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"Number Magic" from Ta Chuan (the Great Commentary)

saharan

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Greetings Clarity community;

I submit the following scholarship for your evaluation and criticism.
Thank you,

saharan

Yao-numbers Pt. 1


ABSTRACT
Yao-numbers or "stick-numbers" are the product of a mathematical transformation of the I Ching's 32 hexagram pairs as presented by King Wen. In the case of twenty-eight pairs of hexagrams, the mates of a pair differ only by 180 degrees of rotation. The last four pairs are complementary opposites as per Fu Xi's hexagram and trigram arrangements.

Yao-numbers seem to call attention to the four pairs of complementary opposites: pair-mates generally have identical yao-numbers except in four cases: (01,02) (27,28) (29,30) (61,62), where the mates have unequal yao-numbers. Again, these four pairs bear the distinction of having been formed from complementary opposites, as opposed to pair formation from figurative inversion or 180 degrees of rotation in the case of the remaining 28 pairs of hexagrams.

The transformation procedure (described later) produces nine discrete yao-numbers from the 32 Wen pairs of hexagrams. The following crude table displays the 64 hexagrams and the yao-number "families" into which they fall, along with yao-numbers and line-analysis (#YIN lines and #YANG lines) of each hexagram.

0 YANG,6 YIN (144) { 1} [2]
2 YANG,4 YIN (168) { 3} [27 29 62]
5 YANG,1 YIN (172) { 6} [(9 10) (13 14) (43 44)]
4 YANG,2 YIN (176) {12} [(5 6) (25 26) (33 34) (37 38) (49 50) (57 58)]
3 YANG,3 YIN (180) {20} [(11 12) (17 18) (21 22) (31 32) (41 42) (47 48) (53 54) (55 56) (59 60) (63 64)]
2 YANG,4 YIN (184) {12} [(3 4) (19 20) (35 36) (39 40) (45 46) (51 52)]
1 YANG,5 YIN (188) { 6} [(7 8) (15 16) (23 24)]
4 YANG,2 YIN (192) { 3} [28 30 61]
6 YANG,0 YIN (216) { 1} [1]
 
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Sparhawk

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We also observe that the four "separated" hexagram pairs: (01,02) (27,28) (29,30) (61,62) [families #1, #2, #8, & #9] all share a peculiar trait -- none of them has a proper Wen inverse as do the other twenty-eight pairs of hexagrams. The pairs formed from these eight hexagrams are not figurative inverses, but complementary opposites. Complementary opposition is the basis of the Earlier Heaven (Xian Tian) trigram arrangement, and the square (8x8) hexagram arrangement, both attributed to Fu Xi.

Nice job, thanks for sharing. Certainly, complementary opposition and binary sequencing are the basis of the so called Fu Xi arrangement.

May I suggest you try to repair the coding of your website to make it visible to all browsers. I can't see the graphics used and tried three different browsers. Otherwise, please advise what encoding did you use for the special characters.

Thank you.
 

saharan

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Character rendering of xiang

Thank you, Luis, for your comments.

Regarding the xiang characters they are 0268C through 0268F located in Unicode block labeled "Miscellaneous Symbols." A good keycaps accessory program should catalog them. The hexagrams used to illustrate the transformation procedure are in Unicode group labeled "Yijing Hexagram Symbols" numbered 4DC0 through 4D44.

I hope to share additional content related to the yarrow oracle, and the Wen and "Fu Xi" modes of categorization. For example, the the yarrow oracle probabilities for generating xiang are (YIN) 4/64 and 28/64, and (YANG) 12/64 and 20/64. While the posted article discusses Wen pairs in the YIN partition: 4 pairs hexagrams and 28 pairs of hexagrams, I hope to soon share a non-trivial YANG partition of 12 pairs and 20 pairs.

The yarrow oracle and the Wen pairings appear to be "entangled;" the arrangement attributed to Fu Xi is likely entangled with these as well.

--shar qaan
 
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saharan

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I suspect (and hope) that Yijing is a representation of the Tree of Life (not a reference to the Kabbalistic version), a peek at the subtle reality that surrounds and gives rise to all phenomena, but it imperceptible, except perhaps in deep meditation or similar states of consciousness.

Tracking its probable origins from Akkado-Assyro-Sumeria (Tablet of Destinies) and West Africa (Ifa) to China, likewise tracking the uncanny similarities of various cultural-mythological heroes and their stories (Mercury/Hermes (Greco-Roman), Fu Xi (China), Odin/Wodin/Wotan (Teutonic), Pacal Votan (Mesoamerican), Buddha (Indo-Asiatic)), has led me to the unshakable suspicion that "all [are] one." This is to say, of course, that there is but one such person, one story, one truth, fractured across time and space.

For example, the magic square of Mercury (planet, deity) is an 8x8 arrangement of the numbers 1 to 64, where columns, rows, and diagonals all sum to 260. Fu Xi's diagram is one such magic square whereby the binary values of the 32 antipodal hexagram pairs always sum to 65, symbolizing divination (1 querent + 64 hexagrams). Such antipodal pairs are always complementary opposites, a concept often discussed in quantum physics. Note: 65 = 13 * 5, 260/65 = 4

Meanwhile, the number 260 is central to the Mayan system of timekeeping (attributed to Pacal Votan). It can be shown that the Mayan Tzolk'in calendar, commonly represented as a 13x20 matrix, can be represented as one octant of an 8x8 magic square. The proverbial rabbit hole goes deeper....
 

saharan

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Screenshots (in context) of digram and hexagram characters used in original post



 
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bradford

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I suspect (and hope) that Yijing is a representation of the Tree of Life (not a reference to the Kabbalistic version)

Actually there is a good chance that Yixue and the Yinyang/Wuxing Jia were the origin of the Qabalistic version of the Tree (Otz Hhayim), via the Arabs. This diagram predates Kircher's first representation of the Tree in the West by four centuries.
http://www.hermetica.info/Taijitu.jpg
 

saharan

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I should have written "not a specific reference," but thank you all the more! Many people equate tree of life with Etz Chaim, but depictions of the Tree of Life are many and widespread. There is even a possibility that the Tablet of Destinies from the Akkado-Sumerian tradition may also be related to Yijing:

http://www.sacred-texts.com/cfu/choc/choc02.htm#fr_12


Actually there is a good chance that Yixue and the Yinyang/Wuxing Jia were the origin of the Qabalistic version of the Tree (Otz Hhayim), via the Arabs. This diagram predates Kircher's first representation of the Tree in the West by four centuries.
http://www.hermetica.info/Taijitu.jpg
 

bradford

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I should have written "not a specific reference," but thank you all the more! Many people equate tree of life with Etz Chaim, but depictions of the Tree of Life are many and widespread. There is even a possibility that the Tablet of Destinies from the Akkado-Sumerian tradition may also be related to Yijing:

http://www.sacred-texts.com/cfu/choc/choc02.htm#fr_12

That's really not very helpful without a picture or some other kind of evidence. If I'm not mistaken, this speculation comes out of Lacouperie's work in the 19th Century. http://en.wikipedia.org/wiki/Albert_Étienne_Jean_Baptiste_Terrien_De_La_Couperie
and discussed by Paul Carus among others.
He really wanted to blame Chinese culture on the near-East. He was a scholar of some note for his day but his speculations haven't survived.
 
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saharan

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Quite right Bradford, the idea is solidly within the realm of speculation at present. I did find a reference to Lacouperie's work in a published work entitled "African presence in Early Asia, Vol. 7, Issue 1" by Ivan Van Sertima and Runoko Rashidi. This work asserts (inter alia) that I Ching, constructed by Akkado-Sumerians of Elam-Babylonia, dating to 2800 BCE was addressed as the Tablet of Destiny known and utilized by antediluvian monarch Enmeduranki, seventh of the aboriginal kings of Sippar (Akkad).

it is comforting to find other individuals here interested in hermetics (and hermeneutics), and the process of integrating legend and mythology with history and relics
 

bradford

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it is comforting to find other individuals here interested in hermetics (and hermeneutics), and the process of integrating legend and mythology with history and relics

As long as you know that I'm equally interested in dismissing things that make no sense.
 

saharan

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With metaphysics widely viewed as falling in the realm of pseudo-science (or worse!), our kind of investigation speculation demands a voice of reason to qualify or balance it, so I wholeheartedly support reasoned dissent, particularly from one qualified to make it. :bows:
 
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saharan

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Here is a published journal article to provide support for the "diffusionist deity" hypothesis.

It may be remembered also, in this connection, that Hermes is represented as the messenger of the Gods and as their interpreter (hermeneutes), that is, precisely, an intermediary between the celestial and terrestrial worlds, and that he has in addition the function of "guide of the souls of the dead" which, in a lower order, is clearly related also to the domain of the subtle possibilities.[5]

It might be objected that in so far as concerns Hermetism, Hermes takes the place of the Egyptian Thoth with whom he has been identified, and that Thoth represents Wisdom, which is related to the priesthood as guardian and transmitter of the tradition; that is true, but since this identification cannot have been made without some reason, it must be admitted that it concerns more especially a certain aspect of Thoth which corresponds to a certain part of the tradition, the part that comprises those branches of knowledge which are related to the "intermediary world"; and the remains that the ancient Egyptian civilization has left behind do in fact show that the sciences of this order were much more developed there and had taken on an importance far more considerable than anywhere else. There is moreover another comparison, we might even say another equivalence, which shows clearly that this objection would have no real bearing: in India the planet Mercury (or Hermes) is called Budha, a name of which the root letters mean Wisdom; here again, it is enough to specify the domain in which this Wisdom (in its essence the inspiring principle of all knowledge) is to find its more particular application when it is related to this specialized function.[6]

Strange though it may seem, the name Budha is in fact identical with that of the Scandinavian Odin, Woden or Wotan;[7]there was thus nothing arbitrary in the Roman assimilation of Odin to Mercury, and in some Germanic languages the day of Mercury (in French mercredi) is still called the day of Odin, which is precisely what the word Wednesday means.

Still more remarkable, perhaps, is the fact that this same name is to be found exactly in the Pacal Votan of the ancient traditions of central America who has moreover the attributes of Hermes, for he is Quetzal cohuatl, the "bird-serpent," and the union of these two symbolic animals (corresponding respectively to the two elements air and fire) is also figured by the wings and the serpents of the Caduceus.[8] One must indeed be blind not to see, in such facts, a sign of the fundamental unity of all traditional doctrines.
 

Sparhawk

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There's always a tendency to speculate that certain "civilization" traits are imported from one place to the other, such as in the Bactrian/Nickel theory, for example, and quite a few others, where one civilization/culture has had an upper hand of sorts, and/or precedence, in developing ideas and they, through trading/commerce, spread to other areas. Well, yes and no. No all ideas were spread as gold coinage. That's way too simplistic. OTOH, there are very simple concepts and ideas, such as complementarity and duality, that are innate to all human beings, since we share one commonly "designed" brain, regardless of cultural and geographical traits, that spawned whole metaphysical movements, of which the Yijing in China is just one example.

To assume that Sumerians were THE civilization that started it all would be, IMHO, misguided. That they were the "chatty" ones, with lots of records left behind, doesn't mean they were better or that preceded any other contemporary civilization in import and scope. Recorded history cannot be taken as a measure of metaphysical advance. There are other indicators, such as artistic expressions, that trump any such connections, tenuous as they are.

Please, bear in mind that visualizing duality and complementarity, and building metaphysics from there, isn't a geographical or historical trait but a universal one.
 

saharan

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Thank you, Luis, for your criticisms. I surely never intended to suggest that apparent historical primacy suggests superiority of any sort (except perhaps in record-keeping). My adulation is for the very universality with which this metaphor appears, rather than for one culture or another. This was also a stated point in the quoted passage, cultural ubiquity of the mythos. A major goal of my efforts is find Yijing's place in the World Tree/Tree of Life mythos. This aim exposes me to confirmation bias, so I am grateful for efforts to help me see past this potential slant.

The 'Akkadian Tablet of Destinies' link is surely the most speculative (weakest) in the bunch. The Teutonic, Egyptian, Mesoamerican, West African, and Greco-Roman links show a fair degree of consistency by themselves, but not enough to solidify the claim.

That they were the "chatty" ones, with lots of records left behind, doesn't mean they were better or that preceded any other contemporary civilization in import and scope. Recorded history cannot be taken as a measure of metaphysical advance.
 
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