Binary Numbers & Drum's Law of Changes - Hồn Trống Việt
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Binary Numbers & Drum's Law of Changes

From the very first articles we said that the Drum is the encoded law of changes, and the Energy level or quantity of the energy expressed in decimal numbers through binary numbers is the minimum knowledge required to find the diagrams on the Drum. Why? Because the binary numbers play a major role in the Drum’s encryption algorithm.

The father of the modern Binary system

Leibniz studied binary numbering in 1679; his work appears in his article Explication de l’Arithmétique Binaire (published in 1703). The full title of Leibniz’s article is translated into English as the “Explanation of 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”.[21] Leibniz’s system uses 0 and 1, like the modern binary numeral system.

Source: Wikipedia,

Fig 1: 64 hexagrams in binary from 0 to 63

There is still debate as to whether he discovered it himself or by virtue of the I Ching. However, to those who study “I Ching”, the more important is the fact that Leibniz recognized that the I Ching used the binary thousands of years ago, as per a quote from the scholar Nguyen Hien Le1 “Between 1679 and 1702, he (Leibniz) corresponded with a Jesuit missionary in China, and thanks to this missionary he learned about the 64 Hexagrams, seeing that the Chinese used only two lines of yang and yin to create the trigrams & hexagrams,  just as he only used 1 and 0 to write every number. He asked the missionary for a copy of 64 of hexagrams based on Phuc Hy’s early heaven 8 trigrams . . . and saw that if he substituted zero for the broken line, the number 1 for the solid line, then 64 hexagrams were exactly 64 numbers from 0 to 63 in his binary system.”

Fig 2: The letter S or energy movement

What makes us surprised is that more than 300 years have been passed since that discovery, very few have thoroughly understood the role of binary numbers in the Book of changes. The evidence is that, until today, although most people accept TTBQ, not many recognize the S curved motion, a fundamental Law of changes manifested right on the TTBQ through a simple act of connecting trigrams of the high to low energy level or vice versa.

That law of spiral movement has been shown & seen on the Drum & its diagrams such as TCV, BQLD & BQHT.

The Drum, Drum’s Law & Binary Numbers

The most important part of the algorithm used to encode “Ngoc Lu” Bronze Drum is the binary numbers. Therefore, without recognition of the linkage “I-Ching”-binary numbers, discovered by Leibniz we cannot decode the Drum.

The application of the binary numbers showed that the authors of the Drum had known about them, and they were probably then called Am Duong numbers because the foundation of the Drum’s law of changes is Am Duong Ngu Hanh (the Yin Yang Five Elements) Theory. It is strange that the Drum applied AD numbers to encrypt AD Theory. Why did the authors of the drum make the algorithm so easy?

With the drum buried deep underground until 1893, inability to see the binary on the Drum is understandable. However, the trigrams & hexagrams were known & available for thousands of years, why no one before Leibniz had seen the linkage & been able to show the numbers from 0 to 7, the binary of 8 single trigrams, let alone the longer & more complicated series from 0 to 63 of the 64 hexagrams? Clearly, that knowledge of AD or binary had been forgotten and, very likely, will be lost if not discovered by Leibniz or, rather, rediscovered.

Fig 3: Drum uses numbers 16 & 18 to encode 2 hexagrams on the round no. 8.

In the Homeland of Fairy-Dragon article, we have seen that the Drum used the binary to encode 2 hexagrams on the round 8, namely the Double Water and Earth Water.

Fig. 4: 16 & 18 are energy level, expressed in decimal numbers through binary.

Another more important evidence shows how well the Drum’s authors understood and were able to proficiently and creatively apply the binary through the following figures.

Fig. 5: The total energy level of 8 trigrams is 28.
Fig. 6: On BQHT, the energy both Yin & Yang section is 14 respectively.

On the ring No. 1, where there are the instructions on how to find the BQHT, is also a place the Drum depicts 14 beams going out & 14 figures returning that represent the total energy level of all 8 trigrams and of each AD or Yin & Yang part of the BQHT (Fig. 7).

Fig. 7: BQHT with Total energy of 28 & of each Yin & Yang section is 14.

Once the authors of the Drum knew the total energy of each part, of course they were able to calculate the energy level of each single trigram & hexagram.

The 3 figures above are undeniable proof that the authors of Ngoc Lu Bronze Drum understood the binary or Am Duong numbers deeply. And very likely that they were the only people who knew & that was the reason why they used the binary in the encoding algorithm.

Their understanding of the binary is so comprehensive that they were able to apply the binary numeral system to not only create 8 trigrams and 64 hexagrams representing everything, but also to encrypt them, to give instructions on the diagrams, rules & laws, and especially to express their view about the universe and human, which is the Am Duong Ngu Hanh (Yin Yang Five Elements) theory.

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