Ancient Origins of Binary Logic

A brief exploration of the magic squares of the I-Ching (Ho Tu and Lo Shu), Binary Code, I-Ching and DNA.


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Ho Tu and Lo Shu

The Ho Tu and Lo Shu

The I-Ching or “Book of Changes” was (mythologically) conceived by Fu Xi, an ancient Chinese sovereign.

Supposedly, a crucial inspiration for the book originally derived from a special sign or “omen”: when Fu Xi witnessed a stunning white horse emerge from the Yellow River, and was intrigued by a pattern of dots upon its side (fanciful versions state that the horse had the head of a dragon). He recorded this pattern, which came to be known as the “Yellow River Map” or Ho Tu (He Tu).

Ho Tu (Yellow River Map)

Interestingly, in Feng Shui, the specific pattern of the Ho Tu (which is a sort of two-layer cycle) is considered to be a mathematical way to describe or refer to the rightward-facing swastika symbol.

Lo Shu (River Scroll)

Many years later, another omen relevant to the I-Ching, known as the Lo Shu or simply “River Scroll” was observed on the back of a tortoise which emerged from the Lo River. This pattern is considered very important in the practice of Feng Shui.

Both the Lo Shu and Ho Tu are “magic squares” – that is, they are special configurations of integers which reveal special meanings and/or have special properties, and act as an info-matrix. These magic squares can provide the basis for mathematical investigations, as explicated in the I-Ching.

Both of these patterns supposedly originated from natural forms (which of course are possessed of an implicit fractal structure). However, it took a special genius to be able to intuit the basic meaning of an end-point pattern from such sparse examples.


Ho Tu Magic Square

Lo Shu Magic Square (Forms Swastika)

I-Ching

The I-Ching itself is based upon the combination of Yang (solid, bright, definite) and Yin (empty, dark, indefinite) principles to produce 64 combinations of 6 lines, called hexagrams. This system was used in antiquity as a means of divination and to describe the natural world.

It is one of the oldest books in the world (extant) and one of the most important, IMHO. However, the modern translations are based upon manuscripts that may not be in the original pattern and spirit of the book – at least one Taoist sect claims to have the original divinatory manuscript – see Opening the Dragon Gate: The Making of a Modern Taoist Wizard by Chen Kaiguo and Zheng Shunchao.

Binary Code

Gottfried Wilhelm Leibniz, a major refiner (and some even would say inventor) of the binary code used today, was notably influenced by the I-Ching – he refers to it in his work Explication de l'Arithmétique Binaire (published in 1703).

Modern computer language is based on binary code, which was based at least in part on I-Ching, which was based on natural patterns points to the ubiquity and importance of a basic binary principle that is at the foundation of metaphysical philosophy, natural philosophy, and technology. The I-Ching played a crucial part in the digital revolution.

DNA and the I-Ching

There is also a connection between DNA and the I-Ching. The discovery of DNA is credited to James Watson and Francis Crick – famously, it has been suggested that Crick admitted that the double helix concept was an inspiration that came to him during an LSD trip, and that if anyone printed the information he would sue them (alleged by Dick Kemp – however this would make sense, as it was known that Cambridge acedemics were using LSD to "boost creativity" during that period, and it would be another simultaneously metaphysical and chemically natural coincidence, similar to the mythical emergence of the Ho Tu and Lo Shu).

In the twentieth century and beyond, philosophers and scholars realized the similarity between I-Ching and DNA and mapped them together (with some conflicting theories).

There are only four base pairs of DNA (Adenine (A), Thymine (T) Guanine (G), and Cytosine (C). These amino acids correspond to the “bigrams” or four primary combinations of yin and yang in the I-Ching.

The 64 Hexagrams and DNA Codons – From Tao of Chaos by Katya Walter

An amino acid “codon” of DNA is a grouping of these base pairs into three sets. There are 64 codons in each codon group, just like the 64 hexagrams of the I-Ching. Each codon acts as a specific command or function.

Additionally, the special dynamics of I-Ching involving the “old family” and “new family” systems, also potentially explain many properties of genetic transformation.

Such works as

  • DNA and the I Ching: The Tao of Life by Johnson F. Yan
  • Tao of Chaos by Katya Walter
  • I Ching & the Genetic Code: The Hidden Key to Life by Martin Schonberger
  • Gene Keys: Unlocking the Higher Purpose Hidden in Your DNA by Richard Rudd

delve into this topic. The books DNA and the I-Ching and Tao of Chaos are highly recommended and are free from any significant post-modern influences.

There are also countless sources on the internet on this subject, with varying degrees of factuality, of course.


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