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Ancient Creation Stories told by the Numbers

by H. Peter Aleff




Footnotes :


1  Coffin Text spells from late Old Kingdom and early Middle Kingdom times, translated in Clagett "Ancient Egyptian Science, a Source Book", Volume 1: "Knowledge and Order", 1989, American Philosophical Society, Philadelphia, 1995, pages 438 to 440.



2  R.T. Rundle Clark: "Myth and Symbol in Ancient Egypt", Thames and Hudson, London, 1959, edition consulted 1991, pages 43 and 78.



3  Sir Alan Gardiner: "Egyptian Grammar", Griffith Institute, Ashmolean Museum, Oxford, first published 1927, third edition consulted 1982, pages 58 and 59: "Writing of the plural and dual", also sign Z 2, page 535: triple repetition or three strokes as plural ending.



4  Karl Menninger: "Number Words and Number Symbols: A Cultural History of Numbers", Göttingen, 1957/8, edition consulted Dover, New York, 1992, page 17.



5   R.T. Rundle Clark: "Myth and Symbol in Ancient Egypt", cited above, pages 45 and 82.



6  (until 1774 when Joseph Priestley discovered oxygen).



7  R.T. Rundle Clark: "Myth and Symbol in Ancient Egypt", cited above, pages 80 and 82.



8  Erik Hornung: "The One and the Many" = "Der Eine und die Vielen: Ägyptische Gottes-Vorstellungen", 1971, edition consulted Wissenschaftliche Buchgesellschaft, Darmstadt, 1993, page 280.



9  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, Coffin Spells 76 and 80, pages 437 and 438.



10  Werner Forman and Stephen Quirke: "Hieroglyphs and the Afterlife in Ancient Egypt", Opus Publishing Ltd., London, and University of Oklahoma Press, 1996, page 82 middle.



11  Sir Alan Gardiner: "Egyptian Grammar", cited above, sign C 11, see pages 79, 191 and 449.



12  R.T. Rundle Clark: "Myth and Symbol in Ancient Egypt", cited above, pages 54, 55, and 273. See also Clagett: "Ancient Egyptian Science", Volume 1 cited above, pages 298 to 300, and note 33 on page 386.



13  From a hymn to Amen-Re, per Clagett: "Ancient Egyptian Science", Volume 1 cited above, page 556.



14  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, pages 531, 538, and 543.



15  Hans Reichenbach: "The Direction of Time", University of California Press, Berkeley, 1971, chapter 30: "Particles Traveling Backwards in Time", pages 262 to 270, quote from E.C.G. Stückelberg and R.P. Feynman on page 264.



16  Dieter Kurth: "Edfu: Ein Ägyptischer Tempel gesehen mit den Augen der Alten Ägypter", Wissenschaftliche Buchgesellschaft, Darmstadt, 1994, page 39.



17  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, pages 258, 297, 302 and 303.



18  Eric Hornung: "The One and the Many", cited above, page 280; also Morenz: "Egyptian Religion", 1960 Methuen & Co., London, 1973, page 23.



19  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, pages 298 and 385 for sources.



20  R.T. Rundle Clark: "Myth and Symbol in Ancient Egypt", cited above, page 53.



21  Richard H. Wilkinson: "Reading Egyptian Art: A Hieroglyphic Guide to Ancient Egyptian Painting and Sculpture", Thames and Hudson, New York, 1992, pages 38 and 39.



22  Paulo Ribenboim: "The Little Book of Big Primes", Springer-Verlag, New York, 1991, page 101.



23  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, pages 303 and 386.



24  Siegfried Morenz: "Egyptian Religion", 1960, translation consulted Methuen & Co., London, 1973, page 33 (from the Ptolemaic temple of Horus in Edfu): "I am Thoth, the eldest son of Re, whom Atum has fashioned, created from Khepri [the rising sun] ... I descended to earth with the secrets of what belongs to the horizon ...".



25  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, pages 304 and 389/90.



26  Alan Gardiner, as quoted in Clagett: "Ancient Egyptian Science", Volume 1 cited above , page 389.



27 Erik Hornung: "The One and the Many", cited above, pages 67 and 204.



28  Coffin Texts, IV, Spell 261, per R.T. Rundle Clark: "Myth and Symbol in Ancient Egypt", cited above, pages 77 and 78.



29  Marshall Clagett: "Ancient Egyptian Science", Volume 1 cited above, page 304.



30 Erik Hornung: "Idea into Image -- Essays on Ancient Egyptian Thought", (Geist der Pharaonenzeit, 1989), translation from Timken Publishers, New York, 1992, page 140.







Numerals and constants  


 tell the creations of numbers and world


The Heh gods who hold up the sky

One of the eight Heh- gods who hold up the sky.  This hieroglyph (Gardiner C 11) was the early numeral for “a million” and also signified “very many”.  It was later replaced by combinations of lower signs in number writing but not in symbolic art

Numerical value:  million(s)

Symbolic meaning:  Creation of the first gods

To transform his self- created One- ness into the millions mentioned in the hymns, Atum began by making the twin gods Shu and Tefnut, called in the Coffin Texts “eternity” and “everlastingness”1

Depending on the version, he made them from his seed or his spittle, but in either case he cloned them out of himself and then embraced them to communicate to them his Ka, or life- force and alter ego2

Atum was thus still present in both of them and could say “I was One and became Three”, and yet, he had produced plurality and thereby the first numbers.  The three into which he had made himself implied already the many to come since the hieroglyphic way to write “many” was to repeat an object three times3, just as in Chinese writing, and similar to the Babylonian system where the number word for “three” formed the plural ending4

Three is the beginning of numbers beyond “you” or “both” or “pair”, and thus the decisive step towards counting.

Shu was the air god, the spirit of life and of eternity, the space between earth and sky as well as the light which filled that space, the wind who drove the solar boat and acted as the captain of its crew5.  He embodied the breath that was the life- sustaining quality of air6.  He was also the mediator between Atum and his multiplicity and acted in some accounts as the creator in detail, comparable to the Demiurge in Plato’s Timaeus7

Shu’s twin sister Tefnut was inseparable from him: if he was the air, she was its life- giving moisture that permeated every breath.  Matching the often lion- headed Shu, Tefnut was shown at times with the head of a lioness, an early example of that animal’s frequent symbolic connection with water.  She was also the Eye of the sun8.  Her nature is further explained in the Middle Kingdom Coffin Texts which identified her expressly with Maat9, the goddess of universal order, justice, and rightness in all domains.

One of Shu’s jobs was to hold up the sky and to keep it separated from the earth, so he created “from the fluids of his flesh”10, or out of himself as he had been made out of Atum, the eight Heh gods to perform this function in his place11

One of these, who represented them all, was the numeral sign for “a million”.  Collectively, they were the Ogdoad or Eightness, and also the “Chaos-gods” or “gods of Unending”

In contexts other than number- writing, the Heh gods are depicted sometimes as humans, sometimes as baboons, and their most typical group portraits showed them as four frog- headed male humans with four serpent- headed female partners.  This symbolized their habitat since frogs and snakes lived in the watery mud and slime with which chaos was often associated. 

Their individual names fluctuated over time but typically described them as what was not: in the Coffin Texts, and later also in the Book of the Dead, they were Endlessness, Nothingness, Inertness or also Nowhereness, and Invisibility or Darkness, each of these in both the male and female forms of the word12.

Though entirely negative and without substance, these qualities of the deep and dark were intensely involved in creation but their exact role remains murky.  In some accounts they acted as the primary creator and produced the primeval egg from which their grandparent Atum or some of his later replacements had hatched in others. 

For those who want modern logic in the ancient myths, this scenario matches the designation of the New Kingdom supreme god Amen- Re as “the bull of his mother”13, meaning that he had fathered himself.  It further echoes the “Book of the Divine Cow” from the same period in which Nun says the sun god is older than those who created him14

This reversal of time also matches current theories in particle physics where “a positron can be regarded as an electron traveling backwards in time”, and some particle behavior has been described as a reversal of cause and effect15.  So, if tiny particles are now allowed such freedom from the constraints of linear time, then why should the great and mighty gods of Egypt not have been able to move at will in their timeless realm where 2 + 2 = 4 and 4 = 2 + 2 are equally valid?

Together with their leader Thoth, the eight gods further helped to determine the proper dimensions of temples (and thus of the cosmos which those temples represented), and they mysteriously formed things while the creator god fashioned16.  

All these creation- helper roles make sense for the non- material and invisible numbers which those gods were.  Obviously, nothing material can be made without numbers -- no animals with four legs, nor people or birds with two, and nothing that has any length or width or height.

The eight number gods also made the first land in Hermopolis where the sun then came forth in a lotus flower17, and they resided in that city which the Egyptians named after them. 

Hermopolis is the name the Greeks gave to that city because it was also the town of Thoth.  The name Thoth meant “Messenger”18, and the Greeks equated him with their messenger- god Hermes who also shared several other traits and deeds with Thoth. 

For the Egyptians, that town of Thoth and of the eight gods who were numbers and could appear in his baboon form, was Khmun, or “Eight-town”, from Old Kingdom times on. It is one of very few places on this planet, if not the only one, that has kept the same name for so long: in Coptic it was Shmoun, and its Arabic name today is el-Ashmunein which has the same meaning of "Eight-town". 

The town of Khmun had also an older name which was the same as that of its nome or province: Wenu or “Haretown”19.  On some coffins from the Twenty- first Dynasty, this name was written with the rabbit we encountered earlier as the hieroglyph of “being”, also on the standard pole for gods, and surrounded together with two human faces by a “tail- in- mouth” cosmic serpent circle with a dividing line along its middle20 that recalls the one between the double ropes in the Shen-Ring. 

The juxtaposition of the two town names equates therefore the eight numeral- gods and their rule- maker Thoth the math with “being” itself.  It thereby hints that the Egyptians had developed the “all is number” doctrine now ascribed to Pythagoras (around 580 to 500 BCE), about as many centuries before its reputed inventor as we live after him.

The eight primeval gods did numeral duty only until about the end of the Old Kingdom. In later times, the scribes found it more convenient to write their big numbers with combinations of lower signs, just as we often write 106 instead of the longer 1,000,000.  However, the “million”- gods remained a staple in funerary art where they usually wore a palm rib on their head. 

The palm rib was the hieroglyph for “year” because the Egyptians counted these by cutting marks into palm ribs which were their tally- sticks.  The densely spaced notches in this “counter-of-years” device on their head made these gods promise “millions upon millions of years” for the afterlife of the deceased. 

And just as we do not always split hairs between numbers too large to grasp and true infinities, the Heh sign for “millions” stood often for the same “eternity” as the Shen-ring and typically held up one of these to make the magic properties of the signs reinforce each other.  Some fine examples of such combinations come from king Tutankhamun’s tomb where they guaranteed to that young deceased “infinities” of years and “life everlasting”21.

Together with the Shen- Ring, the Heh- gods came as close to infinity as the artists’ repertoire reached.  The practical- minded ancient Egyptians seem to have found this sufficient, just as few people in our time seem to lose much sleep worrying over the fate of our earth which will ultimately be engulfed by the sun, a few billion years from next Sunday. 

The million- sign was therefore a logical choice for reaching up to the sky which seemed similarly remote.  The ancient numeral designer’s idea that large numbers can progress all the way to the sky survives today, even though we may no longer take that metaphor as literally as the ancient Egyptians may have taken theirs. 

For instance, the modern mathematician Paulo Ribenboim muses, in discussing the search for the factorization of ever larger numbers: 

"It is likely that this activity will go on unabated. Heaven is the limit!...”22.

The eight gods of the “million”- sign supply also another link from earth to heaven. They plus the firstborn twins Shu and Tefnut add up to ten and so formed the first decad, one decimal step down from the unreachable sun and cosmos of the Shen- Ring, down to the real world and to the highest numeral used by dwellers on earth which was ten to the sixth power

If the Shen-Ring had been a number, this decimal step would have made it the seventh power of ten. Since the Shen- Ring was totality and completeness and represented the creator god, this six- plus- one numeral system evokes the common cubit of six palms which becomes the royal or sacred cubit when it is completed with the seventh palm, and the six-part Horus-Eye which needs a seventh part to make it whole

(The addition of the seventh unit also anticipates the biblical week which has six common days usable for everyday actions plus a sacred seventh day that reconnects with the infinite and so makes it complete.) 

Just as completing the Horus- Eye fractions involved Thoth’s magic of the infinitely small, so the step from the million to the all- encompassing royal domain and universe of the Shen- Ring seemed infinitely large but was bridged by the mysterious “gods of Unending” who held up the sky and belonged to Thoth.

Since these number gods could be shown as baboons, they were a form of Thoth the inventor of numbers.  Thoth appears also as their father23 instead of their traditional maker Shu.  In an inscription from the Ptolemaic Horus temple in Edfu, Thoth even says he is the firstborn of the sun god24.  He thereby identifies himself again with Shu the usual firstborn. 

That firstborn god claimed also in one of the Coffin Texts to be Hike (or Heka), the Divine Word as “Magic”, and so established yet another connection with Thoth the “Lord of the Divine Word” and master of magic25

Hike  the magic is often accompanied by Sia, the planning intelligence, and by Hu, the creative word of command.  Hike is their mysterious efficacy by converting their plans and commands into reality and action, just as Thoth did in his functions of scribe, messenger, and vizier of the high god. 

(Even among gods, it is not enough to issue orders, but someone has to do the job;  magic and mathematics were about the only candidates with the required credentials, and Thoth was the master of both.) 

At times, Hike is even identified with Sia and Hu whom the sun god “invented upon emerging from the waters of Nun to aid him in the creation and governance of the world”26.  

These helpers assist the creator and direct his solar boat just as Shu the driving breeze does27. R.T. Rundle Clark comments that these and Shu 

“are all really the same principle or god, the Demiurge, the first- born child of the original spirit.”28 

It appears that Shu et al. are further the same as Thoth the inventor of creative words who is, like Shu, also “the One who gives Life to men”29, and he who charts the course of that solar boat.

The identification of Shu the invisible air who created the “million”- gods with Thoth and the invisible number world parallels the ancient association of Shu’s twin sister Tefnut with Maat

Maat the goddess of Rightness and Justice embodied any and every type of order, both in the human sphere and in nature, and she was closely linked with truth in measuring, weighing, and counting30 which were all Thoth's turf.  Maat included therefore the beautiful order that is inherent in the number world the way moisture is inherent in breath.

Shu had fashioned the eight number gods “out of his own flesh”.  He himself was thus made of the same stuff as those numbers, and so was Atum who had made Shu the same way and whose essentially identical successor Amen then stated explicitly that he had made himself into millions. 

This oneness of the physical creation with that of the number world suggests that the disciples of the ancient numeral designer(s) conceived these two creations as simultaneous and interwoven events, caused by the ten emanations or facets of one original god.  These ten facets were also the first ten numbers

These numbers or gods were all equally invisible, non- material, neither begotten nor issued from a womb.  They were the instruments of creation, foreshadowing the Ten Sefirot or number spirits who played the same role in the Jewish traditions that led to the Kabbalah and whom we will discuss later in this book. 

The universe of the Shen- Ring was thus made from a duality of matter and number, and these were as equivalent to the early Egyptians as matter and energy are to us.

Accordingly, we can read the “million”- sign not only as a symbol for Shu and Tefnut/Maat plus the eight Heh-gods at the beginning of the physical creation.  That sign stands equally for the first ten numbers and/or ordering principles, and for the role of these in shaping the number world and its harmonies. 

We can also see those frog- headed Heh-gods as parents of the next lower numeral which was a tadpole for 100,000:

Continue to Tadpole Proliferation


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