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.
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.
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.
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).
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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