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Portable Dragon, RGH Siu, index-order

jstnparsons

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Hello,
Anyone here know the original or first instance of the order of hexagrams used to describe the index, pp. iv & v of RGH Siu's 'The Portable Dragon'? Or who 'invented' it? Sources wherein it is described in more detail?

in 'received' numbers, it looks like this (and is read top-bottom, left-right: 1,44,13,...):

01 25 57 41 18 63 51 40
44 61 30 11 55 64 35 24
13 26 58 59 56 20 03 07
10 34 50 22 17 27 46 15
09 06 49 54 32 19 62 16
14 37 28 53 31 04 45 08
43 38 12 21 47 36 29 23
33 05 42 6o 48 52 39 02

'binary notation' might look like this (still read: 63,31,47,...):

63 39 27 49 25 42 36 20
31 51 45 56 44 21 05 32
47 57 54 19 13 03 34 16
55 60 29 41 38 33 24 08
59 23 46 52 28 48 12 04
61 43 30 11 14 17 06 02
62 53 07 37 22 40 18 01
15 58 35 50 26 09 10 00

may you never have to swallow your chewing-gum,

-Justin
 
L

lightofreason

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Its a line journey map bottom to top.

Start with 1 yin working upwards (1 (all yang),44 (1st),13(2nd),10(3rd),09(4th),14(5th), 43(6th)) then move to 2 lines as pairs (33 (1&2),25(2&3),61(3&4),26(4&5),34(5&6) )

then pairs seperated by one line:

06 (1 & 3)
37 (2 & 4)
38 (3 & 5)
05 (4 & 6)

then sep by 2 etc etc:

57 (1 & 4)
30 (2 & 5)
58 (3 & 6)
50 (1 & 5)
49 (2 & 5)
28 (1 & 6)

Threes:

12 (1,2,3)
42 (2,3,4)
41 (3,4,5)

and so on - the last lot are 5 yin lines [24,07,15,16,08,23) getting finally to 6 yin.

SO -- we have a mapping of yin moving 'up' as singles, pairs, triples etc etc.

This is NOT a recursive pairs sequencing, it is an order based rigidily on sequence 'up' hexagrams and should be ordered more as:

01 (all yang)
44,13,10,09,14,43 (1 yin)
33,25,61,26,34 (two adjacent yin)
06,37,38,05
..
..
..
24,07,15,16,08,23 (5 yin)
02 (all yin)

oh - and finally consider this sequence 1 - 6 - 15 - 20 - 15 - 6 - 1
Analysis of the above line dynamics indicate the summing of lines to 'fit' the above sequence and so 1 all yang hexagram, 1 all yin hexagram, 6 one yin hexagrams 6 one yang hexagrams, 15 2 yin , 15 2 yang, 20 in mixes of 3 x 3 - this is the binomial theorem (1+x)^n where x = 1, n = 6 - coefficients add to ... 64 (1+6+15+20+15+6+1)

See such pages as:

http://ptri1.tripod.com/

... and note the link to the Sirpinksi gasket, order from noise through containment etc etc

Chris.
 
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jstnparsons

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sources & citations?

Hi Chris,

Thanks for the link; I'm actually looking more for sources from w/in the tradition of the Yi, Chinese and historical; like you, I enjoy teasing out the formal characteristics of the gua and their arrangements, but I would like some historical data to compare them with. I'm also interested in teasing out what 'philosophy' it represents, if any, again on the traditional end. Anyone?
 
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lightofreason

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jstnparsons said:
Hi Chris,

Thanks for the link; I'm actually looking more for sources from w/in the tradition of the Yi, Chinese and historical; like you, I enjoy teasing out the formal characteristics of the gua and their arrangements, but I would like some historical data to compare them with. I'm also interested in teasing out what 'philosophy' it represents, if any, again on the traditional end. Anyone?
http://en.wikipedia.org/wiki/Joseph_Needham
 

bradford

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Hi Justin-
I have the old hardbound edition of Siu, "Man of Many Qualities"
No such diagram here.
My guess is that it's an old Han Dynasty "Ba Gong" or
Eight Palace arrangement
If you can scan and send me a jpeg I'll look closer at the algorithm,
which might be a clue to its date of origin.
But, might as well say it - there is only one true and perfect
arrangement in an 8x8 grid, even if it came along 2000 years later.
That's of course Shao Yong's Xian Tian
bradford@hermetica.info
 

bradford

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Cross-posted from Midaughter

The diagram does exist on the cover of my edition, but in an artsy
form that's useless for getting gestalts.
It doesn't seem to be based on the ba gua, now that I look at that,
and that may rule out the ba gong or the "eight palaces" of Jing Fang
(76-37 bce). Since it seems to be about lines rising and falling,
I suspect the source might be Xun Shuang (128-190 ce), a Xiang Shu
scholar from the later Han who developed theories of Rising and
Falling Lines (Sheng Jian Yao).
 
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lightofreason

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bradford said:
...Since it seems to be about lines rising and falling,
I suspect the source might be Xun Shuang (128-190 ce), a Xiang Shu
scholar from the later Han who developed theories of Rising and
Falling Lines (Sheng Jian Yao).
It does not "SEEM" to be anything - it is the I Ching expression of the binomial theorem. It forms a pair with the binary sequence (aka Shao Yung's 8x8) where the binomial 8 x 8 orders the distribution of yin/yang lines in hexagrams (1 all yang, 1 all yin etc etc to fit the 1-6-15-20-15-6-1 format but in the matrix it also orders the hexagrams in each group rising bottom-up) and the binary sequence the order of derivation of the hexagrams (and so the pairs focus) bottom up.

If you rotate all of the hexagrams in the binary sequence you get the changing line sequence (aka applying recursion 'up' a hexagram) for hex 01 (and so in reverse for 02 - note this sequence also covers the line XORs for aspects of a hexagram.)

What THAT does is show you a method to derive 'binary' matrices sensitive to hexagram pairs of 'opposites' beyond 01/02 (which is what the natural binary sequence gives you)

Given the method we discover a 'logic of relationships' focus. Thus the natural binary 8 x 8 give us pairs reflecting "X is to Y as 02 is to 01". This works globally (23 is ro 43 as 02 is to 01) and locally (02 is to 23 as 02 is to 01).

To derive all of the others (and so, for example, "X is to Y as 23 is to 43") you map out the recursion 'up' a hexagram (changing line orders) and then rotate the resulting sequence to give you the derived 'binary' sequence; the structure is no longer binary, it is the qualities that are. Here the focus us NOT at a global level but at a local level (the global pairs retain the natural binary orderings)

See more re horizontal/vertical matrices for hexagrams in

http://members.iimetro.com.au/~lofting/myweb/icmatrices.html

Chris.
 

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