Derivation of the Timewave from
the King Wen Sequence of Hexagrams
by Terence McKenna

Figure 1
The idea that time is experienced as a series of identifiable elements in flux is highly developed in the I Ching. Indeed the temporal modeling of the I Ching offers an extremely well-developed alternative to the "flat-duration" point of view. The I Ching views time as a finite number of distinct and irreducible elements, in the same way that the chemical elements compose the world of matter. For the Taoist sages of pre-Han China time was composed of sixty-four irreducible elements. It is upon relations among these sixty-four elements that I have sought to erect a new model of time that incorporates the idea of the conservation of novelty and still recognizes time as a process of becoming.

The earliest arrangement of the hexagrams of the I Ching is the King Wen Sequence. It was this sequence that I chose to study as a possible basis for a new model of the relationship of time to the ingression and conservation of novelty. In studying the kinds of order in the King Wen Sequence of the I Ching I made a number of remarkable discoveries. It is well known that hexagrams in the King Wen sequence occur in pairs. The second member of each pair is obtained by inverting the first. In any sequence of the sixty-four hexagrams there are eight hexagrams which remain unchanged when inverted. In the King Wen Sequence these eight hexagrams are paired with hexagrams in which each line of the first hexagram has become its opposite, (yang changed to yin and vice-versa).

The question remains as to what rule or principle governs the arrangement of the thirty-two pairs of hexagrams comprising the King Wen Sequence. My intuition was to look at the first order of difference, that is, how many lines change as one moves through the King Wen Sequence from one hexagram to the next. The first order of difference will always be an integer between one and six. When the first order of difference within pairs is examined it is always found to be an even number. Thus all instances of first order of difference that are odd occur at transitions from one pair of hexagrams to the next pair. When the complete set of first order of difference integers generated by the King Wen Sequence is examined they are found to fall into a perfect ratio of 3 to 1, three even integers to each odd integer. The ratio of 3/1 is not a formal property of the complete sequence but was a carefully constructed artifact achieved by arranging hexagram transitions between pairs to generate fourteen instances of three and two instances of one. Fives were deliberately excluded. The fourteen threes and two ones constitute sixteen instances of an odd integer occurring out of a possible sixty-four. This is a 3/1 ratio exactly.

Figure 1 shows that when the first order of difference of the King Wen Sequence is graphed it appears random or unpredictable. However when an image of the graph is rotated 180 degrees within the plane and superimposed upon itself it is found to achieve closure at four adjacent points as shown below:

Figure 2

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