- Table of Contents
- Introduction
- Part One
- Part Two
- The Luo Shu - 3x3 Magic Square
- The Enneagram and the Lo Shu
- 5x5 Magic Square
- 7x7 Magic Square
- 9x9 Magic Square
- 11x11 Magic Square
- 13x13 Magic Square
- Discussion - 13x13 Magic Square
- 15x15 Magic Square
- 17x17 Magic Square
- 19x19 Magic Square
- 21x21 Magic Square
- 23x23 Magic Square
- 25x25 Magic Square
- 27x27 Magic Square
- The Significance of the 27x27 Luo Shu Magic Square
- Part Three
- Bibliography
Time and Space
The Luo Shu is a tool that helps to correspond the two important concepts of time and space by means of the mathematics of the gnomon (or right angle triangle theorem) and the numbers of the calendar. Magic squares in the Luo Shu format are ordered spatial arrangements of numbers that are fields with a qualitative component that represent the total archetypal order of the universe and the axis mundi.
The significance of a numbering system that enabled humankind to measure weights, distances, and time was to establish a political and moral order. In early China, number was the tool of ordering the universe and the Luo Shu was a most powerful cosmo-magical time-space yin yang symbol.
The art of discovering Pythagorean triads in magic squares in the Luo Shu format is an example of translating the language of numbers that provide a formula for measuring space, known as the Pythagorean Theorem. It is most interesting that all magic squares in the Luo Shu format have at least one Pythagorean Triad in this matrix arrangement of numbers, that this triad occurs in the middle of the square, and that the triad involves the two key numbers of the square: the center number and the order (size) of the square.
It is also noteworthy to realize that this is the one mathematical relationship that allows a charting of terrestrial and celestial landmarks making this formula the most useful mathematical equation known to ancient humankind.
The numbers of the calendar (the number of days in a week, the number of days and weeks in a season, the number of days in a year) are all contained in the 13x13 and 27x27 Magic Squares. These numbers seem to travel together in the progression of higher order magic squares and form geometric patterns that involve right angles called polyabolas.
The Luo Shu has always been associated with Time and Space as well as calendar making but these connections have only received cursory attention. The understanding of the mathematics of the gnomon and using the magic squares to help interpret the language of numbers begins to shed light on the Chinese interpretation of the cosmo-magical influences that the Luo Shu had on the ordering of time and space.
Before this could be realized, numbers would have to be created. The foundation of numbering could very well have been established by measuring (and documenting) the shadow length of the gnomon in order to identify the solstices and equinoxes. The shadow and the gnomon form a right angle hence the root origin of the carpenter’s square and the art of numbering.
The mathematical connection of the calendar (measuring time) lies with the 13x13 magic square and the 27x27 magic square. These two squares are connected by the
The Numbers of the Calendar:
1. Seven - the number of days in a week
2. Thirteen - the number of weeks in a season
3. Eighty-five - the center number of the 13x13 magic square
4. Ninety-one - the number of days in a season
5. One Hundred Sixty Nine = 13 squared
6. These numbers add up to 365, and form a triabolo in the 27x27 Magic Square.
7. The squares of 13 and 14 play integral roles in both these magic squares.
The number that helps to decode the language of numbers is the number seven. In the code, the number thirteen is the seventh odd number, a very significant occurrence as odd numbers carry more relevance in the Chinese and Pythagorean numerology schemes than even numbers. The number fourteen is the seventh even number.
The 27x27 magic square is the relationship of the seventh even and seventh odd numbers, squared.
The addition of these numbers generates the center number of the square, 365.
The subtraction of these numbers generates the size or order of the square, 27.
The 13x13 magic square is the square of the seventh odd number and has 85 as the center cell. Ninety-one is positioned in the lower right corner of the square. Ninety one also represents the sum of all the numbers one through thirteen.
Most interesting in the 13x13 magic square is the product of (13)(13) and 85 equals 14,365 - the sum of all the numbers in the square with two familiar numerical components if one takes the liberty to use the comma to separate the one number into 14 and 365.
This exercise has demonstrated some of the guidelines utilized in understanding the language of numbers:
1. Seven is a key number as are the seventh odd, seventh even, seventh prime, and seventh odd prime numbers.
2. Magic Squares in the Luo Shu format can be better understood as the relationship between two consecutive numbers, squared.
3. Squares of significant numbers (numbers of the calendar) may hold noteworthy cell positions in some magic squares.
4. Commas can be used to separate one number into two numbers.
5. The constants and total sums of smaller squares may hold noteworthy cell positions in some larger magic squares.
6. Inverse of numbers of highest significance, such as numbers of the calendar, may also play significant role.
7. Counting the number of rows or columns that are spaced between numbers of significance demonstrates the harmonic and geometric balance of the field of numbers.
8. Odd Numbers will always occupy the horizontal and vertical axis of any Magic Square in the Luo Shu format. This forms a cruciform (the ya - shape) or cross shape and this shape was symbolic of the convergence of the four cardinal directions and represented centrality. The shape was used in the royal tombs during the Shang dynasty, temple design, and in art.