Magic Square of Mercury
Trigram & Hexagram Math
Mathematical "Magic Squares" have a rich and interesting history! Some are thought to be 4500 years old or much more. The earliest known Magic Square is a 3x3 square, traditionally known as the Luo River Scroll, or more recently, as the Magic Square of Saturn. It is attributed to the Chinese sage, Fu Hsi. The 64 sequential Binary Numbers of the I Ching are also attributed to Fu Hsi. Perhaps he was well aware of at least one 8x8 Magic Square, commonly known as the Magic Square of Mercury. It is very interesting that the 81 Tetragrams of the Tao Te Ching, by Lao Tzu, can also be formed into a traditional 9x9 pattern known as the Magic Square of the Moon. In pre-Christian Europe, seven different magic squares were assigned to seven astronomical bodies. This was done as follows: Saturn a 3x3 square, Jupiter a 4x4 square, Mars a 5x5 square, the Sun a 6x6 square, Venus a 7x7 square, Mercury an 8x8 square and the Moon a 9x9 square.
When the two Trigrams of each Hexagram are replaced with their corresponding modern numerical value, this pattern emerges.
When the two Trigrams of each Hexagram are replaced with their corresponding numerical value, this pattern emerges.
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When the 64 binary Hexagrams are translated into modern
Aribic numerals, the result is shown below:
Only three of those are discussed here, the Magic Square of Saturn, the Magic Square of Mercury and The Magic Square of the Moon. The fourth magic square, discussed later, is one discovered by this author, although it may have also been discovered by someone else presently unknown.
Here, the traditional 8x8 Magic Square of Mercury is treated in the same manner as Fu Hsi's Square was earlier. Each binary hexagram is replaced with the more modern numerical equivalent. Notice the eight numbers in each of the two Long Diagonals total 260,as do the numbers in each row and column.
Notice the eight numbers in each of the two Long Diagonals add up to 260, the same as those found in Fu Hsi's Square. That's not too surprising, since they are the same numbers.
When the Two Trigram Numbers in each Hexagram are added
together, the following pattern arises. Notice the eight number 9's
in one Long Diagonal, all total 72. The eight consecutive even numbers in the other Long Diagonal, also all total 72, just as they do in Fu Hsi's Square. The eight numbers in each row and column total 72 as well.
When the Two Trigram Numbers in each Hexagram are subtracted, the following pattern arises. Notice the eight 0's in one Long Diagonal, naturally all total 0. The eight consecutive odd, positive and negative numbers in the other Long Diagonal, also all total 0, just as they do in Fu Hsi's Square. The eight numbers in each row and column total 0 as well.
Magic Square History
Magic Square 2