From Ba-Gua To I-Ching To Super Computers

Most people in the West, and probably even in the Far East, assume that everything about the modern world was the exclusive achievement of Western Europe during and after the Industrial Revolution, and that Far Eastern cultures, especially China, contributed little if anything to the creation of our modern, technological world. This gross misconception is the predictable result of a widespread and deep-rooted historical amnesia. Intellectual giants such as Leibniz, Voltaire, and Carl Jung knew otherwise. They appreciated the enormous intellectual debt the West owed to China and Far Eastern civilization.

The average Chinese person today has little if any understanding about how a whole range of key Chinese inventions enabled Europe and America to progress scientifically and technologically to where they are today.

Fu Xi (伏羲)

Fu Xi (伏羲) discovered the HeTu (河图) - "Yellow River Chart" on the back of a mythical dragon-horse that emerged from the Luo River (洛河). The HeTu(河图) that Fu-Xi discovered inspired him to create the Ba-Gua, known as Primordial Bagua (先天八卦 - Xian Tian Ba Gua). which form the basis for the philosophy in the Book of Changes - I Ching (易经).

As the creator of Eight Trigrams (八卦), which form the basis for the philosophy in the Book of Changes (I Ching), Fuxi (伏羲) has been revered by Chinese scholars as the originator of the I Ching (易经), an ancient divination text and the oldest of the Chinese classics.

 I-Ching (易经)

King Wen of Zhou (周文王 1152 – 1056 BC) improved the 8 trigrams in their various permutations to create the 64 hexagrams of the I Ching.

I-Ching is based on the taoist duality of yin and yang, eight trigrams (Bagua) and a set of 64 hexagrams ("sixty-four" gua), analogous to the three-bit and six-bit binary numerals. I-Ching were in use at least as early as the Zhou Dynasty of ancient China.

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz, 1 July 1646 – November 14, 1716), a German philosopher and mathematician, was researching for the binary system when he received a copy of I-Ching (Yi Jing) sent to him by a Jesuit priest - Joachim Bouvet. He immediately recognized that the I-Ching symbols of solid and broken bars are isomorphic to the 1 and 0 digits of binary system, and greatly surprised that a binary system was already used by Fu Xi thousands of years before him.

A diagram of I Ching hexagrams sent to 
Gottfried Wilhelm Leibniz from Joachim Bouvet

Joachim Bouvet (Chinese: 白晋 or 白進, courtesy name: 明远) (b. Le Mans, July 18, 1656 – June 28, 1730, Peking) was a French Jesuit who worked in China, and the leading member of the Figurist movement.

Leibniz is usually credited with the early development of the binary number system (base 2 counting, using only the digits 0 and 1), although he himself was aware of similar ideas dating back to the I Ching of Ancient China.

Leibniz was so amazed with the I-Ching that he went on to write an article titled : “Explanation of the binary arithmetic, which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi”. This code is the basis for all current modern computers.

Because of the ability of binary to be represented by the two phases "on" and "off", it would later become the foundation of all modern computer systems, and Leibniz's documentation was essential in the development process.

Leibniz wrote:"...What is amazing in this reckoning is that this arithmetic by 0 and 1 is found to contain the mystery of the lines of an ancient King and philosopher named Fuxi, who is believed to have lived more than 4000 years ago, and whom the Chinese regard as the founder of their empire and their sciences. There are several linear figures attributed to him, all of which come back to this arithmetic, but it is sufficient to give here the Figure of the Eight Cova, as it is called, which is said to be fundamental, and to join to them the explanation which is obvious, provided that one notices, firstly, that a whole line — means unity, or 1, and secondly, that a broken line -- means zero, or 0.

The Chinese lost the meaning of the Cova or Lineations of Fuxi, perhaps more than a thousand years ago, and they have written commentaries on the subject in which they have sought I know not what far out meanings, so that their true explanation now has to come from Europeans. Here is how: It was scarcely more than two years ago that I sent to Reverend Father Bouvet, the celebrated French Jesuit who lives in Peking, my method of counting by 0 and 1, and nothing more was required to make him recognize that this was the key to the figures of Fuxi. Writing to me on 14 November 1701, he sent me this philosophical prince's grand figure, which goes up to 64, and leaves no further room to doubt the truth of our interpretation, such that it can be said that this Father has deciphered the enigma of Fuxi, with the help of what I had communicated to him. And as these figures are perhaps the most ancient monument of science which exists in the world, this restitution of their meaning, after such a great interval of time, will seem all the more curious.

The agreement between the figures of Fuxi and my Table of Numbers is more obvious when the initial zeros are provided in the Table; they seem superfluous, but they are useful to better show the cycles of the column, just as I have provided them in effect with little rings, to distinguish them from the necessary zeros. And this agreement leaves me with a high opinion of the depth of Fuxi's meditations, since what seems easy to us now was not so at all in those far-off times. The binary or dyadic arithmetic is, in effect, very easy today, with little thought required, since it is greatly assisted by our way of counting, from which, it seems, only the excess is removed. But this ordinary arithmetic by tens does not seem very old, and at least the Greeks and the Romans were ignorant of it, and were deprived of its advantages. It seems that Europe owes its introduction to Gerbert, who became Pope under the name of Sylvester II, who got it from the Moors of Spain.

Now, as it is believed in China that Fuxi is even the author of Chinese characters, although they were greatly altered in subsequent times, his essay on arithmetic leads us to conclude that something considerable might even be found in these characters with regard to numbers and ideas, if one could discover the foundation of Chinese writing, all the more since it is believed in China that he had consideration for numbers when establishing them. Reverend Father Bouvet is strongly inclined to push this point, and very capable of succeeding in it in various ways. However, I do not know if there was ever an advantage in this Chinese writing similar to the one that there necessarily has to be in the Characteristic I project, which is that every reasoning derivable from notions could be derived from these notions' characters by a way of reckoning, which would be one of the more important means of assisting the human mind."

Why computers use binary number system?

The circuits in a computer's processor are made up of billions of transistors. A transistor is a tiny switch that is activated by the electronic signals it receives. The digits 1 and 0 used in binary reflect the on and off states of a transistor.

Computers use binary - the digits 0 and 1 - to store data. A binary digit, or bit, is the smallest unit of data in computing. It is represented by a 0 or a 1. Binary numbers are made up of binary digits (bits), eg the binary number 1001.

Computer programs are sets of instructions. Each instruction is translated into machine code - simple binary codes that activate the CPU. Programmers write computer code and this is converted by a translator into binary instructions that the processor can execute.
All software, music, documents, and any other information that is processed by a computer, is also stored using binary.

Everything on a computer is represented as streams of binary numbers. Audio, images and characters all look like binary numbers in machine code. These numbers are encoded in different data formats to give them meaning, eg the 8-bit pattern 01000001 could be the number 65, the character 'A', or a colour in an image.

The more bits used in a pattern, the more combinations of values become available. This larger number of combinations can be used to represent many more things, eg a greater number of different symbols, or more colours in a picture.


It is mind-blowing for You to realise that the very foundation of every computing device now in use has its root in the ancient divination text of the I-Ching.
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