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Ancient Creation Stories told by the Numbers

by H. Peter Aleff

NUMERALS

Numerals Introduction

Horus Eye Fractions

Creation by numerals

Shen Ring Universe

Heh God Millions

Tadpole Proliferation

Finger Counting

Lotus Rise

Rope Geometry

Vault of Heaven

Upright Life

 

CONSTANTS

Seshat's trade tools >>

Seshat's Luxor portrait

Seshat's emblem

 

Narmer mace signs

Narmer mace picture

Narmer's constants

Pi sun and phi moon

Ancient Pi values

Early math

Greek lateness

Egyptian polymaths

Mesopotamian ideas

Holy Number diagrams

Egyptian contributions

Egyptian sources

Our ignorance

Hermetic secrets

Mace month & year

Early star month

Early solar year

Constant e of Osiris

Osiris' death date

Khasekhem's statues

Heb-Sed rebel pictures

Djoser's Heb Sed court

 

Creation by constants

Genesis Equations

Creation Prelude

Ark to Altar line

Ladder to heaven

King Solomon's Pi

Number perceptions

Golden ratio properties

Golden ratio prehistory

Woman Wisdom

Constant e of growth

Outer limit circle

Temple dimensions

Matching traditions

Auspicious latitudes

Reader responses

 


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Footnotes :

 

(1) Ronald J. Williams: “The Sage in Egyptian Literature”, pages 19 to 30 in John G. Gammie and Leo G. Perdue, editors: “The Sage in Israel and the Ancient Near East”, Eisenbrauns, Winona Lake, 1990, see page 27 for a description of Seshat’s “House of Books”.

 

 

(2) Erik Hornung: "Idea into Image, Essays on ancient Egyptian Thought", 1989, translation consulted Timken Publishers, New York, 1992, Chapter 6: "The Temple as Cosmos", pages 115 to 129; see page 118 for "By ceremonially establishing a temple, the Egyptians reenacted creation"

 

 

(3) Coffin Texts Spell 80, as translated in Marshall Clagett: "Ancient Egyptian Science, a Source Book, Volume 1: Knowledge and Order", American Philosophical Society, Philadelphia,1989, page 438.

 

 

(4) Siegfried Morenz: “Egyptian Religion”, 1960, translation consulted Methuen & Co., London, 1973, page 268.

 

 

(5) Sir Alan Gardiner: “Egyptian Grammar”, Griffith Institute, Ashmolean Museum , Oxford, first published 1927, third edition consulted 1982, sign R 20, page 503.

 

 

(6) Manfred Lurker: “The Gods and Symbols of Ancient Egypt”, 1974, edition consulted Thames and Hudson, New York, 1988, page 109.

 

 

(7)  Seshat did so for a deceased coffin owner whom his inscription addressed directly, as quoted in Werner Forman and Steven Quirke: “Hieroglyphs & the Afterlife in Ancient Egypt”, University of Oklahoma Press, Norman, 1996, page 77.

 

 

(8) Photograph by Werner Forman, in Werner Forman and Steven Quirke: “Hieroglyphs & the Afterlife in Ancient Egypt”, University of Oklahoma Press , Norman, 1996,  page 11.

 

 

(9) Sir Thomas Heath: “A Summary of Pythagorean Mathematical Discoveries”, pages 329 to 331 in Kenneth Sylvan Guthrie, compiler and translator: “The Pythagorean Sourcebook and Library”, Phanes Press, Grand Rapids, Michigan, 1987.

 

 

(10) With apologies to Molière who used this term in his "Imaginary Invalid" to castigate disbelief in the pompous pronouncements of the medical doctors he mocked in that comedy.

 

 

(11) Mark Nathan Cohen: "Health and the Rise of Civilization", Yale University Press, New Haven, 1989, page viii.  Cohen ascribed this well formulated definition of an academic discipline to "a colleague".

 

 

(12) George H. Hollenback: "The Myth of Egyptian Pi", Skeptic, Volume 5, Nr. 4, 1997, as posted at www.thehallofmaat.com, page 5 of my 8-page printout from that posting.

Update 2013: the website at that link is now offline and the URL for sale. For a blog with a similar flavor of misconstruing that alleged math error in the Bible, see http://gospelofreason.
wordpress.com/2007/06/
13/god-said-pi-3-stand-by-your-beliefsdammit/
#comment-4921

 

 

(13)  Else Christie Kielland: “Geometry in Egyptian Art”, Alec Tiranti Ltd., London, 1955.

  

 

 

 

  

 

  

Numerals and constants  

 

 tell the creations of numbers and world

 
 


Maat soul-mate Seshat convicted for possessing pot and undeclared math
 

Seshat's role and pedigree

Seshat was the ancient Egyptian goddess of temple layout and mistress of scribes, and she presided over the "House of Life".  This institution, also called the "House of Books", was a sort of library and proto-University where knowledge was stored and taught, particularly knowledge about sacred traditions and rituals (1)

Seshat's most prominent task was to assist the king in “stretching the cord” for the layout of all temples and other royal buildings, as shown on many wall reliefs and mentioned in many texts from the earliest Palermo Stone Annals on.  

In Egypt, as in most other ancient cultures, temples were designed as images of the cosmos, and building one was each time equivalent to the creation of the cosmos it represented (2).  The cord- stretching must therefore also have preceded the original making of the universe.  Its importance there still reverberates in the Bible when God asks Job:

“Where were you when I laid the earth’s foundations? (...) Who stretched his measuring- line over it?” (Job 38:4-5)

Being present at the beginning of the Egyptian creation was a privilege usually reserved for the creator god(dess) and the few gods s/he made first. In one of the most popular versions of the Egyptian myth, the only ones around back then were Atum and his twin emanations Shu and Tefnut whom Coffin Texts Spell 80 calls "eternity" and "everlastingness" and others have interpreted as Shu = the air and Tefnut + the moisture contained in the air.  

However, Seshat's implied role there does not conflict with that usual telling.  The same Spell also identified Shu's sister Tefnut with Maat who personified the world order, and it quotes Atum himself as saying: 

"Tefnut is my living daughter ... her name is Maat" (3).   

The primordial Maat, in turn, manifested herself not only as Tefnut but also as Seshat. Seshat embodied the rightness of temple geometry the way Maat personified the rightness of the entire cosmos which the temple was meant to mirror, so Seshat was really a reflection of Maat.  

Seshat was also the sister or daughter of Thoth (4), the god of measuring and numbers and calendrical order.  She functioned as patroness of scribes just as Thoth was their patron, and she allotted years to the king just as Thoth did. In other words, Seshat the geometer was also a female version of Thoth the math, and she as well as Thoth both were manifestations of Maat the cosmic harmony.
 
Like Maat and Thoth, Seshat is attested from the dawn of history on.  Most probably, she goes back even much earlier, to the beginnings of agriculture, or at least to the time when the growing population density first obliged farmers to protect their acreage from encroachments by neighbors. 

It is easy to understand how Seshat the cord-measuring goddess could have evolved from the recurring need to re-survey the farmers’ fields after each annual inundation. This task was vitally important in a country where everyone depended on the harvest from those fields.  

To keep the peace, all parties needed to be convinced that the land allocations as well as the tax assessments were done fairly, and this need must have led early on to great interest in the rope-stretching geometry and area calculations that decided these matters on the spot and for all to see. Who would have wanted to waste their carefully saved seed grain on ground that might later turn out to be not theirs?

Comparable to some branches of modern science, this math-based rope-stretchers' craft provided verifiable and repeatable results and so became the ultimate arbiter of conflicting land claims. The respect its practitioners commanded rested not just on the local chief's enforcement powers but above all on the infallible order of the mathematics behind their methods.  

In tune with the ancient Egyptian view of nature and of the supernatural, the geometers personified various aspects of this invisible but controlling mathematical order in figures such as the generalists Maat and Thoth, and their more specialized facet Seshat.  

It was also consistent with the ancient Egyptian visual canon that the artists who portrayed Seshat the rope- stretching goddess of measuring and geometry would have labeled her with  pictures of her principal tools, or with easily recognizable symbols for these. Indeed, they combined evocations of these tools ingeniously in her emblem.

Seshat's rope in her emblem

Many Egyptologists have long speculated about the emblem which Seshat wore as her head dress. Sir Alan Gardiner described it in his still category-leading “Egyptian Grammar” as a “conventionalized flower (?) surmounted by horns” (5).  His question mark after “flower” reflects the fact that there is no likely flower which resembles this design. 

Others have called it a “star surmounted by a bow” (6), but stars in the ancient Egyptian convention had five points, not seven like the image in Seshat's emblem.  This number was so important that it caused king Tuthmosis III (1479 to 1425 BCE) to call this goddess Sefkhet-Abwy, or "She of the seven points". Also, in some detailed pictures of Seshat the canopy above that seven-pointed "flower?" does not at all resemble "horns" or a "bow". 

There is no need for such groping speculations because the various elements in Seshat's emblem simply depict the tools of her geometer's trade in the hieroglyphic manner.  

Her seven-pointed “flower” or “star” is an accurate image of a hemp leaf. This leaf is typically made up of seven pointed leaf parts that are arranged in the same pattern as the most prominent sign in Seshat's emblem.  Hemp is, and has long been, an excellent material for making ropes with the low-stretch quality required for measuring cords, particularly when these are greased to reduce variations in their moisture content which would influence elongation.  

The characteristic leaf of the plant used in making these ropes was thus a logical choice for the emblem designer who wanted an easily recognized reference to Seshat's job. This leaf is so unique that it is hard to confuse with other plants. 

Hemp is said to be native to Central Asia, and its presence in pre-Dynastic Egypt is not otherwise documented. However, the hemp leaf in Seshat's emblem shows that the ancient Egyptian rope-stretchers used hemp for their measuring cords, and that Seshat cannot deny her now illegal patronage and ownership of this psycho-active plant.  

Add to this flagrant evidence that in Coffin Texts Spell 10, "Seshat opens the door of heaven for you" (7), and the case against her is solid enough to get her busted if she still plied her drug-promoting trade today.


Seshat as the Ten of Tens

Even worse, the other elements of Seshat's emblem openly reveal that she taught and practiced mathematical skills and analytical thinking.  These are abject anachronisms which today's mainstream scholarship has strictly forbidden to ancient Egyptians and particularly to Seshat's gang of temple architects. 

But this devious divinity now undermines the infallibility of those who guard today's academic dogmas, never mind that she had performed that same guardian-of-knowledge job herself back when she still had tenure as patroness of libraries and learning and scribes. Back then, she helped the scholars of her time to preserve their traditions and beliefs, but now she overturns some of today's received ideas:

In some detailed pictures of Seshat, the “horns” or “bow” that formed a vaulted frame around the hemp leaf in Seshat’s head-dress resembles neither of these but is simply a large numeral “ten” with a much smaller “ten” perched on its top.  You can see this, for instance, in a carefully sculpted and well preserved picture of her among reliefs from around 1250 BCE in the Luxor temple(8), and in the  enlarged view of her emblem there at www.recoveredscience.com/const289seshatemblem.htmd in that comedy.

This double picture of the base for the ancient Egyptian decimal system is plainly an allusion to the numbers that governed Seshat’s sacred geometry, from the largest powers of ten that encompassed the universe to their and its reduced replication in the temples she helped to lay out.  

The powers of ten that formed the ancient Egyptian numeral system counted all there was, and they also illustrated how all that got there in the first place.  Indeed, the sequence of the signs for these powers described the creation of the universe from those very numerals, plus the origin of the numbers themselves.  When read with the ancient symbolic meanings of its signs, that sequence organizes into a coherent and logical narrative many surviving bits and pieces of seemingly separate Egyptian creation myths which we know only from later fragments.  

You find the unique picture strip tale of this dual creation by and of the numbers beginning at www.recoveredscience.com/const101egynumeralsintro.htm .  

These numeral signs were in place from the beginning of the pharaonic civilization, and they  already spelled out the timeless idea that numbers form a separate and permanent reality which rules the fleeting one we live in, and that ultimately "All is number".  

The same idea of a number world ruling ours behind the scenes supplied five thousand years later the screen script for the science-fiction movie "The Matrix", except that the number machines in this modern version are evil.  

In the Egyptian version, by contrast, numbers were benevolent.  The largest among them held up the sky and the other ones helped with creating the world.  Moreover, their interplay produced the “ankh” symbol for “life” and “breath” which was at the core of the pharaonic ideology and provided its long untiring drive.  So much for five millennia of efforts to tackle what makes the world tick.

Modern scholars credit this sophisticated recognition of a hidden numerical order behind the tangible world to the Pythagoreans and their pupil Plato, even though the ancient biographers of the cult leader Pythagoras all say that he had picked up most of his mathematical knowledge in Egypt.  

The creation stories built into the pharaonic signs for the powers of ten demonstrate now clearly that the famous doctrine "Number is the principle, the source, and the root of all things" dates back to the beginnings of hieroglyphic writing, and that Pythagoras had learned it from the Egyptians, at a time halfway between us and the numeral designer(s) who had first recorded the ancient beliefs about the nature of numbers in a few simple symbols their followers used daily from then on. 

Seshat's geometry in her emblem

The same portrait of Seshat in Luxor also documents another debt that Pythagoras owed to his Egyptian teachers.  At the center of the rope- representing hemp leaf in her emblem you find a pentagram.   Its design is slightly distorted to accommodate the stem on which it perches above her head, but it is cut well enough to allow no doubt what figure the artist meant to show. 

The pentagram is a mathematically astonishing figure which is closely linked to the "golden ratio" phi.   As illustrated on the page www.recoveredscience.com/const305goldendrawings.htm , and as explained in the chapter about the prehistory of that ratio, at www.recoveredscience.com/const305goldenprehistory.htm , the construction of a pentagram requires a knowledge of the golden ratio and thus of analytical geometry (9).  The two are so interwoven that some disciples of Pythagoras used the pentagram as a symbol for this geometry and as a recognition sign among fellow members of his mathematical cult.  

It also appears that the Luxor sculptor cut this symbol in Seshat's head dress already with the same meaning of "geometry", some seven centuries before Pythagoras. 

Hieroglyph designers never picked their emblem pictures at random but always invested much thought into how best to distill the essence of what they wanted to convey.  Seshat's pentagram in her Luxor portrait works as a perfectly context- fitting symbol for advanced geometry, used as an additional determinative for that hemp- rope- stretching and number- crunching "Ten of Tens", the mistress of cutting- edge temple geometry.  

This is where Seshat commits the unpardonable crime of lèse faculté (10) against those mainstream historians of science who claim  that the "golden ratio" and any analytical geometry were unknown in pre- Hellenic Egypt.  

These absolute authorities base their claim for the alleged absence of phi from pharaonic Egypt on the fact that it is not mentioned in the exactly eight mostly fragmentary documents with obvious mathematical content that survive from thousands of years of mathematical activities by millions of people in a country a thousand kilometers long.  See www.recoveredscience.com/const131egyptiansources.htm for a list and discussion of those eight scraps.

This minuscule sampling of mathematical traces is limited mostly to papyrus and leather which do not survive well in the moisture of the habitable areas along the Nile.  The few documents we have were preserved in the dry desert sands where the dead got buried.  Strangely enough, very few tomb owners seem to have picked mathematical page- turners as their favorite reading material for potentially boring stretches among the millions upon millions of years in their afterlife.

However bizarre any argument from absence may be under these circumstances, some mainstream writers use it to prove the poverty of Egyptian math with the time- tested academic proof methods of forceful assertion and frequent repetition in chorus.  After all, an academic discipline has been defined as a group of scholars who have agreed not to ask certain embarrassing questions about key assumptions (11), and this is how the colonialist denial of non- European achievements remains today's received wisdom. 

Ignoring the lack of surviving documents from Egypt allows these historians thus to continue crediting the invention of analytical thinking to the glorious Greeks.  Instead of examining their own assumptions, they summarily dismiss as "extreme Afro-centrists" (12) all those who dare to suggest that the ancient Egyptians may have known phi, or, perish the thought, even a decent approximation to the circle ratio pi.  

On the other hand, if we replace this lingering Euro- centrist dogma with logic and reason, then we must include in our sampling the examples of Seshat's work that were preserved in stone, such as her pentagram in Luxor, or the layouts and dimensions of many temples and tombs.  We must also consider the proportions in much pharaonic art, from paintings to furniture, as illustrated, for instance, in Else Christie Kielland’s “Geometry in Egyptian Art” (13).  

In some of these structures or objects, phi and other mathematical constants pop up much too frequently for said scholars' automatic claim that all these occurrences are random, and their patronizing assertions that the Egyptian builders and craftsmen were unaware of what they were doing

In addition to these mathematical fingerprints in buildings and art, it also turns out that the entries in various ceremonial number groups, such as the so-called "booty lists" in some royal inscriptions, were carefully crafted to produce striking and symbolically significant combinations of constants with the quantities listed and/or the ratios between them.  

All this evidence strongly suggests that there existed an unrecognized body of mathematical knowledge which was not included in those eight surviving scraps.  

An analysis of such an expanded sampling shows beyond reasonable doubt that Seshat is guilty of having practiced much symbolic numerology and undeclared analytical mathematics, as you can see in the chapters about king Narmer's mace, beginning at www.recoveredscience.com/const122Narmermaceconstants.htm , and about some other meticulously composed ceremonial number groups that were based on Egyptian methods and appear to have influenced some important passages in the Bible

 

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