The Language of Numbers

The arrangement of numbers into a Magic Square reveals a language in terms of practical math that the ancient Chinese found useful and was part of a revered system of faith that was referred to as the Yi Jing. The Pythagorean Theorem exists within every Magic Square in the Luo Shu format and teaches the fundamentals of algebra which in turn could give man the tools to measure distances.

This math is the basis for land surveying as well as for charting the stars. The Chinese believed that the movement of the stars and celestial events such as eclipses greatly influenced life on earth. This use of numbers would help man to establish some order over the apparent chaos of the heavens; the Chinese believed that numbers (or math) contained a higher intelligence and if used properly could have a positive effect on the yin yang balance. The objective of the Yi Jing is for man to be at one with Heaven and earth and this math was used to help achieve this end.

The language of numbers is revealed through patterns when numbers are arranged in squares such as magic squares and in columns, such as Eratosthenes's Sieve. Every odd number (except one) has its arrangement of numbers in a Magic Square in the Luo Shu format and an arrangement of numbers in columns that yield patterns that can lead to a practical use of math and the right angle triangle theorem.

This language is based on the arrangement of whole numbers from one to the highest number, which is the square of the odd number of interest. For example, the number three is represented by arranging the numbers 1 thru 9 (3 ² ) in a square and in two columns:

4   9   2             The most basic magic square is the 3x3 magic square
3   5   7             and can be represented by arranging the first nine
8   1   6             numbers in a square.

 A New Definition of Magic Squares in the Luo Shu Format         

1. The Luo Shu or Order 3 Magic Square reveals an arrangement of numbers so that each row, column and the two major diagonals all add up to the same number. This is the conventional definition of a Magic Square.
2. In addition to this definition, a Magic Square in the Luo Shu format is the relationship between the squares of two consecutive numbers. In the case of the 3x3 Magic Square, it is a relationship between the squares of numbers 1 and 2. Example:

2²  -  1²  =  3                  1²  +  2²  =  5 

                                    left of center cell                  center cell

3.  A Pythagorean triad of numbers is always generated in these three cells in any Magic Square in the Luo Shu format ( in green ). Demonstration  

Several other common characteristics of cell position can be described in mathematical language so that all Luo Shu Magic Squares reflect the same pattern.  The Pythagorean triad is one important example.

The two most important numbers of the 3x3 magic square:

5 occupies the center axis 
3 determines the size of the square.    

The product of these two numbers equals the constant of the square, or the number that represents the sum of any column, row, or main diagonal.

The product of [size of the square]² and the center number equals the sum of all the numbers in the square.

The center number, the constant, and the sum of all the numbers in a Luo Shu Magic Square are referred to as the numbers generated by a specific order or size of square.  

NUMBERS OF SIGNIFICANCE

Numbers that generate information are numbers of significance.  Numbers that create Pythagorean triads are of utmost significance as are numbers that have calendrical significance.  Numbers such as these can offer functional information on Time and Space. 

Numbers generated by Luo Shu Magic Squares include Pythagorean triplets and interesting patterns associated with the solar cycle of 365 days.  It is understood that there are about 365.25 days in a year, but for this consideration of the theories proposesd by these writings, only whole integers are considered.

For example, the number 0 and the next number, 1, which represent the first pair of consecutive numbers, do not generate a Magic Square (table of first seven Luo Shu Magic Squares).  The first pair of numbers that do are the first pair of whole integers, 1 and 2. 

The constant and sum total of a Magic Square were considered sacred numbers and were assigned sacred names by the Kabbalists and Alchemists.  These numbers became associated with the planets.  At least in the 13x13 Luo Shu Magic Square, and the 27x27 Luo Shu Magic Square, numbers are generated that are known in the Yi Jing as the numbers of the calendar.