Symbolic images and numerology belong to the very essence of the alchemists’ mentality. The use of symbols and numbers convey a much deeper communication, or language, and therefore, have a much more profound affect on the subconscious than the mere words of philosophy or mythology.  The most profound symbols are archetypes, symbols that live as ideas in our subconscious but link us to a collective society, as if archetypes are an intellectual vestige of an earlier civilization.

Magic squares play a vital role in alchemy and magic.  Magic squares have a long history as talismans that date back 2,000 years. Magic squares possessed magical qualities that could ward off bad spirits or bring good luck. Magic squares in the Luo Shu format form a “set” of magic squares that are closely related to the Pythagorean Theorem (see last post).

3x3				5x5						7x7
Magic Square				Magic Square						Magic Square
										22	47	16	41	10	35	4
				11	24	7	20	3		5	23	48	17	42	11	29
4	9	2		4	12	25	8	16		30	6	24	48	18	36	12
3	5	7		17	5	13	21	9		13	31	7	25	43	19	37
8	1	6		10	18	1	14	22		38	14	32	1	26	44	20
				23	6	19	2	15		21	39	8	33	2	27	45
										46	15	40	9	34	3	28
SATURN				MARS						VENUS
LEAD				IRON						COPPER
EARTH				FIRE						METAL
BLACK				RED						GREEN
ONYX				RUBY						EMERLAD
CROCO				HORSE						DOVE

Table One:  The first three magic squares in the Luo Shu format with each demonstrating a unique Pythagorean triplet of numbers.  Each magic square has an alchemical correspondence with a specific planet, metal, element, color, stone, and animal. 

Magic Squares and the Kabbala

We are all familiar with how the vast majority of people, for thousands of years as well as presently, believe in the influences of the planets on the character of humankind. The early Chinese, the Kabbalists, the shamans and magis all developed systems to obtain the most auspicious of these influences that the planets may impart.

The Kabbalists assigned names and symbols to each planet.  These signs were followed by magic squares.  The signs and magic squares for the planets have been published in several books, one of the first by Cornelius Agrippa, who completed De occulta philosophia in 1510.  The set of magic squares also appeared in books by Luca Pacioli, De viribus quantitates (1498), and Athanasius Kircher, Arithmologia (1655).  Magic squares were popular during the Italian Renaissance and were known to the famous artists, mathematicians, and astronomers of the time. 

Magic Squares and Symbols

Time and space have always been important concepts to philosophers, mathematicians, and scientists.  The carpenter’s square and the magic square are ideal symbols for time and space with the history being Chinese in origin. 

A prosperous, evolving civilization begins with the gnomon, an astronomical instrument which served as the keeper of time for thousands of years.  The light of the sun would cause a shadow from the gnomon to appear on the ground and measuring this shadow would determine the time of year.

 It was because of the gnomon and  the ordering of sequential time that allows for the necessity of Numbers and the preservation of the “Numbers of Time.” 


Understandably, this took years of observing and record keeping but this was the method to determine summer and winter solstice. 

The definition of gnomon, in Webster’s Dictionary, indicates that the word is inherently related to the carpenter’s square.  In Joseph Needham’s Science and Civilisation in China (page i of any volume), the words carpenter’s square and gnomon are used interchangeably:

The carpenter’s square is no ordinary tool, but the gnomon for measuring the lengths of the sun’s solstitial shadows.

Therefore, the carpenter’s square measures time via the role of the gnomon and measures space via it’s graduated numbers of measurement in combination with the right-angle triangle theorem (the Pythagorean Theorem). 

                                                        
The gnomon, the most important astronomical instrument known to civilization for thousands of years.

The Chinese Connection to the Carpenter’s Square

A very old Chinese pictogram, 工 (gong), refers to an artisan who carries his carpenter’s square; the glyph is used in many words and also has a relationship with music and astronomy.  Another very old pictogram, 曲 (chu, ju, or jue) also means carpenter’s square.  One can see that, according to Mathew’s Chinese – English Dictionary (1956), the glyph is related to many words, but like 工 (gong), is also related to music.  Alfred Schinz, in his book The Magic Square (1996), reports that the pictogram 曲 is based on the 3x3 grid of the magic square and appeared on oracle bones dating to the Shang dynasty (1100 BC).

If we re-examine table one above, we can observe Pythagorean triplets of numbers in the shape of a right angle or gnomon residing at the heart of each magic square.  A gnomon shape of Pythagorean numbers in a 3x3 grid can explain why a pictogram such as 曲 (chu) means carpenter’s square. 

Another interesting link exists with the English definition of gnomon with that of the Chinese.  Referring to Webster’s Dictionary once again, the fourth definition of gnomon is canon or tenet. 

This relates to the Chinese phrase 規矩 (gui chu) which combines the pictograms for the compass and carpenter’s square and means:  following the rule of tradition and moral standards for establishing order; the way things should be.  Measuring the shadow of the gnomon involved following the rules of tradition thereby creating a moral standard.  Therefore, the ancient method to establish order involved using mathematical tools and traditional ways of observing and documenting the numbers of the shadow length.  Thus, the English definition of gnomon referring to canon or tenet, that is, the way things should be may lead one to believe that the etymology of the Greek derived word gnomon may have a Chinese connection.

The importance of the gnomon to civilization was documented by the early Chinese in one of the oldest math books known, the Zhou bi suan jing, The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven, wherein it states, “the combination of the right angle with numbers (the carpenter's square/gnomon) is what guides and rules the universe.” 

These Chinese pictograms from thousands of years ago represent one of the earliest written languages known to linguists.  The use of mathematical symbols with the incorporation of traditions were the basis of some important words (pictograms) in the Chinese language and demonstrates the heavenly role the magic square played in early Chinese civilization.  Diagrams such as the Chinese magic square contain vestiges of knowledge of the most ancient human beings, reveal a mystical mathematical vision, and may even be a link to a primitive, universal language.

Numbers, the right-angle triangle theorem, the carpenter’s square, and the gnomon are inter-related with the magic square, alchemy and magic; all of which make correspondences to math, time, and space.  Symbols and archetypes are a natural result from the traditional and repetitive use of these functional tools that help advance the prospects of human evolution and prosperity. 

       

Mosaics from Ravenna, Italy represent some of the finest examples of early Christian art from the fifth to tenth century.  It may be a far-fetched theory, but the symbols on the religious garments simulate the carpenter’s square and the Chinese 工 (gong) pictogram.  Art historians have no explanation for these markings.  However, it is known that in the middle ages, the Christian hierarchy was obsessed with obelisks, gnomons, astronomy instruments, Pythagorean symbolism, numerology, and magic squares, in other words, instruments of time and space.  Was there a Chinese influence on early Christian art and architecture?

This blog is dedicated to mathematics and the magic square – to learn more about how the magic square influenced Chinese civilization as well as early Christian art and architecture, please order my book, Number Time Archetype.

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Introduction

For the benefit of those new to this site, this post will serve as an introduction to this blog and to my book, Number Time Archetype.  Please understand that this is an ongoing effort that is now entering its thirteenth year.

Galileo once remarked that the world is a book written in mathematical language alluding to the theory that the mysteries of nature can be solved by simply examining the math.  Throughout modern history geniuses such as Plato, Pythagoras, Da Vinci, Durer, Galileo, Newton, and Leibniz acknowledged that mathematics was necessary for the evolution and prosperity of humankind.

However, the world of math could only begin with the advent of numbers.  Therefore, a numbering system would be the impetus of human evolution and prosperity.

Numbers are a language unto themselves at the ready to impart wisdom upon humankind for the purpose of evolving and prospering.  The language of numbers would provide humankind with the tools and mathematical formulas to manage time and space: time as in the numbers of the calendar and space as in the Pythagorean Theorem.  The arrangement of numbers into squares would reveal this information.  These squares of numbers are called magic squares.  The following represents the simplest magic square:

The Chinese 3x3 magic square known as the Luo Shu.
Note that all the rows, columns, and diagonals add to fifteen, the magic constant.

This arrangement of the first nine numbers would become the Chinese model to impart a perfect cosmic order to space of political or religious importance such as space dedicated to temple design, city planning, royal tomb design, and agricultural ceremonies in traditions that would last over a two thousand five hundred year period.  As the Chinese were the most advanced civilization during this time (about 1,000 BC to 1,500 AD) and because math is the root basis of the technology of such supremacy, insights into the Luo Shu can access a portal into the Chinese reverence for numbers as well as the math that led to the conquering of time and space.  

The concept of number was so critical to the success of humankind that the early Chinese incorporated the iconography related to math, astronomy, and agriculture into the pictographs and glyphs of the Chinese language.  The combination of pictographs with subtle messages of morality (that is, tradition) built in to the glyphs would form a comprehensive model of writing which would allow the political administrative state a psychological control of authority over a population through the use of language.  With symbolic pictographs, the Chinese language tells a story of a society's advancement and makes correspondences to the role of humankind in relation to Heaven and earth for the benefit of agriculture that emphasizes a moral tradition or a moral code of conduct.  Math would prove to be the foundation of this advancement and played a significant role in language symbolism. 

As the 3x3 magic square grid is the root origin of such important Chinese words such as qu (old style: 曲) = the carpenter's square and music, tien (典) = a rule, canon,  xing = to rise, to prosper,  jing (井) = well (water), and  ya (亞) = the cosmic center; it becomes apparent that the Luo Shu magic square and the concept of "number" were sacred and played an important role in the philosophy of the Chinese language, which uses the Luo Shu pattern of nine to help establish order over chaos through the use of math and tradition.

Unlike the western system of treating numbers strictly as numerical entities to be manipulated by formulas, the Chinese philosophy of numbers (number) would correspond to various numerical systems intended to impart cosmic order.  Magic squares represented an ideal number system and were an important source for these "cosmic" or "sacred" numbers.  For instance, the center in the Chinese system and the center number in Luo Shu magic squares represent several significant concepts.  The center represents the axis mundi or where the four cardinal directions meet.  It is considered the meeting place of Heaven and earth, a most important concept in temple design.  The center of a Luo Shu magic square also represents the axis mundi and can be calculated by the following method:

Let x equal any odd number greater than 1, then

These numbers will always be part of a Pythagorean triplet as well as being "centered" numbers making these numbers doubly significant.   For example, if x is 7, then the center between one and 49 is 25 which is part of the 7-24-25 Pythagorean Triad. In other words, x and the center number are the two odd components of the Pythagorean triplet.  (In the Pythagorean and Chinese numerology systems, odd numbers are superior to even numbers, this would be one reason why.)

Example: the 7x7 magic square and some of the features unique to magic squares in the Luo Shu format.

   x = the size of square = 7
  y = the center = 25
magic constant = (x)(y) = 175
∑x = ∑7 = 28
∑x² = ∑49 = x²y = 1,225
note the cross of odd numbers that run thru the horizontal and vertical axis

The Pythagorean Theorem served as the mathematical backbone for the understanding and ordering of the cosmos, as well as land surveying and water management on the terrestrial earth.  The importance of the Pythagorean Theorem cannot be understated and was thusly recognized by the early Chinese as its symbol, the carpenter's square, shoulders the legacy as one of the most important icons in Chinese philosophy.  In language, the use of the Chinese character for carpenter's square ju, 矩, when combined with the Chinese character for compass gui, 規, forms a new word, gui ju, 規矩, which means to establish order, a moral code, or the way things should be.  The early Chinese placed extreme importance on the concept that to establish order a moral standard must be followed and astronomical tools and math would be essential.  In art, the carpenter's square symbolism can be found in the royal tombs of kings.  In astronomy, the carpenter's square also symbolized the gnomon - the most important astronomical instrument known to humankind for thousands of years.

The gnomon was simply a stick in the ground whose shadow length would determine the approximate time of year between winter and summer solstice.  The painstaking tradition of measuring, recording, saving, and studying the shadow length data for thousands of years, i.e. calendar making, was part of the moral standard to evolve and prosper and was essential to the role of the king.  The shadow of the gnomon was in a right angle relationship to the gnomon thereby generating a right angle whose measurements would satisfy the Pythagorean Theorem.  Therefore, the gnomon, the right angle, and the carpenter's square were symbols of time and space.

The gnomon, the Luo Shu (math and the concept of number), music, and astronomical tools had special status among the early Chinese as these were instruments that helped humans to connect with Heaven for the betterment of humankind.  The Luo Shu was an important element of Chinese philosophy as it represented a musical source, an astronomical correspondence, and a mathematical system that enabled the Luo Shu to become a spiritual tool to establish order and bring humankind in harmony with Heaven and earth. 

The secret to the Luo Shu is the following formula that allows expansion of the 3x3 magic square into larger magic squares that all exhibit features in common but the most significant is that a Pythagorean triplet of numbers appears at the heart of each square.

        X = size of square

Y = X² + 1 ÷ 2 = the center
X, Y, and Y - 1 always generate a Pythagorean triplet

Part Two of this book looks at all the higher order magic squares which will reveal the philosophy as to why the early Chinese considered the Luo Shu the perfect model to express cosmic order.

The Chinese civilization was not the only culture to be greatly influenced by math, the concept of number, and magic squares.  The Christian community, which borrowed from many cultures and religions, also was greatly influenced by Pythagorean and Chinese numerology, which share many commonalities.  

This book will reveal for the first time the influence of the Luo Shu on early Christianity.  There is no question that monks from as early as the eighth century were incorporating magic square symbolism onto the covers of some of the worlds' most valuable books.  This blog and book will point out, also for the first time, the use of the carpenter's square in early Christian iconography.  Some experts on early Christian art and architecture such as Joseph Strzygowski believe that the early ground plan for church design (the cross-in-square plan also known as the quincunx) was based on oriental influences.  There can be no doubt of the Luo Shu influence on Chinese temple design, feng shui, and geomancy.  Did the Luo Shu influence early Christian church design?  Was there an earlier connection between the Chinese and early Christianity than previously thought?

These are the exciting questions that my book and blog will attempt to answer.  But the story does not stop here.  The Luo Shu was an important influence during the Italian Renaissance when artists, architects, and mathematicians were re-discovering the wisdom possessed by the ancients.  Luca Pacioli, who was a roommate and teacher of Leonardo da Vinci, was known to be an avid magic square enthusiast.  Was the Luo Shu an influence on Leonardo da Vinci, Donato Bramante, Albrecht Durer and other great artists, mathematicians, and architects?  And finally, were the Jesuits (who infiltrated China as early as the sixteenth century) after early Chinese documentation of the Luo Shu?  The art works of Athanasius Kircher (mid 1650s) and Ferdinand Verbiest (late 1660s) suggest with certainty the Jesuits were keenly interested in the Luo Shu. 

Needless to say, the Luo Shu geometric pattern was used prolifically by the early church in the same manner as the early Chinese.  This book will attempt to prove with mathematical certainty that the magic square was the geometric model used on the covers of several Christian manuscripts.  If this is true, then the magic square was a part of Christian iconography as early as the eighth century, thus pushing back the timeline by five hundred years when the magic square made its western appearance.

Following the story of the Luo Shu is like following the evolution of humankind over the course of thousands of years, weaving its way through many cultures who were advanced in the arts and were seeking spiritual harmony thru mathematics.  Much of this knowledge has been lost over time and much is considered "secret".   This is the book that explains the secret language of numbers, the language of Heaven that was gifted to us humans for the advancement of humankind.  

        ONLY $36.50