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Introduction to The Language of Numbers Demystified
The language of numbers can best be understood by examining the math behind the Magic Square. Understanding this math allows construction of a Magic Square of any size. The higher order Magic Squares seem to communicate a language in the form of numbers and give revelatory information about time (as in the calendar) and space (as in the Pythagorean Theorem).
This book, The Language of Numbers Demystified will provide a new deifinition of a Magic Square in the Luo Shu format. This book will make associations with Chinese iconography and early Christiian art that have not been asserted in the past. This book will uncover a discovery about a Pythagorean triad of numbers that occurs in each and every Magic Square in the Luo Shu format, this has never been revealed until now. This book will have a set of higher order Magic Squares that has never been published before.
The ancient Chinese were well aware of this secret Math and revered the 3x3 magic square, the simplest Luo Shu. This reverence is elaborated upon in books by Schinz, Needham, von Franz, Granet and demonstrated by the ancient Chinese in the their agriculture, in the layout of their ancient cities and villages, in the architecture of some of their sacred temples (the Ming Tang Temple in particular), in their money (the Chinese “bi” coin), and in the Yi Jing (“Book of Changes”).
Agriculture was integral to prosperity for the Chinese in ancient times and most cultures have fertility mythology related to death and regeneration. Wheat and the star Sirius were archetypes of ancient Egyptian culture as were grain and the Great North Star to early Chinese culture. Both cultures used Mathematics to bring some understanding and order to the chaotic cosmos in order to harness these influences to their maximum benefit upon their annual harvest.
The ancient Chinese relied on the Luo Shu pattern of nine divisions as a tool to maximize their effort to impart a balance of yin yang forces and used the pattern on a daily basis. Fertility mythology, the concept of the Luo Shu, and the heavens were emphasized in the characters of the language of the Chinese as well as in the annual rituals performed by the emperor himself. The symbol for well (“jing”) also symbolizes the division of nine pattern for the layout of rice paddies, (Willams, Outline of Chinese Symbol and Art Motives, p. 1-4) is also known as the jingtianzhi . Literally, jingtianzhi means “the well (water) field system of the holy field of nine squares,” (Schinz, The Magic Square , p. 9). Thus, the inter-relationship of the heavens, agriculture, and mathematics is evident in the symbols of the Chinese language.
The pattern of nine also played a role in temple design in Chinese culture. The Ming Tang (Ming Thang) temple was one of the most sacred and only the emperor and his inner circle had access. The Ming Tang temple has several translations, one of which is “The House of the Royal Calendar.”
This author believes that the Chinese used the higher orders of Magic Squares in this temple for astronomical purposes and knew that numbers represented a language which if understood would yield revelatory information about the Cosmos, Time, and Space.
The number of days in a season, the number of days in a year, and the number of days of the human gestation period are emphasized in the language of numbers using the higher order Magic Squares as the interpreter (gnomon). The word gnomon is derived from the Greek which means: interpreter, discerner, carpenter's square, pointer, or sundial. The carpenter's square is the symbol for the gnomon and is the connection between the Pythagorean Theorem, the Luo Shu, the path of the sun, and the calendar. The gnomon represented man's first sophisticated mathematical instrument to establish an order to the cosmos.
One note of interest is that every Magic Square (in the Luo Shu format) reveals a Pythagorean triad of numbers in the most important cells of the Magic Square, that is the center cell and two adjacent cells. This in itself represents a significant contribution to the understanding of ancient Chinese mathematics and of Magic Squares.
The fact that a Pythagorean triad presents itself in every Magic Square (in the Luo Shu format) is a beautiful example of how this arrangement of numbers is a form of communication, or language. The Chinese were familiar with the Pythagorean Theorem probably 1500 years before Pythagoras was born and knew its great importance to inhabitants of the physical world. Brownowski (The Ascent of Man) states boldly that the Pythagorean Theorem is the most important mathematical theorem to mankind as it describes the space that man moves about.
This reverence the Chinese culture had for the Luo Shu and the pattern of nine can be better understood by realizing that these Magic Squares were connected with algebra and could generate sacred numbers such as the numbers of the calendar. This reverence was further demonstrated by the use of the gnomon to follow the Sun which is recorded in ancient texts such as The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven (Zhou bi suan jing). Classic works have traditionally associated the Luo Shu with Time (calendar) and Space (Pythagorean Theorem) without further explanation.
This book hopes to provide a basis to further understand the Luo Shu as a model for Time and Space as well as the Chinese reverence for this magical square.
A discussion on early Chinese culture would be incomplete without a mention from Sir Joseph Needham, the great sinologist from Cambridge who wrote Science and Civilisation in China , in seven volumes. This book relies heavily from Volume III, Mathematics and the Sciences of the Heavens and the Earth .
Other books/references that proved invaluable to this work: