recoveredscience.com              We offer surprises about      and numerals and their ancient religious uses     in our e-bookAncient Creation Stories told by the Numbersby H. Peter Aleff

Footnotes :

[1] Sir Alan Gardiner: “Egyptian Grammar”, Griffith Institute, Ashmolean Museum, Oxford, first published 1927, third edition consulted 1982 : see signs E 20, E 21, and C 7 on pages 460 and 449.

For the meaning of “sickness”, see R.T. Rundle Clark: “Myth and Symbol in Ancient Egypt”, Thames and Hudson, London, 1959, edition consulted 1991, page 115 top.

[2]  Emma Brunner-Traut: “Ancient Egypt -- Homeland of the medieval-European Dragon?” pages 109 to 116 in Gelebte Mythen: Beiträge zum altägyptischen Mythos”, 1981, edition consulted Wissenschaftliche Buchgesellschaft, Darmstadt, 1988.

Numerals and constants

tell the creations of numbers and world

The constant of growth and Osiris

As if all the above numerological hits in the composition of the mace quantities were not enough, the sum of its items contains an additional constant that must also have greatly impressed the ancient number researchers if they already knew it, despite its lack of citations before modern Renaissance times.  This is the constant of compound interest e = 2.71828... which rivals phi as a mathematical model of renewal and regeneration.

You find this remarkable number described on the page about “The constant e of growth and renewal”, including a summary of how little we know about its origins and how easily it could have been derived by Stone Age grain farmers computing their yields, long before its modern documentation.

The sum of the three quantities listed on the mace produces not only pi divided by phi, as shown above, and a tenth of 12 phi, but also a significant fraction of e.  It turns out that this sum is close to one of the relatively rare nodes in the number fabric where these three major constants so closely mesh with integers as well as with each other.

 Quasi-equation node of integers and constants Narmer's mace total :1,942,000 / 1,000,000 = 1.94200 Difference 10 e / 14 = 1.94163 0.0191% 12 phi / 10 = 1.94164 0.0006% Pi divided by phi = 1.94161 0.0010%

Of course, there is no proof that the mace designer was aware of e and of its relationship to the total of his quantities.  Yet, there are some possible clues in how well this and other compositions of numbers with that constant fit the ancient mythological context which seems to reflect the behavior of those numbers.

If we continue the above thought experiment and ponder how the ancients would have viewed this constant of compound growth e in case they happened to know it, then we can infer that the symbolic associations with its mathematical properties would probably have caused them to link or identify it with divinities related to growth, fields, and fertility or renewal.

One prominent candidate for this job in Egypt was Osiris, the ruler of the dead and pioneer of renewal by resurrection who functioned also as the grain god of fertility and growth in the fields.  His myth asserts that his twin brother Seth murdered him and cut his body into 14 pieces In the language of symbolic values for constants, this matches the division of 10 e by 14 that produces Narmer's magic total and thereby also phi and pi.

The cult of Osiris is said to have originated in the Nile Delta of Lower Egypt which provided the papyrus- marsh setting for major parts of the myth.  References to this myth are attested only from the Fifth Dynasty Pyramid Texts on, and there is no direct written evidence for the worship of Osiris before then, or for the evolution of his myth.

However, the myth must be at least as old as the bad reputation of Osiris' brother Seth which is based on it, and that predates the invention of the hieroglyphs.  The designer(s) of these knew Seth  as an unruly character because they used this god's emblem, a fantasy creature known to Egyptologists as the “Seth- animal”, as the determinative that illustrated the meanings of words such as “turmoil”, “confusion”, “sickness”, “storm”, and “rage”.  Here are the three hieroglyphic signs for Seth [1]:

 ´ 5  '

Another reason why the myth of Osiris must be much older than its first written traces is that the contest between Osiris' son Horus and Seth established the religious foundations of kingship.   The king bore the title of Horus from the beginning of dynastic Egypt on and derived his legitimacy from Horus' hereditary right to rule Egypt which he had to defend against Seth.

Pharaonic artists of all periods, from the First Dynasty on, depicted their Horus- king in the same iconic pose of spearing Seth in the form of a hippopotamus which still served as the model for many medieval pictures of Saint George slaying the dragon[2].

Some scholars have proposed that Osiris' division into 14 pieces reflects that god's relationship with the moon.  The moon waxes for 14 days and then loses a piece each day for another 14, just as Osiris was cut into 14 pieces.  Then it disappears into the darkness, again like Osiris, and reappears two or three days later, resurrected like that god.

They may well be right, although the full moon does not visibly gain or lose pieces for two to three days and the count is therefore artificial.  However, one interpretation of a symbolic event does not rule out others, and the more connections that event can evoke the more powerful it becomes in magical thinking.

To emphasize the connection of Narmer's number node with 14, we can also rewrite the above quasi- equations to obtain

10 phi x e / pi = 14.00014..

This striking relationship of the three major constants and the base of the decimal system with the Osirian 14 suggests the reasoned speculation that the mythical dismemberment of Osiris into those 14 parts might reflect the division of  e by 14 in the magical total that unites the constants and that Narmer's sculptor incorporated into his mace.  The numbers were there first and certainly did not bend lateron to some myth maker's will.

On the other hand, if the myth maker cared about the relationships in the invisible realm where  numbers dwelled, and presumably also the gods, s/he would probably have tried to describe and emulate those relationships in her or his stories, including that amazing quasi-equality near the division of the Osirian e into 14 parts.

Another clue that Osiris may indeed have been connected with e appears in the date of his  dismemberment into those 14 pieces: