The Chinese Magic Square has always been known to have correspondences with Time and Space. This post will demonstrate how the 13x13 magic square and the 27x27 magic square communicate the numbers associated with the keeping of time and therefore were integral to the foundation of Chinese metaphysics. We start with the 13x13 magic square, the numbers of the calendar, and conclude with the grand daddy of all magic squares, the 27x27 magic square in the Luo Shu format.
THE 13X13 MAGIC SQUARE
Table 1. The significant numbers of the 13x13 magic square are highlighted in red, Pythagorean triplets highlighted in purple. The magic constant of the square is 13 x 85 = 1,105. Significant numbers of any magic square in the Luo Shu format will occupy these positions. One can see the Pythagorean triplet of numbers for the 15x15 magic square. Note also the cross of odd numbers that occupy the vertical and horizontal axis.
If numbers are in fact a language, then the most important feature for numbers is to provide functional information about Time and Space. Magic squares in the Luo Shu format do exactly this.THE NUMBER 13
The number 13 is part of the 13 – 84 – 85 Pythagorean triplet.
The most intriguing number is the number 7 and it's connection to the calendar; note that the number 13 is the seventh odd number, and the number 14 is the seventh even number.
The numbers 13 and 85 are the result of the difference and addition of the squares of two consecutive numbers.
(7x7) - (6x6) = 49 – 36 = 13 (the order of the square) and adding the squares generates:
(7x7) + (6x6) = 49 + 36 = 85 (the center number of the square).
Therefore, the 13x13 magic square is based on the consecutive numbers six and seven.
These numbers, 13 and 85, represent the odd numbers of the 13 – 84 – 85 Pythagorean triplet.
The sum of all the numbers one through 13 equals 91. This is a most important number that corresponds to the calendar as there are 91 days in a season.
The following odd numbers are numbers that describe Time and Space. Time as in the numbers of the calendar and Space as in the Pythagorean Theorem:
- 7 – the number of days in a week
- 13 – the number of weeks in a season and part of the 13, 84, 85 Pythagorean triplet
- 85 – part of the 13, 84, 85 Pythagorean triplet
- 91 – the number of days in a season
- 169 - part of the 13, 84, 85 Pythagorean theorem
- 7 – is the odd component of the square, which is based on 6 & 7
- 13 – is the size or order of the square
- 85 – is the center number of 1 thru 169 and is the center number of the square
- 91 – is the sum of the numbers 1 thru 13
- 169 - the 13x13 magic square in the Luo Shu format is the arrangement of the first 169 numbers in this square
- And most important, these numbers add up to 365 - the number of days in the solar cycle, linking the significant numbers of the 13x13 magic square with the center number of the 27x27 magic square.
Table 2. The 27x27 magic square (the square of the sun) demonstrating the triabolo of numbers that represent the significant numbers of the 13x13 magic square thus linking the two squares that make calendrical correspondences. The magic constant of this square is 27 x 365 = 9,855. Note also the cross of odd numbers that occupy the vertical and horizontal axis.
The 27x27 magic square is based on the numbrers 13 and 14:
(14x14) - (13x13) = 196 - 169 = 27 (the order of the square) and (14x14) + (13x13) = 196 + 169 = 365 ( the center number of the square).
The numbers 13, 27, 378 (the sum of the numbers 1 thru 27), 365 and 729 (27x27) represent the signifcant numbers of the 27x27 magic square. All magic squares in the Luo Shu format have their significant numbers in the same relative position, only select magic squares will have a self contained triabolo of numbers representing this concept: the 11x11magic square, the 19x19 magic square, and the 27x27 magic square have triabolos with the 11x11 magic square having a triabolo of numbers that correspond to the 5x5 magic square; and the 19x19 magic square having a triabolo of numbers that correspond to the 9x9 magic square; and the 27x27 magic square having a triabolo of numbers that correspond to the 13x13 magic square. Only odd numbers are involved.
The triabolo is a geometric shape that links the significant numbers of one magic square with a larger magic square. The 27x27 magic square is the most superior of all magic squares as it has the numbers of the calendar, as does the 13x13 magic square, but also has the number 365 as its center number. Plato refers to this important square in his book The Republic , chapter nine when Socrates states, "a king who rules with wisdom lives exactly 729 times more pleasantly than one who rules through tyranny" (find section 293, footnote 3, scroll down about three quarters of the script). Plato is writing in code and is referring to the 27x27 magic square: the number 729 is 27 squared, or the square of 27, that is to say, the 27x27 magic square with 365 as it's center number. Read the entire paragraph and you will see that Socrates refers to the calendar as well. From the Bible (Book of Revelation), "Man is the beast, he is wisdom, and wisdom is the understanding of nature and the numbers that rule the universe. His number is 666, (the sum total of all the numbers in the 6x6 magic square, one thru thirty six, in alchemy, the square of the sun, which symbolizes illumination, wisdom)."
1. The 13x13 and 27x27 magic squares in the Luo Shu format are related to Time as in the numbers of the calendar, and Space as in the Pythagorean Theorem.
2. The number seven plays a key role.
3. Odd numbers have a higher status than even numbers.
4. Odd numbers are created by taking the difference of the squares of two consecutive numbers, eg:
(1x1) - (0x0) = 1
(2x2) - (1x1) = 3
(2x2) - (1x1) = 3
(3x3) - (2x2) = 5
(4x4) - (3x3) = 7
5. The center number of Luo Shu format magic squares are created by taking the sum of the squares of two consecutive numbers:
(1x1) + (0x0) = 1, no magic squre
(2x2) + (1x1) = 5; center of the order 3 magic square
(2x2) + (1x1) = 5; center of the order 3 magic square
(3x3) + (2x2) = 13, center of the order 5 magic square
(4x4) + (3x3) = 25. center of the order 7 magic square
Therefore, magic squares in the Luo Shu format are based on two consecutive numbers
The pictogram ch’ü, 曲 – crooked, bent; wrong, false. When this pictogram is used with chi, 尺 – a foot (ten Chinese inches) – the new words formed are 曲尺 – carpenter’s square (although this is a very old usage of this glyph).
This pictogram for jing, 井 – a well, a pit, the shaft of a mine – projects the easiest visual to correspond to the 3x3 grid of the Luo Shu magic square. The pictogram demonstrates the legacy of the Well Field system or Holy Field, jing tian, a philosophical approach used for political influence as to the roles of society and government concerning agricultural. Evidence for the use of this ninefold division can be traced back to the Shang dynasty, c. 1,500 B.C. (亲耕– the emperor personally and symbolically plows the field).
Other words that correspond to the Luo Shu grid are diăn, 典 – a statute, a law, a code, a canon, documents, records; and words associated with ritual and ceremony – and xīng, 興 – to prosper, to rise, to flourish (old usage of glyph). Words that use the ch’ü glyph in a suspiciously similar fashion are nung, 農 – agriculture, to farm, farmer – and li, 禮 – sacrificial vessel – and associated with words for propriety, worship, and ceremony.
7. If
the meanings of words that derive from the Luo Shu were threads to a story,
then the legend of the Luo Shu would emphasize math as a source of wisdom and
using the carpenter’s square/gnomon will allow society to evolve and prosper
in an agriculturally based community.
The application of functional mathematics resulted in a more advanced civilization with such long traditions that customs were to be standardized so that the way things should be done became canon (law) and memorialized into posterity thru language, symbols, and ceremonies that corresponded with the calendar. This is the pathway for a society to conquer chaos, evolve, and prosper.
The Chinese magic square is the perfect model of Time and Space and is symbolic of establishing order thru the application of functional mathematics. The symbols that result have survived in civilization for over three thousand years. This blog is dedicated to the understanding of the math and symbols generated from the Luo Shu, a complicated but understandable "set of magic squares".
