“What we term Completion [Tetragram 73] is enduring achievements that cannot be changed.”
(Yang Xiong, The Canon of Supreme Mystery ( 太玄經 ), “Autocommentaries”, page 342; translated by Michael Nylan, State University of New York Pres, 1993)
▄▄▄▄▄ ▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
|Tai Xuan Jing tetragram #||52 - Du - Measure - Maß - 1220|
Many people read or at least have heard of the classic Chinese treatises known as the Zhou Yi (Yi Jing) and the Tai Xuan Jing. Legend and history disagree about the authorship of the first, the extraordinary book based on the binary combinations of broken (yin) and unbroken (yang) lines. These combinations form a very complex series of 64 hexagrams. The second book, with a series of 81 figures, was written by Yang Xiong (born 53 B.C., died 18 A.D.).
Yang, a noted scholar of the Chinese Han Dynasty, combined Confucian and Daoist philosophical principles, building on the Zhou Yi (Yi Jing), to produce a complex and intriguing book. Different to the Yi Jing, Yang’s book used a ternary numbering base (the lines are unbroken, once and twice broken, to signify Heaven, Earth and Man, respectively). The combination of numbers were arranged in the form of a counting sequence starting comprising a total of 81 tetragrams. Also different from the Yi Jing, the sequence is straightforward, consisting of a direct, increasing count of the base numbers.
The book is not difficult to read, but it’s full depth escapes the reader who lacks other references, in particular regarding the social, philosophical and political context of the Han period. Even without such knowledge though, use of the book is straightforward albeit different from the normal interpretation methods that have grown around the Yi Jing. The Tai Xuan Jing can be read as a calendar of the Chinese agricultural year, for example, with numerous references to the weather of each stage of the seasons and the natural life-cycles.
For the definitive source on the Tai Xuan Jing I refer the reader to Ms. Michael Nylan’s translation, with introduction, commentaries and notes, under the title “The Canon of Supreme Mystery”, published in 1993 by State University of New York.
The tetragram shown above is generated by a PHP script with each page refresh. The randomisation of the sequence relies on the default PHP interpreter mt_rand function, and hence it is not very strong. Recreating the complex Tai Xuan Jing manual “throw” method was not my goal in this case though. Instead, I just wanted to publish a dynamic generator of the tetragrams, thinking that this may be the first time this has been done on the Internet — I am aware of several web pages with references to the book and static representations. (1) To achieve this representation I modified a Yi Jing PHP script originally developed by David Parsons in 2002, adapting the algorithms to the different number base and other characteristics of Yang’s system.
At a different level, the ternary counting system employed by Yang tends to support the widespread notion that the Yi Jing (which was the “model” followed by the philosopher), is also based on a numerical structure. Nevertheless, it is clear that Yang made several “design decisions,” for example, when opting for a straight incremental count, limiting the strokes to four, and using a base 3 numerical series. My script also draws the tetragram from the top down, as prescribed by Yang Xiong.
These “evolutionary” but paradoxically “conservative” modifications, led me to think of a further extension of the system by introducing a base 4 numerical system while keeping Yang’s 4 lines (the tetragram). Other variations are certainly possible, for example using six lines and four types of lines on base 4. This page contains some experimental variations of that order. Two particularly interesting are the composition of a series of four tetragrams, as shown here: http://carlos-trigoso.com/2017/11/11/four-lines-four-times/
When keeping the hexagram depiction, the base 4 combinations give rise to all the possible instances of the Ji Ying due to the following: As is known by the Yi Jing scholars, behind the Classic hexagrams, there is another level of combinatory derived from the “strong” and “weak” variations of the yin and yang lines. In reality, the Yi Jing hexagrams generate combinations of four clases of lines. (To note the traditional Yi Jing “throwing” methods allow for the generation of those “strong” and “weak” variations of the lines.)
“Octograms” built on those lines are quite intriguing, especially when showing the superposition of tetra-, hexa and octograms: http://carlos-trigoso.com/2016/12/11/octograms-1/
A lot remains to be said about the “meaning” of the new figures. For the Yi Jing and the Tai Xuan Jing the interpretations are anchored in what the tradition, the commentators and the translators have presented. Symbolism is not too different when comparing the Zhou Yi with the Tai Xuan: both refer ultimately to the Yin Yang Chinese tradition, notwithstanding Yang Xiong’s departure from the tradition with the introduction of the “third line” (twice broken line). What could be the “fourth” (thrice-broken) line mean?
In my speculations I tend to see the fourth (four-segment) line not as a “weak yin” but as a modern, contemporaneous symbol complementary to Yang Xiong’s “Man.” To explain: in the same way as Yang’s innovation introduces a third force in the symbolic landscapes of the Yi Jing (Man standing between Heaven and Earth), the fourth line introduces the *works of man* the *product* of human activity, standing aside, contra-posed to Man, derived from human action but somehow in opposition to it.
This reading could become interesting if –following the Yi Jing hexagram figures, which are traditionally read as composed by two “trigrams” — a similar figure or visualisation is adopted: A series of perspectives appear if we contemplate the octograms. Instead of micro-pictures represented by the 8 trigrams, where we see only natural forces, both in Yang Xiong’s tetragrams and in the proposed enhancements we find richer vistas, with combinations of natural and human or human-produced forces.
There is then a progression, from 64 scenarios generated by the binary combinations of the Yi Jing, moving on to the more complex 81 combinations of the Tai Xuan Jing, and reaching now to the 256 combinations of the enhanced four-line tetragram or the 65536 combinations of the base 4 octogram (note the whole sequence starts at zero).
Probably a whole life could be dedicated to write the poems or riddles to match the new tetragrams, and several lifetimes to the higher combinations, but at least there is some pleasure in the intuition of the new landscapes opening up in the horizon still under the light of the Classics.
(1) See for example: http://www.russellcottrell.com/VirtualYarrowStalks/TaiXuanJing.htm