The I Ching Binary System And Natural Phenomena by Stanley Tomshinsky

Building Trigrams

Each of four two-line elements can generate two different trigrams by adding an active or passive line. It is these trigrams that unite to form the hexagrams.

These four two-line elements happen before the trigrams and should not be confused with the corresponding line-units that make up the hexagram. Their number equivalents are the same in both cases.





In 1974, while thinking about how one's actions are an extension of one's self, I likened it to the multiplication of one's self. This thought led me to the decimal system.

By squaring any number and then applying the reduction method, one comes up with the four numbers 1,4,7 and 9:

1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16 = 7
5 x 5 = 25 = 7
6 x 6 = 36 = 9
7 x 7 = 49 = 13 = 4
8 x 8 = 64 = 10 = 1
9 x 9 = 81 = 9

So that:
1 = 1 = 1 and 8
4 = 2 = 2 and 7
9 = 3 = 3, 6 and 9.
7 = 4 = 4 and 5

For an extended version of this project go to page, "A Number System".

It is this number-method that I used to construct the trigrams from the four two-line elements: a 1 element makes 1 and 8 trigrams and so on. .

While building a trigram sequence that would bring the trigrams opposite their counterparts on a number wheel respecting a numerical order, I tried these four pairs of numbers and it worked.




Interacting Trigrams

While studying this wheel, the thought came to me that the principle of interaction would hold true for the two directions of a circular arrangement. I placed the clockwise wheel on the inside and the counter-clockwise wheel on the outside.


Each, of the eight wheel-turns, contains the hexagrams opposite their counterparts as well as the hexagrams with the same trigrams in a reversed order. It is all very symmetrical.

There are eight possible combinations respecting a numerical order that form this type of symmetry, but I believe that the one presented above expresses the norm. There are sixteen possible combinations that while respecting a numerical order create asymmetrical arrangements of hexagrams. Then there are those combinations which don't have a logical numerical order.

To make a wheel: print this image twice, paste them on cardboard, cut out the inner circle of one, and unite it with the outer circle with a small nail.




Interacting Hexagrams

In "The Richard Wilhelm Translation of the I Ching" there is a trigram wheel called the "Fu Hsi Sequence of Earlier Heaven". It dates back 3,000 years. It is symmetrical, but does not follow an exact numerical order. Three pairs of trigrams follow an order, but a forth pair is reversed. Considering the fact that those noble scholars presented this sequence, I made a wheel that produced its eight cycles. The following two pages are scans of the 1978 originals. In the first, hexagrams with the same trigrams are indicated. They are always opposite their counterparts. In the second, each hexagram's DNA equivalent is noted using the previously indicated method.





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