The Significance of the Lo Shu

On a deeper level, the simplest Lo Shu, the 3x3 magic square, was symbolic of all magic squares in the Lo Shu format.  It represented the art form of numbering  (a natural way to arrange numbers in squares) and the origin of mathematics presented to Humankind from Heaven. 

The art of numbering and mathematics provided the tools necessary to describe Time and Space; the Lo Shu had within its framework a formula which allows the construction of higher order magic squares.  A language of numbers presents itself in the form of important mathematical relationships such as algebra and the Pythagorean theorem within these magic squares of numbers. 

Correspondences of the measurement of time with magic squares that contain the “numbers of the calendar”  has been the traditional role of the Lo Shu in the Book of Changes.  These numbers are found in the 13x13 magic square and the 27x27 magic square. 

The Lo Shu became the tool that could describe Time and Space and, therefore, became the model archetype that symbolized a methodology of how to establish universal order through a moral and traditional  standard that placed humankind at one with Heaven and earth.  

The following are the features as to why the Lo Shu was sacred and its pattern replicated in places of political and religious importance for thousands of years in the early Chinese culture.

1. A pythagorean triad appears in every magic square in the Lo Shu format. 

This is related to the gnomon  and was essential in land surveying and measuring celestial distances.  This also contributed to the formation of a calendar.  Learning to apply the right angle triangle theorem led to an understanding of algebra as well as the number of days in a season (91).

2. The numbers of the calendar are generated in the higher order magic squares. 

Five numbers form a triabolo, a geometric shape composed of three right angle triangles.  A triabolo forms first in the 11x11 Magic Square, then the 19x19 Magic Square, the 27x27 Magic Square, and every eighth square, all in the Luo Shu format.  The triabolo consists of five numbers that are the basis of a different Magic Square.  In the 27x27 Magic Square, a triabolo of five numbers represent the numbers of the calendar, and these same numbers are the basis of the 13x13 Magic Square.

3. The Ya – shape (or cruciform shape) is replicated in every magic square in the Lo Shu format. 

The numbers of heaven, odd numbers, always occupy the horizontal and vertical axis of any magic square.  The ya or cruciform shape is the ground plan for temple design and is symbolic of centrality or the convergence of the four cardinal directions.  More importantly, the Ya shape is a math icon symbolic of the Lo Shu.

4. The reverence for the Lo Shu and numbers influenced the creation of certain Chinese characters and this played an important  role in writing and authority of the State administration.  Examples: jing (well), mi (rice), ya (centrality), pei tou (north, peck measurement), gong (carpenter's tool), keui chu (to establish order). 

5. The practical use of the Lo Shu led to a belief that this magic square contained the tools to establish universal order and was used for prognostication purposes.    

The esoteric or deeper meaning  of the Luo Shu concerns the math of the gnomon and the numbers of the calendar.  One who can identify the four seasons with accuracy and formulate a calendar could bring some order to the apparent chaos.  Documenting the length of the shadow of the gnomon, and saving these records for hundreds of years gave the early Chinese insight into measuring the four seasons.  The relationship of the four seasons and the right angle triangle theorem can not be denied. 

The gnomon and magic squares in the Luo Shu format have in common the model for Time  (the numbers of the calendar) and Space (the Pythagorean Theorem). 

Throughout history, be it Chinese, Persian, or early Christian , the math of the Lo Shu and its higher orders was never to be made public.  It was considered to be the secret science of the priest-kings, also known as sages. 

Fu Hsi and the Great Yu were two of early China’s great leaders, although they could have been mystical figures and served as the vehicle to establish the canons of early Chinese authority.  The Yi Jing is one such canon and includes the tradition of the Lo Shu which is referred to as the River Document. 

Esoteric symbols such as the carpenter’s square and the pattern of nine (the jingtienzhi, the ya– shape, and the 3x3 magic square) survived for thousand of years.  The true meaning of these symbols has been long forgotten.

The earliest text that gives a clue to this math is the Zhou bi suan jing, reportedly written in the sixth century BC but its tradition could be much older.  Of interest is the English translation, “The Arithmetical Classic of the Gnomon and the Circular Paths of the Heavens”, which seems to be self explanatory. 

Sir Joseph Needham’s treatment of this text on pages 22 and 23 (Science and Civilisation in China, Vol. III , 1972) is invaluable (actually, the volume is a classic, perhaps one of the most important publications on Chinese civilization ever published).   The text proposes that the “art of numbering” ( the Lo Shu?) proceeds from the carpenter’s square, or gnomon. 

The Chinese words suan and shu occur together in ancient and medieval texts with such frequency as the meaning implies “the art of arithmetic” for the purpose of calculating the prognostication of fates. 

Therefore,  a possible esoteric meaning of  “Lo Shu” could be the use of permutations and combinatory math (of the progression of the higher order magic squares) to create a calendar and prognosticate the destiny of humankind. 

Therefore, it is quite possible that the early Chinese believed in the Lo Shu as a mathematical language of numbers that enables humankind to control its destiny.