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Ancient Creation Stories told by the Numbers

by H. Peter Aleff

 

 

  

Footnotes :

 

[1] André Pichot: “La naissance de la science”, Gallimard, Paris, 1991, translation consulted “Die Geburt der Wissenschaft -- Von den Babyloniern zu den frühen Griechen”, Wissenschaftliche Buchgesellschaft, Darmstadt, 1995, see subchapter: “Die Zahlenmystik”, pages 92 to 94.  

 

[2] Simo Parpola: “The Assyrian Tree of Life: Tracing the Origins of Jewish Monotheism and Greek Philosophy”, Journal of Near Eastern Studies, Volume 52, July 1993, Number 3, pages 161-208.  

 

[4] David R. Fideler, in his “Introduction” to Kenneth Sylvan Guthrie, compiler and translator: “The Pythagorean Sourcebook and Library”, Phanes Press, Grand Rapids, Michigan, 1988, page 29.

 

[5] Kenneth Sylvan Guthrie, compiler and translator: “The Pythagorean Sourcebook and Library”, cited above, quoting Aetius, Plac. I. 3; Dox. 280, page 308 top.

 

[6]  As illustrated in Maitland A. Edey et al.: “The Sea Traders” , Time-Life Books, New York, 1974, page 131 left, credited to the Archives Photographiques Musée du Louvre.

 

[7]  J. E. Cirlot: “A Dictionary of Symbols”, Dorset Press, New York , 1991, page 351.

 

[8] David R. Fideler, in his “Introduction” to Kenneth Sylvan Guthrie, cited above, page 28 bottom.

 

[9] Kenneth Sylvan Guthrie,  cited above, translating Aetius, Plac. I. 3; Dox. 280, page 307 bottom.

 

[10] Kenneth Sylvan Guthrie, cited above, quoting Theon of Smyrna, page 317 top; see page 41 for date and title of Theon’s work.

 

[11]  Otto Neugebauer: “The Exact Sciences in Antiquity”, first published by Brown University Press, 1957, edition consulted Dover , New York , 1969, pages 35 to 38, plus Plates 6 and 7.  

See also the newer reconstruction and discussion of the Plimpton tablet Neugebauer had identified, in John H. Conway and Richard K. Guy: “The Book of Numbers”, Copernicus - Springer Verlag, New York , 1996, pages 173 to 176. 

 

 

[12]  Richard H. Wilkinson: “Symbol and Magic in Egyptian Art”, Thames and Hudson, London, 1994, pages 126 and 127.   

 

 

 

  

 

  

Numerals and constants  

 

 tell the creations of numbers and world

 
 


Holy n
umber diagrams

With a reasoning that seems quite rational in the context of a world ruled by gods of sun and moon whose cycles in turn obeyed numbers, the Mesopotamian sages treated numbers as religious symbols of fundamental importance, as supernatural beings that ruled the manifestations of nature[1].  They identified each of their gods with a number that defined them and their interactions, and they condensed this arithmetical pantheon into a mystic diagram of numbers with three columns which they venerated as the "tree of life".  

 
 

In slightly modified form, that tree of numbers and of life still survives in the Jewish Kabbalah as its central chart of the Ten Sefirot.  These are body-less number spirits who act as mediators between God and the world and as God's fingers or tools for its creation and maintenance.  Their name derives from the Hebrew word "sefer" for “number” which led to English "cipher", and they represent the numbers from one to ten, each with its own mystic name and symbolic functions. 

 
 

The Kabbalah is often said to date only from the early second millennium of our era because this is when its “founding book”, the Zohar, was written.  However, many of its teachings are much older, and the Assyriologist Simo Parpola showed that its Sefirot diagram corresponds closely to the Assyrian number diagram for the Tree of Life from about 1200 BCE.  The two match in such detail that coincidence can be safely excluded [2].  

The ancient Egyptians' attitude towards numbers was similar, and they seem to have devised their own diagram of the first ten numbers.  As in the case of their writing system, they appear to have used the same basic idea as their neighbors but developed it in their own characteristic way.  

No example of this diagram is known from ancient Egypt itself, but it stood at the core of the doctrine taught by Pythagoras (ca. 580 to 500 BCE).  As we saw earlier, this Greek leader of a number- venerating religion had picked up much of his mathematical knowledge in the Near East and particularly in Egypt.   His most sacred representation of his teachings about NUMBER was a diagram that arranged ten dots in four decreasing layers to form a pyramid.   

Pythagoras called that ten-dot triangle the Tetractys and used it as a mystical symbol for the perfection of  Number and of its elements.  According to the ancient writers about his doctrine, the ten dots in this number triangle represented the numbers from one to ten as well as all the numbers.   

picture of Tetractys

The Tetractys distilled the timeless reality of NUMBER to its essence.  Here is how one modern scholar described the heavy freight of ideas the Pythagoreans loaded onto this little triangle that could:

“... it is an image of unity starting at One, proceeding through four levels of manifestation, and returning to unity, i.e. Ten.  In the sphere of geometry, One represents the point, Two represents the line, Three represents the surface, and Four the tetrahedron, the first three- dimensional form.  

Hence, in the realm of space the Tetractys represents the continuity linking the dimensionless point with the manifestation of the first body; the figure of the Tetractys itself also represents the vertical hierarchy of relation between Unity and emerging Multiplicity.  

In the realm of music, it will be seen that the Tetractys also contains the symphonic ratios which underlie the mathematical harmony of the musical scale:  1:2, the octave;  2:3, the perfect fifth;  and 3:4, the perfect fourth.”  [Since it also weaves together odd and even, as in the mathematical harmony of the Universe]  “... the Tetractys, or the Decad, was called Kosmos (world order), Ouranos (heaven), and Pan (the All).“[4]

One of the ancient compilers of information about Pythagoras further reported as part of the latter’s teachings about the Tetractys that

our soul is composed of [this diagram] which is intelligence, understanding, opinion, and sense, from which things come every art and science, and we ourselves become reasoning beings.”[5]  

Pythagoras held the Tetractys, this perfect numerical and geometrical model of cosmic wholeness and celestial order, in such high esteem that he had his disciples invoke its discoverer in their oath of loyalty to his mathematics- venerating religious society: 

“I swear by the discoverer of the Tetractys / Which is the spring of all our wisdom / The perennial fount and root of Nature.”[8]

Another version swears this oath “by him that transmitted to our soul the Tetractys, the spring and root of ever- flowing nature”[9]

Theon of Smyrna, the second- century CE author of “Mathematics Useful for Understanding Plato”, quoted the oath as sworn “by the one who has bestowed the Tetractys to the coming generations, source of eternal nature, into our souls”.  He added that “the one who bestowed it was Pythagoras, and it has been said that the Tetractys appears indeed to have been discovered by him.” [10] 

However, that claim seems as overstated as the often repeated assertion that Pythagoras discovered the theorem about the squares over the sides of a right- angled triangle.  We learned that theorem in school with his name, but the Babylonians knew it at least a thousand years before he was born[11].

Tetractys before Pythagoras

The beginnings of the Tetractys figure are lost, but at least a century or two before Pythagoras, the Carthaginians already represented their goddess Tanit as a Tetractys- shaped triangle.  They often made that triangle into a very stylized human figure by adding a head- like circle on top and two arms to its side[6].  Sometimes they also showed her triangle with the pair of horns[7] that expressed Divinity around the ancient Mediterranean because Tanit was their supreme goddess who had created the world and established its order.

Carthage was a colony founded by Phoenicians, and Pythagoras had close links to these.  His father hailed from Phoenicia, and Pythagoras made that country his first stop on his study journey.  Phoenician  traders had also long been in close contact with Egypt, so the Carthaginians' use of that symbol is consistent with its proposed origin along the Nile even though no traces of it were found there. 

Another clue for the proposed origin of the Tetractys in Egypt is the striking distribution of prime numbers in larger arrays of this type.  The stair- like patterns formed by these primes appear to have inspired the angles of the mummy passages through most of the pyramids.  It seems that these passages were numerical stairs to the invisible beyond, as I propose in my book "Prime Passages to Paradise"

Number personalities

Similarly, the properties and virtues the Pythagoreans assigned to each of the ten numbers that correspond to the Tetractys dots are likely to reflect an amalgam of their teacher's sources, including a major share from Egypt.

According to the Egyptologist Richard Wilkinson, the ancient Egyptians 

“[held] quite a few numbers to be sacred or ‘holy’ but accorded the numbers themselves this element of sanctity and significance only inasmuch as abstract principles had become associated with them”[12].

Modern reconstructions of these principles as used in Egypt are, of course, at best fragmentary, but a record of those the Pythagoreans associated with the first ten numbers survives in the writings of Iamblichus, one of the Master's biographers who wrote centuries after his death.  

Those lists are quite long for each number, and some of the attributions overlap.  However, plugging in a selection of meanings from the lists for each number- dot in the Tetractys lets us tentatively reconstruct a probably Egyptian counterpart to the diagrams of the Kabbalah's Ten Sefirot and of the Assyrian Tree of Life which also symbolized the universe and its number- ruled order

 
 

Tetractys today

The use of that Tetractys- triangle as symbol for the Divinity and its world order survives today in the triangle- symbol for the Christian Trinity.  You find it illustrated, for instance, on the US dollar bill above the pyramid with the motto Novus Ordo Seclorum (The New Order of the Centuries).

scan picture from dollar bill

 

By placing that Divine triangle atop a picture of an Egyptian pyramid, the Masonic designer of that bill expressed the perceived antiquity of the symbol.  There was no documented evidence in his day that it had come from Egypt, nor is there any today, but the circumstantial evidence suggests that he was right.

Here again, it seems that the Egyptians shared with the Mesopotamians the basic concept that numbers were supernatural and related to each other in specific ways that could be pictured, and they again adapted that idea in their own unique fashion.  

Similarly, some ancient Egyptians were probably familiar with the basic principles of Mesopotamian arithmetic, but they developed their own unique methods for manipulating numbers. These worked so well that people around the Mediterranean kept using them for more than a thousand years after the last pharaoh died.
 

 

 

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