The binary numeral system – where each position is written as a 0 or 1 – forms the foundation of all modern computing systems. In essence, binary code produces a representation of reality; it is behind the digital images we view on LCD screens, the music we listen to on CDs, and the movies we watch. It is sometimes difficult to conceive that we can reconstruct scenes from around the world and carry out highly advanced computing functions using only two numbers.

One of the most famous mathematicians of the 17 th century, Gottfried Wilhelm Leibniz, is credited with inventing this important numeral system. Although the people of the remote island of Mangareva were using a type of binary system for their trading systems centuries before Leibniz, given their remoteness it is likely that Leibniz came up with binary code independently – Mangareva is a tiny 18 square kilometres island located halfway between Easter Island and Tahiti.

So how did Leibniz discover a code that would form the foundation of every computing system around the world? According to David Walter , writer of the ‘weird things’ column in the Guardian, Leibniz received his inspiration from a 5,000-year-old Chinese text known as the I-Ching, or Book of Changes.

The I-Ching is one of the oldest of the Chinese classic texts and divination systems and is thought to pre-date recorded history. Although the oldest manuscript that has been found dates back to the Warring States period (475 – 221 BC), traditional Chinese accounts assert that its origins trace back to the 3 rd millennium BC and was passed down as oral tradition. Ancient Chinese legend says that I Ching originated with the mythical Fu Xi, one of the earliest legendary rulers of China (2800 BC-2737 BC), reputed to have had the 8 trigrams revealed to him supernaturally. By the time of the legendary Yu 2194 BC – 2149 BC, the trigrams had supposedly been developed into the famous 64 hexagrams of the I-Ching.

The 8 trigrams. Image source: Wikipedia

The solid line represents Yang, the creative principle, while the open line represents Yin, the receptive principle. Together, they express the idea of complementarity of changes. The hexagrams combine two trigrams together. With six such lines stacked from bottom to top there are 64 possible combinations, and thus 64 hexagrams represented, each with their own meaning and interpretation. To use the I-Ching, a person uses either coin tosses or yarrow stalks to generate a hexagram and receive their divination statement.

A representation of I-Ching trigrams and hexagrams. Photo source .

Walter explains that the 64 hexagrams claim to represent the archetypal situations of human life itself: “In the philosophy of the I-Ching, reality is not entirely real. It is something more like a dream or an illusion. This dream of reality arises from the binaries of Yin and Yang, as they play out their infinite combinations. It's not surprising then, from the I-Ching's perspective, that anything in the dream of reality can be represented as a model of its binary constituents, in a string of 1s and 0s, processed by a computer.”

Leibniz was so influenced by the philosophies ingrained within the I-Ching that he titled his paper on the new arithmetic: "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".

According to Walter, Liebniz's insight from the I-Ching was that even the most complex aspect of reality could potentially be represented in the binary form as 1s and 0s. In his article Explication de l'Arithmétique Binaire (1703) Leibniz wrote that he found in the hexagrams a base for claiming the universality of the binary numeral system. He took the layout of the combinatorial exercise found in the hexagrams to represent binary sequences, so that ¦¦¦¦¦¦ would correspond to the binary sequence 000000 and ¦¦¦¦¦| would be 000001, and so forth.

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

Featured image: A copy of the I-Ching. Photo source .

By April Holloway