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FYI....
-----Original Message-----
From: Chris Lofting [mailto:ddiamond@ozemail.com.au]
Sent: Wednesday, 27 February 2002 4:08
To: Ichingplus
Cc: Yijing_Iching
Subject: vertical vs horizontal binary sequences
Hi all,
I think we are getting close to 'something' so here are some items for your consideration:
Horizontal Binary (a sequence derived through recursion and here put into block form of eight octets - for full sequence format see level 6 of http://pages.prodigy.net/lofting/DIAG1.gif):
02 23 08 20 16 35 45 12 (base:earth)
15 52 39 53 62 56 31 33 (mountain)
07 04 29 59 40 64 47 06 (water)
46 18 48 57 32 50 28 44 (wind)
24 27 03 42 51 21 17 25 (thunder)
36 22 63 37 55 30 49 13 (fire)
19 41 60 61 54 38 58 10 (lake)
11 26 05 09 34 14 43 01 (heaven)
Vertical Binary (derived from within hex 01 line changes - http://pages.prodigy.net/lofting/binhex.html)
02 24 07 19 15 36 46 11 (top:earth)
16 51 40 54 62 55 32 34 (thunder)
08 03 29 60 39 63 48 05 (water)
45 17 47 58 31 49 28 43 (lake)
23 27 04 41 52 22 18 26 (mountain)
35 21 64 38 56 30 50 14 (fire)
20 42 59 61 53 37 57 09 (wind)
12 25 06 10 33 13 44 01 (heaven)
What is noticable here is the numbering in that each position in each block reflects the pairing we see in the traditional (aka king wen) sequence (e.g. 02 23 08 20 in the horizontal binary block maps to 02 24 07 19 in the vertical binary block.) IOW if I put each row from each block together the resulting pattern is all full rotations of hexagrams e.g. first row of each block:
02 23 08 20 16 35 45 12 (base:earth - horizontal top row)
02 24 07 19 15 36 46 11 (top:earth - vertical top row)
These full rotations are reflected in the ordering of King Wen:
.01 ..02 .03 05 07 09 11
(01) (02) 04 06 08 10 12 etc
Possibly whomever did the ordering 'compressed' those hexagrams that do not change structure expression (as in 01,01 became 01 etc). BUT also note the diagonal in each of 02-to-01 and the invarience in position of hexagrams 02, 01, 61, 62, 29, 30, 27, 28 - marked out here as [] :
[] 24 07 19 15 36 46 11 (top:earth)
16 51 40 54 [] 55 32 34 (thunder)
08 03 [] 60 39 63 48 05 (water)
45 17 47 58 31 49 [] 43 (lake)
23 [] 04 41 52 22 18 26 (mountain)
35 21 64 38 56 [] 50 14 (fire)
20 42 59 [] 53 37 57 09 (wind)
12 25 06 10 33 13 44 [] (heaven)
[] 23 08 20 16 35 45 12 (base:earth)
15 52 39 53 [] 56 31 33 (mountain)
07 04 [] 59 40 64 47 06 (water)
46 18 48 57 32 50 [] 44 (wind)
24 [] 03 42 51 21 17 25 (thunder)
36 22 63 37 55 [] 49 13 (fire)
19 41 60 [] 54 38 58 10 (lake)
11 26 05 09 34 14 43 [] (heaven)
In the horizontal or 'usual' binary sequence (aka Fu Hsi) the derivation method ensures development such that the hexagram sequence is left-to-right in the form of eight octets, each octet being made-up of all hexagrams that have a common BASE trigram. The top trigrams reflect change applicable to the octet.
In the vertical binary sequence the method ensures that development is such that we still form octets but these are now controlled by the TOP trigram being common to all hexagrams in each octet with the bottom trigrams reflecting change across the octet.
(1) Note in the above that if we repeat all rotations including 'doubles' (as in 02 02) we get into an interesting property raised some time ago re alchemy and sequences of 72, not 64 (see http://www.ozemail.com.au/~ddiamond/SEMGROUP.html for the original, incomplete, draft) BUT if we include the 'invarience' identified above then we are back to 64 (but then see (3) below)
(2) Note that in the patterns of deriving context hexagrams in IC+ the emphasis is on swapping the trigrams of the changed hexagram to get the cause of the change. Note that this method actually 'jumps' binary sequences where 23 in the horizontal gives us 15 in the vertical and as such 15 is in the more 'temporal' sequence (this area needs work...)
(3) The pairing in the traditional 'king wen' sequence reflects the vertical+horizontal sequence binary pairs - IOW the traditional sequence seems to summarise the pairings where 01,01 02,02 03,04 05,06 ....29,29 30,30 etc where the invariant entries are in fact 'compressed' into 01 02 .... 29 30. (thus 03 vertical binary is 04 horizontal binary and vica versa - but then this could also be reflected in 01,02...?)
(4) As identified in recent IC+ posts, the vertical binary sequence (http://pages.prodigy.net/lofting/binhex.html ) has a strong 'temporal' element (cyclic but not reversible?) when compared to the 'traditional' Fu Hsi binary sequence (horizontal sequence) that reflects more structural relationships such that the traditional sequence (kin wen) pairings reflect 'space/time' mappings. This leads to the speculation that, for example, 03/04 share a spacetime 'box' with each the reciprical of the other (03 in SPACE becomes 04 in TIME and visa versa....) 01 has its own box as does 02 and some others (the rotations reflect stuctural invarience and so no apparent differences in expression...'pure' forms) As such each pair reflects the sharing of the one space by A/NOT-A. In the 'pure' formats there is no distinction of A/NOT-A (but that does not mean there is no *interpretation* of NOT-A) IOW each hexagram serves two expressions - spacial/structural and temporal and the pairs in the traditional sequence can be used to reflect that combined with the mirroring of the octets (see http://pages.prodigy.net/lofting/cracked.html )
The 'issue' here is the 'compression' of 01,01 into 01 and 02,02 into 02 in that we can apply the 'time/space' interpretations to 01,02 as a pair BUT they do NOT share the same locations in the two sequences - which is what the pairings relate to so 01,01 and 02,02 compressed to 01 02 seems more 'consistent' with the model....
Happy reflections ;-)
Chris.
------------------
Chris Lofting
websites:
http://pages.prodigy.net/lofting
http://www.ozemail.com.au/~ddiamond
http://www.eisa.net.au/~lofting
Lists:
http://www.yahoogroups.com/group/semiosis
http://www.yahoogroups.com/group/ichingplus
-----Original Message-----
From: Chris Lofting [mailto:ddiamond@ozemail.com.au]
Sent: Wednesday, 27 February 2002 4:08
To: Ichingplus
Cc: Yijing_Iching
Subject: vertical vs horizontal binary sequences
Hi all,
I think we are getting close to 'something' so here are some items for your consideration:
Horizontal Binary (a sequence derived through recursion and here put into block form of eight octets - for full sequence format see level 6 of http://pages.prodigy.net/lofting/DIAG1.gif):
02 23 08 20 16 35 45 12 (base:earth)
15 52 39 53 62 56 31 33 (mountain)
07 04 29 59 40 64 47 06 (water)
46 18 48 57 32 50 28 44 (wind)
24 27 03 42 51 21 17 25 (thunder)
36 22 63 37 55 30 49 13 (fire)
19 41 60 61 54 38 58 10 (lake)
11 26 05 09 34 14 43 01 (heaven)
Vertical Binary (derived from within hex 01 line changes - http://pages.prodigy.net/lofting/binhex.html)
02 24 07 19 15 36 46 11 (top:earth)
16 51 40 54 62 55 32 34 (thunder)
08 03 29 60 39 63 48 05 (water)
45 17 47 58 31 49 28 43 (lake)
23 27 04 41 52 22 18 26 (mountain)
35 21 64 38 56 30 50 14 (fire)
20 42 59 61 53 37 57 09 (wind)
12 25 06 10 33 13 44 01 (heaven)
What is noticable here is the numbering in that each position in each block reflects the pairing we see in the traditional (aka king wen) sequence (e.g. 02 23 08 20 in the horizontal binary block maps to 02 24 07 19 in the vertical binary block.) IOW if I put each row from each block together the resulting pattern is all full rotations of hexagrams e.g. first row of each block:
02 23 08 20 16 35 45 12 (base:earth - horizontal top row)
02 24 07 19 15 36 46 11 (top:earth - vertical top row)
These full rotations are reflected in the ordering of King Wen:
.01 ..02 .03 05 07 09 11
(01) (02) 04 06 08 10 12 etc
Possibly whomever did the ordering 'compressed' those hexagrams that do not change structure expression (as in 01,01 became 01 etc). BUT also note the diagonal in each of 02-to-01 and the invarience in position of hexagrams 02, 01, 61, 62, 29, 30, 27, 28 - marked out here as [] :
[] 24 07 19 15 36 46 11 (top:earth)
16 51 40 54 [] 55 32 34 (thunder)
08 03 [] 60 39 63 48 05 (water)
45 17 47 58 31 49 [] 43 (lake)
23 [] 04 41 52 22 18 26 (mountain)
35 21 64 38 56 [] 50 14 (fire)
20 42 59 [] 53 37 57 09 (wind)
12 25 06 10 33 13 44 [] (heaven)
[] 23 08 20 16 35 45 12 (base:earth)
15 52 39 53 [] 56 31 33 (mountain)
07 04 [] 59 40 64 47 06 (water)
46 18 48 57 32 50 [] 44 (wind)
24 [] 03 42 51 21 17 25 (thunder)
36 22 63 37 55 [] 49 13 (fire)
19 41 60 [] 54 38 58 10 (lake)
11 26 05 09 34 14 43 [] (heaven)
In the horizontal or 'usual' binary sequence (aka Fu Hsi) the derivation method ensures development such that the hexagram sequence is left-to-right in the form of eight octets, each octet being made-up of all hexagrams that have a common BASE trigram. The top trigrams reflect change applicable to the octet.
In the vertical binary sequence the method ensures that development is such that we still form octets but these are now controlled by the TOP trigram being common to all hexagrams in each octet with the bottom trigrams reflecting change across the octet.
(1) Note in the above that if we repeat all rotations including 'doubles' (as in 02 02) we get into an interesting property raised some time ago re alchemy and sequences of 72, not 64 (see http://www.ozemail.com.au/~ddiamond/SEMGROUP.html for the original, incomplete, draft) BUT if we include the 'invarience' identified above then we are back to 64 (but then see (3) below)
(2) Note that in the patterns of deriving context hexagrams in IC+ the emphasis is on swapping the trigrams of the changed hexagram to get the cause of the change. Note that this method actually 'jumps' binary sequences where 23 in the horizontal gives us 15 in the vertical and as such 15 is in the more 'temporal' sequence (this area needs work...)
(3) The pairing in the traditional 'king wen' sequence reflects the vertical+horizontal sequence binary pairs - IOW the traditional sequence seems to summarise the pairings where 01,01 02,02 03,04 05,06 ....29,29 30,30 etc where the invariant entries are in fact 'compressed' into 01 02 .... 29 30. (thus 03 vertical binary is 04 horizontal binary and vica versa - but then this could also be reflected in 01,02...?)
(4) As identified in recent IC+ posts, the vertical binary sequence (http://pages.prodigy.net/lofting/binhex.html ) has a strong 'temporal' element (cyclic but not reversible?) when compared to the 'traditional' Fu Hsi binary sequence (horizontal sequence) that reflects more structural relationships such that the traditional sequence (kin wen) pairings reflect 'space/time' mappings. This leads to the speculation that, for example, 03/04 share a spacetime 'box' with each the reciprical of the other (03 in SPACE becomes 04 in TIME and visa versa....) 01 has its own box as does 02 and some others (the rotations reflect stuctural invarience and so no apparent differences in expression...'pure' forms) As such each pair reflects the sharing of the one space by A/NOT-A. In the 'pure' formats there is no distinction of A/NOT-A (but that does not mean there is no *interpretation* of NOT-A) IOW each hexagram serves two expressions - spacial/structural and temporal and the pairs in the traditional sequence can be used to reflect that combined with the mirroring of the octets (see http://pages.prodigy.net/lofting/cracked.html )
The 'issue' here is the 'compression' of 01,01 into 01 and 02,02 into 02 in that we can apply the 'time/space' interpretations to 01,02 as a pair BUT they do NOT share the same locations in the two sequences - which is what the pairings relate to so 01,01 and 02,02 compressed to 01 02 seems more 'consistent' with the model....
Happy reflections ;-)
Chris.
------------------
Chris Lofting
websites:
http://pages.prodigy.net/lofting
http://www.ozemail.com.au/~ddiamond
http://www.eisa.net.au/~lofting
Lists:
http://www.yahoogroups.com/group/semiosis
http://www.yahoogroups.com/group/ichingplus