We offer surprises about     

and numerals and their ancient religious uses     in our e-book

Ancient Creation Stories told by the Numbers

by H. Peter Aleff




Footnotes :

1  Marshall Clagett: “Ancient Egyptian Science”, Volume 2, Calendars, Clocks, and Astronomy”, American Philosophical Society, Philadelphia, 1995. pages 29 and 30.


2  Marshall Clagett: “Ancient Egyptian Science”, Volume 2, cited above, page 9 bottom.


3  Marshall Clagett: “Ancient Egyptian Science”, Volume 2, cited above, pages 6 and 47.


4  Marshall Clagett: “Ancient Egyptian Science”, Volume 2, cited above, page 31 top.


5 Lynn E. Rose: “The Astronomical Evidence for dating the end of the Middle Kingdom of Ancient Egypt to the Early Second Millennium: A Reassessment”, Journal of Near Eastern Studies, October 1994, pages 237 to 261.  


6  Members of the David H. Koch Pyramids Radiocarbon Project: “Dating the Pyramids -- How Tiny Organic Bits in the Ancient Gypsum Mortar offer Evidence of Age as well as Clues to the Fabric of Egyptian Life”, Archaeology Magazine, September/ October 1999, pages 26 to 33, quote on page 30 top.


7  Based on J. Baines and J. Malek: “Atlas of Ancient Egypt”, Oxford , 1980, and O. Neugebauer an R.A. Parker: “Egyptian Astronomical Texts, Volume 1”, Providence and London , 1960, as cited in Marshall Clagett: “Ancient Egyptian Science: a Source Book”, Volume 1: “Knowledge and Order”, American Philosophical Society, Philadelphia, 1989,”, pages 629 to 640.

8  J. McKim Malville, Fred Wiendorf, Ali A. Mazar and Romauld Schild: “Megaliths and Neolithic astronomy in southern Egypt ”, Nature, April 2, 1998 , pages 488 to 490.


9  James O. Mills: “Astronomy at Hierakonpolis”, 1990 Conference of the Society for Africanist Archaeologists in Gainesville , Florida , as reproduced in Marshall Clagett: “Ancient Egyptian Science”, Volume 2, cited above, pages 498 to 506, also Figures III. 106 a and b.







Numerals and constants  


 tell the creations of numbers and world


The ancient Egyptian solar year 

To find the 365- day calendar year in Narmer’s time is no real surprise.  Marshall Clagett’s comments in his sourcebook on “Ancient Egyptian Science” about “The Origin of the Civil Calendar” :

“... two indications in the early Annals seem to be plausible evidence that the civil calendar of 365 days was in use at least by the time of the beginning of Shepsekaf’s reign [2472 to 2467] in the fourth dynasty and irrefutable evidence for that of Neferirkare’s [2446 to 2426] in the fifth since the year shared between each of these pharaohs and his predecessor (probably in the first case and certainly in the second) adds up to twelve months and five days.”1

This civil year was supposed to start with the heliacal rising of Sirius, that is the time when this star became again visible in the morning after being blotted out by sunlight for some 70 days2.  Around that day, the Nile normally also began to rise for its annual inundation.  

However, 365 days are about a quarter day short of the 365.2422 days it takes sun and earth to complete their cycle, so the civil calendar slipped against the observable phenomena.  Every four years Sirius returned another day later, and so did the high waters.  In about 1,460 years, their risings drifted this way through the entire year until the first appearance of Sirius fell again on New Year’s day and so began a new “Sothic period”, named after the Egyptian word for Sirius. 

These were also the rare years when the calendar season called “inundation” coincided again with the actual flood.  In between, the waters rose during the second season named for the “emergence” of the land from the receding waters, and for centuries after that the Nile valley dwellers saw the waters rise during the third season which they kept calling “harvest” or “low water”. 

The glaring mismatch between the official designation and the observed fact did not seem to bother the priestly guardians of the calendar.  To the contrary, they were so fond of it that when pharaoh Ptolemy III tried in 238 BCE, with his Decree of Canopus, to introduce leap days to keep time in tune3, these loyal and devoted subjects of this foreign ruler ignored him roundly.  

The Egyptians continued their “wrong” but by then traditional and hallowed system, just as we keep the months named in Latin seventh to tenth in our calendar as ninth to twelfth because a couple of thousand years ago the Roman Senate switched the start of our year capriciously, for local political reasons, from the natural awakening of early Spring to hibernation- encouraging January 1.

The periods when these risings of Sirius actually started together with the calendrical year were, according to some modern reconstructions, 1321-1318 BCE, 2781-2778 BCE, and 4241-4238 BCE4.  Some scholars think therefore that this calendar was introduced around 2780 BCE.  Others propose that the 365- day year could have been adopted earlier, and a few centuries or so later some king with more common sense than the Roman Senate decided it should begin with those natural markers, the risings of Sirius and of the Nile . 

As to the accuracy of the reconstructions which tie the Middle and New Kingdom regnal dates to our own calendar, there are some major uncertainties in the correlations of Sirius risings in Egyptian records with our year counts, and some authors argue that the available data are not at all a firm anchor for the chronologies that are tied to them5.  

Similarly, Old Kingdom events are computed backwards from these unreliable astronomical reckonings with the help of fragmentary king lists and could be even farther from the mark.  For instance, in a recent study of organic remains scraped from cracks in the pyramids, “the radiocarbon dates averaged 374 years older than the historical dates of the kings with whom those pyramids are associated”6.  

Some of the differences may be due to the ancient reuse of old materials, but we should keep in mind that the Egyptian dates from the consensus chronology which I use in this book7 are less secure than their precise numbers seem to suggest.  The older ones could easily be off by a century or two.

In any case, the Nile dwellers must have known an accurate length of the solar year from very early on because marking the solstices had long been one of their concerns.  

More than a thousand years before Narmer, some pre- agricultural cattle herders in southern Egypt built a circle of stone slabs and oriented one of its two sight lines to the summer solstice sunrise8.  Also, a preliminary report about some petroglyphs near Hierakonpolis, associated with nearby deposits from between about 3900 and 3300 BCE, suggests that the lines in the main drawing may have marked the elevation angles of the winter and summer solstices9.  

This attention to the solstices would make sense for farmers because following the movements of sun and stars helps them to determine the vitally important times for sowing and reaping, and people around the world have therefore observed these angles and motions from at least the beginnings of agriculture on, if not earlier to anticipate the migrations of herds and game animals.

Once people become interested in such astronomical measurements it does not take them long to get reasonably good results because counting the days for a few dozen or so periods minimizes the influence of the errors in the first and last sightings and cancels out all the others.  The 365- day year could therefore easily have been devised long before Narmer’s mace, and the ratio of 3.65 in his "booty list" is thus in tune with its time.  

Summing up, the astronomical constants for the month and the year on Narmer's mace fit right in with what else we know or can reasonably infer about the ancient sky watchers.  The mathematical constants phi and pi, on the other hand, appear on that mace long before anyone anywhere was supposed to be aware of their existence.  

The intentional presence of phi and pi on the mace seems hard to believe against the received wisdom that the mathematics implied were far beyond its designer's horizon.  However, it becomes even harder to assign the many "coincidences" of ancient mathemagic to random chance as you evaluate them in the context of ancient beliefs about numbers.  

For instance, the total on that mace seems to include still another constant which presents us with an even greater anachronism. 



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