Chinese, Yi Jing, 8 Triagrams, Tàijí, Taoist

Chinese, 8 Triagrams

This image to the left: shows the eight trigrams (the three-bit numbers) in the millennia-old Chinese Xiantian arrangement. Start from the bottom and read the triplets counter-clockwise: 000, 001, 010, 011, 111, 110, 101, and 100. 

The right half is in ascending binary order whereas the left half is in descending order. Note that this causes the complement of each trigram to be on the opposite side of the circle.

In the middle of the figure is the symbol of Tàijí, "the Extreme Ultimate". Tàijí is the unity from which everything originates: the unity splits into duality, the duality splits in four, the four splits in eight etc. 

The Taoist universe consists of an infinity of binary data - yins and yangs constantly turning into each other. The only unchanging thing is the ultimate principle itself. Trigrams can be found everywhere. The flag of South Korea contains the four symmetrical three-bit binary numbers. In the Feng Shui system (mega-fashionable in the West nowadays) you may even hang binary numbers on your walls because you believe in their magical power of modifying the energies inside the building.

Three is the smallest amount of bits that allows for a "true RGB palette" (one bit for each of the red, green and blue components). Incidentally, the Chinese trigrams have also been traditionally associated with colours. The image at the right side of the page, presents the six-bit binary combinations in two different arrangements: an eight-by-eight matrix (in ascending binary order) and a "xiantian"-ordered circle. 

The figure was composed in the 11th century by Shào Yong, the famous philosopher and oracle who believed that this was the original "xiantian" order in which the legendary emperor, Fú Xi, discovered the hexagrams millennia ago. 

Centuries later, the German philosopher G.W.Leibniz received a copy of this figure from Jesuits who were trying to convert Chinese people into Christianity.

Leibniz was so astonished by this figure that he went on to write the first European text about binary mathematics (Explication de l'arithmetique binaire, 1705). Later, Leibniz also wrote some interesting stuff about the relationship of binary numbers to the very essence of the universe, but that's a different story.  Yì Jing ("I Ching") is the ancient book that presents the sixty-four hexagrams and associates them with names and mysterious verses.  

It is basically an oracular handbook ("give me a random number and I'll tell you what lies ahead"), but because of its highly-honoured status in the Chinese culture, its "message" was very thoroughly examined during the millennia.

The properties of the six-bit numbers were studied by examining them as whole entities (symmetry, yin/yang constitution, visual shape etc.), and in small pieces (the properties of every sub-trigram, and also the properties of each bit separately). In the Pythagorean numerology, natural numbers had mystical properties, even personalities of their own. Similar numerology was applied to binary combinations in the ancient China.

In the Yì Jing divination, each line of the result can be either static or changing (the resulting hexagram is always turning into some other hexagram).  

This gives 4096 possible readings. A man named Chiao Kan actually wrote 4096 rhymed verses to describe every possible transition. After this, philosophers started to speculate about transitions between transitions.

In the words of Shú Xi: If from the 12-line diagrams we continue generating undivided and divided lines, eventually we come to 24-line diagrams, for a total of 16,777,216 changes. Taking 4,096 and multiplying it by itself also gives this sum. Expanding this we do not know where it ultimately ends. 

Although we cannot see its usefulness, it is sufficient to show that the Way of Change is indeed inexhaustible. No one was poetical enough to write out all the 16,777,216 second-order transitions, however. What might make the six-bit code especially divine even for modern people is the fact that it is used in the genetic code that describes the hardware of every living organism on this planet. (In fact, a "genetic byte" consists of three symbols from an alphabet of four, but the amount of information is exactly the same).

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