After long consideration I have settled for a composite structure to depict most of what I have found in the traditional Chinese mantic systems of the Zhou Yi Jing and the Tai Xuan Jing. An important aspect of this synthesis is formal, and starts with the view that the Yi simbolisations are visual images, elementary “figures” and their combinations.
The synthesis was necessary for first to bring together the rich insights and imagery of both traditional systems, but also to express more fully the mathematical foundations of the same exhaustively.
The image shown above, generated with a more complex PHP script, combines the Yi Jing and the Tai Xuan Jing with the “wider” and more complex combination arising from a base 4 counting system (with four types of lines).
In a single figure this allows us to re-use the elementary trigrams of the Yi Jing, which cannot be surpassed in terms of condensation of meaning and form, and the calendar-like figures of the Tai Xuan Jing.
The figure, composed by 12 lines, simultaneously shows three tetragrams and four trigrams. In turn the trigrams can be read by forming at least three hexagrams.
The text lines shown to the right of the image are the basic readings of the figures and their parts.
Initially I considered a “nona-gram” formed by three trigrams, as this would present an interesting image already. Finally I settled for the dodecagram (shown above), less compact and perhaps less image-like, only because it produces more material for interpretation.
Despite the joined-up forms here discussed, I want to emphasise that the key to the expansion is the introduction of the fourth line, that is the expansion of the underlying number system to base-4.
Now, in the whole picture, using the four trigrams, I think it is very productive to associate these four levels to the four lines: The “innermost” trigram, the “bottom” one, sits in the position of the person or the family; the second one, higher up, sits in the position of the Subject, that is the social exterior (the social mediation); the third one is then the Agent, or the concrete mediation (the medium or tool of the actor, be it individual or collective); and the fourth one, at the top is the complete exterior, the maximally distant Object. This sequence is not definitive though. Should we follow the top-down Tai Xuan Jing order or the bottom-up Yi Jing order?
Despite the remaining issues, this brings already some guidance for the reading, but we should not forget the components as each one of them can be directly associated with the original texts. The hexagrams can refer us back to the Yi Jing, and the tetragrams can be easily found in the Tai Xuan Jing. The only difficult is here to translate the four lines, interpreting the lines according to base-2 and base-3 numbering systems.
The texts to the right of the figure present some of these translations.
A final note: I am using now PHP 7.0 and the native cryptographic-quality random number generator that is available through it. The work continues.