexagram and rotating the resulting sequence I derive another sequence that in some way identifies pairs of hexagrams that share a theme determined by the hexagrams at the poles of the sequence - in other words this derived sequence is equivalent of the 'natural' binary sequence and as such reflects the same properties.
IOW - for hexagram 23, the first eight hexagrams in the changing line sequence (reflecting recursion of 23) are:
23, 27, 04, 41, 52, 22, 18, 26... to 43
Rotate these gives us:
24, 27, 03, 42, 51, 21, 17, 25.... to 44
What is this sequence? Functionally it is the equivalent of the 'naturally derived' binary sequence of the I Ching that focuses on hexagrams 01/02 but is here applied to the pairing of 24/44 - IOW the pairs in this sequence reflect a 24/44 masking that brings out the qualities of 24/44 across all of the hexagrams. For example, the 03,42 relationship is 'about' the newness of 24, the 'beginning' (or 'born again', return to), interacting with the element of transition (seduction, persuation to the 'other' side etc) of 44 expressed in the 'augmentation' of 42.
In the pairing of 17, 25 we can identify the same process where 17 focuses on a 'new' faith, a new belief, and 25 focuses on the expression and so an act of persuation (or attempted). Overall the particular sequence reflects the rule:
X is to Y as 24 is to 44, Y is to X as 44 is to 24.
Thus in the 'true' binary sequence, derived from recursion of yin/yang, the pairs at level [6] reflect X is to Y as 01 is to 02, 02 is to 01. Thus 02,23 is a small difference of devotion issues - integrating (02) vs differentiating (23), whereas 02, 01 is a huge difference in integration overall (02) vs differentiation over all (01).
In the traditional sequence, where the sequence is given as 01 to 64 and reflects a derivation of the sequence through recursion (see http://pages.prodigy.net/lofting/cracked.html), the focus is of X is to Y as 01 is to 64, 64 is to 01. (and so 01 is to 02 as 01 is to 64, 03 is to 04 as 01 is to 64, 05 is to 06 as 01 is to 64 etc etc etc)
Each possible recursively-derived sequence of hexagrams serves as a tool for analysis of relationships of hexagrams through analogy at the particular level as well as at the general level. This capability stems from the method used by the species with which to derive information - recursion (see the IDM pages - http://pages.prodigy.net/lofting/idm001.html)
Note the above is no complete - there are issues re the properties of the hexagram sequences of changing-line patterns and their link to five-phase theory (see http://pages.prodigy.net/lofting/icfive0.html)
Chris.
http://pages.prodigy.net/lofting
[What is presented here is a property of recursion that is reflected in interpretations of hexagrams pairs etc in the I Ching].
A tool useful in computer programming is that of 'masking'. Basically one uses a pattern of 'bits' (0s and 1s) to draw-out a pattern in a particular sequence of bits. We can detect this process at work in the I Ching through our use of recursion where we have:
[0]
[1] yin (0)/ yang (1)
[2] 00, 01 / 10, 11 [digrams]
[3] 000, 001, 010, 011 / 100, 101, 110, 111 [trigrams]
...
...
[6] 000000 ..... / ..... 111111 [hexagrams]
Thus each level gives us a finer set of distinctions that are the PARTS of the WHOLE at [0]. (also see graphic - http://pages.prodigy.net/lofting/btree.png )
The process of recursion ensures the whole is in all parts (each level is in fact the whole just re-presented with finer details) and that includes the prime distinction at [1] above such that at level [3] we find PAIRS of trigrams that reflect interpretations of the trigrams from the perspective of level [1], the basic yin/yang pair.
Thus at level [3] we have pairings of (000,001), (101,011), (100,101), (110,111) interpreted in the context of the general qualities of [1]. This means that in the pair 000,001 the 000 element reflects qualities of 'yin-ness' compared to the qualities of 001 that reflect qualities of 'yang-ness' where these differences fall within the bounds of the sameness of both elements, namely their initial bits of 00 - the top line is thus the 'difference'.
This interpretation is applied across all of the above pairs allowing for detailed analysis of the differences in the elements of these pairs created by the process of recursion.
Given this 'pair perspective' we can also apply level [2] as a mask in that it draws out the qualities from sets of fours, quartets, as does the application of level [3] that draws out qualities of sets of eights - octets.
When we move to level [6], the level of the 64 hexagrams, so we have five previous levels usable as filters for interpreting differences (and samenesses) in hexagram relationships. Thus, for a basic analysis of 64-hexagram sequences we have at least(a) the qualities of the individual hexagrams (and so each hexagram can be interpreted as a whole, as T'ai chi, - level [0]) and (b) the shared qualities of pairs of hexagrams as determined by the nature of the pair at [1]. IOW the pair at level [1] act as a mask to bring out relationships in the hexagram pairs at level [6].
In the binary sequence of the I Ching the pair at level [1] reflects the 'pure' differences of, the competitive nature of, yin vs yang as well as the cooperative nature of yin and yang. The differences are LOCAL at level [6] focusing on pairing adjacent hexagrams as in hex 02 - 000000 compared to hex 23, 000001 where the difference is in the top line and reflects subtle differences in concepts of integration (yin top line) vs differentiation (yang top line). As we move 'outwards' from these pairs so the differences become increasingly global until we reach the level of pairing hex 02 ( 000000 at one end of the sequence) with hexagram 01 (111111 at the other end of the sequence) where the difference is globally 'opposite' (light vs dark) but also globally 'cooperative' (male + female).
What we notice here is that the poles of the 64-hexagram sequence, level [6], reflect the properties of the generic pairing at level [1] - thus at [1] I have '0/1' whereas at [6] I have '000000/111111' - IOW the generic quality remains constant.
Thus, for the eight hexagrams of the binary sequence of hexagrams starting at the hexagram 02 end (000000) we have:
02, 23, 08, 20, 16, 35, 45, 12......
Applying the level [1] filter, so in the pair of 02/23, 02 is to 23 as 02 is to 01, 23 is to 02 as 01 is to 02. Or 08 is to 20 as 02 is to 01 etc etc to the other end of the sequence where we have 43 is to 01 as 02 is to 01 (but limited to a top line difference). With the association of 'integrating' to yin and 'differentiating' to yang so hexagrams 02 and 23 are BOTH reflective of devotion to others/another (determined by the base trigram) but differ at the top line where the yin line of 02 reflects a focus on devotion expressed through integration whereas the yang line of 23 reflects a focus on devotion expressed through differentiation through the act of 'pruning', of cutting back the chaff to reveal the wheat ('stripping the bed' where the bed symbolises what one 'rests' upon - one's belief system)
This particular order of hexagrams, derived from recursion of yin/yang gives us fundamental relationships of yin/yang described at level [1] as 'yin/yang' and at level [6] as whole hexagrams but also as pairs reflecting the fundamental yin/yang relationship. As such we can order the sequence of hexagrams into relational pairs that move from a tight association to a distant opposite/complementary association e.g.
02, 23
02, 08
02, 20
02, 16
...
...
02, 01
What is of interest with the 'naturally' derived sequence of 64 hexagrams, where we have applied recursion to yin/yang, is that if I rotate all of the hexagrams in the sequence I will derive a new sequence which is in fact the sequence of changing line combinations possible through the hexagrams of 01 or 02 (depending on which direction you read the sequence - see the example for hexagram 01 - http://pages.prodigy.net/lofting/lofting/h01lnx.html).
Thus, for the eight hexagrams of the binary sequence of hexagrams starting at the hexagram 02 end we have:
02, 23, 08, 20, 16, 35, 45, 12......
Rotate these and we have:
02, 24, 07, 19, 15, 36, 46, 11 where this sequence reflects the initial eight hexagrams derived through applying recursion to hexagram 02, where the order of change is:
02 - no change
24 - change line 1 of 02
07 - change line 2 of 02
19 - change lines 1 and 2
15 - change line 3
36 - change lines 1 and 3
46 - change lines 2 and 3
11 - change lines 1, 2, and 3
..
..
..
..
01 - change all lines of 02
(these two types of sequences are shown for all hexagrams in http://pages.prodigy.net/lofting/icmatrix.html)
What is of interest here is that, from the derivation of the binary sequence of hexagrams I can use level [1] of that derivation to interpret hexagram pairs at level [6]. Rotate that level [6] sequence and I get a sequence for changing line patterns through hexagrams 01/02, a sequence also explicitly derivable from applying recursion to either hexagram 01 or hexagram 02. Implicit here is that by applying recursion to *any* hexagram and rotating the resulting sequence I derive another sequence that in some way identifies pairs of hexagrams that share a theme determined by the hexagrams at the poles of the sequence - in other words this derived sequence is equivalent of the 'natural' binary sequence and as such reflects the same properties.
IOW - for hexagram 23, the first eight hexagrams in the changing line sequence (reflecting recursion of 23) are:
23, 27, 04, 41, 52, 22, 18, 26... to 43
Rotate these gives us:
24, 27, 03, 42, 51, 21, 17, 25.... to 44
What is this sequence? Functionally it is the equivalent of the 'naturally derived' binary sequence of the I Ching that focuses on hexagrams 01/02 but is here applied to the pairing of 24/44 - IOW the pairs in this sequence reflect a 24/44 masking that brings out the qualities of 24/44 across all of the hexagrams. For example, the 03,42 relationship is 'about' the newness of 24, the 'beginning' (or 'born again', return to), interacting with the element of transition (seduction, persuation to the 'other' side etc) of 44 expressed in the 'augmentation' of 42.
In the pairing of 17, 25 we can identify the same process where 17 focuses on a 'new' faith, a new belief, and 25 focuses on the expression and so an act of persuation (or attempted). Overall the particular sequence reflects the rule:
X is to Y as 24 is to 44, Y is to X as 44 is to 24.
Thus in the 'true' binary sequence, derived from recursion of yin/yang, the pairs at level [6] reflect X is to Y as 01 is to 02, 02 is to 01. Thus 02,23 is a small difference of devotion issues - integrating (02) vs differentiating (23), whereas 02, 01 is a huge difference in integration overall (02) vs differentiation over all (01).
In the traditional sequence, where the sequence is given as 01 to 64 and reflects a derivation of the sequence through recursion (see http://pages.prodigy.net/lofting/cracked.html), the focus is of X is to Y as 01 is to 64, 64 is to 01. (and so 01 is to 02 as 01 is to 64, 03 is to 04 as 01 is to 64, 05 is to 06 as 01 is to 64 etc etc etc)
Each possible recursively-derived sequence of hexagrams serves as a tool for analysis of relationships of hexagrams through analogy at the particular level as well as at the general level. This capability stems from the method used by the species with which to derive information - recursion (see the IDM pages - http://pages.prodigy.net/lofting/idm001.html)
Note the above is no complete - there are issues re the properties of the hexagram sequences of changing-line patterns and their link to five-phase theory (see http://pages.prodigy.net/lofting/icfive0.html)
Chris.
http://pages.prodigy.net/lofting